Evolution of the Kondo Lattice Electronic Structure Above

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PHYSICS 0 applicability of the Luttinger theorem for CeCoIn5 was chal- regime, for which we introduce the label TK, is roughly estimated lenged. It was suggested that both these findings might arise by the resistivity minimum crossover (∼200 K) from the lattice somehow from crystal-field excitations. phonon scattering contribution to the electrical resistivity (21). In the present work, we use both ARPES and DFT+DMFT The true mathematical onset of logarithmic Kondo scattering is calculations, including both spin–orbit and crystalline electric- in fact infinity. In dilute f moment systems, the resistivity pro- field (CEF) splittings of the f states, to investigate the T - file eventually plateaus to a constant value below TK. Resistivity dependent electronic structure of the Kondo lattice system profile scaling behavior in a La dilution study of CeCoIn5 has CeCoIn5. Resonant enhancement of the ARPES Ce 4f spec- determined a very small value of TK ≈ 1.7 K (22), and TK ≈ 5 K tral weight is used to highlight Fermi-level (EF) participation of was also estimated from the temperature at which the entropy f electrons in the three-dimensional (3D) FS, whose detailed obtained from specific heat measurements (23) reaches a value 1 topology is revealed using measurement from two orthogonal of 2 Rln2. (001) and (100) surfaces. Experimentally we confirm, but in For a dense periodic array of f magnetic moments, intersite much greater detail, the general sense of previous ARPES find- coupling between f electrons (schematically represented by over- ings of f -electron participation in the FS to temperatures much lapping Kondo screening clouds in Fig. 1B) leads to coherence higher than T ∗, far into the logarithmic T regime of “incoher- of the f -c scattering and a downturn in the resistivity. Hence the ent” Kondo spin–flip scattering. The DFT+DMFT calculations transport lattice coherence temperature T ∗ is identified experi- agree with this finding and elucidate the role(s) of CEF f states mentally as the resistivity maximum, ∼45 K in CeCoIn5. Partial in this high-T behavior. Specifically, the DFT+DMFT spec- screening of the f moments in the two intermediate T regimes in tral functions explicitly show and confirm the concept (20) of a Fig. 1B and partial coherence below T ∗ are important concepts ∗ 0 T -dependent crossover of the Kondo resonance effective degen- for our understanding, which naturally allow for TK < T < TK. eracy of the two lowest CEF f states. However, our DMFT The broad crossover behavior and T -scale definitions are further results show that crystal-field excitations do not lead to a fail- discussed in SI Appendix, section S.1. ure of the Luttinger theorem at low T and we show that none A final low T scale specific to CeCoIn5 derives from its prox- of the current ARPES data for CeCoIn5, including our own, can imity to a nearby antiferromagnetic quantum critical point in support such a dramatic claim. Ce(Co,Rh)In5. Its unusual T -linear resistivity profile below 20 K The T scales specific to CeCoIn5 are illustrated in rela- is thought to be a signature of this quantum criticality. Addition- tion to its resistivity profile in Fig. 1A with schematic images ally, analyses of two other spectroscopic signatures of quantum of the Kondo lattice screening T regimes in Fig. 1B. First, criticality, T linearity of the Kondo f -peak width and E/T the single impurity Kondo temperature TK corresponds to the scaling of the Kondo f -peak lineshape, have recently been per- crossover from a logarithmic regime (extending far above TK) formed on CeCoIn5 using scanning tunneling microscopy (STM) of incoherent spin–flip scattering with antiferromagnetic Kondo (24) and ARPES (19). coupling (described by perturbation theory) to a nonperturba- tive strong Kondo coupling regime that ultimately leads to a fully Three-Dimensional Fermi Surface k Locations screened Kondo singlet ground state (well below TK). The high- The temperature dependences of three different f -c hybridiza- temperature onset appearance of the –ln(T ) Kondo scattering tion configurations, schematically shown in Fig. 1C, are studied.

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Fig. 1. Kondo lattice hybridization concepts and f-c hybridization configurations. (A) Identification of the Kondo temperature TK, lattice coherence temper- ∗ ature T , and other T transitions (main text) relative to the temperature-dependent resistivity of CeCoIn5.(B) Schematics of four different Kondo screening temperature regimes. (C) Schematic spectral image plots of three different f-c hybridization configurations found in CeCoIn5 shown for low and high temperatures. (D) Bulk Brillouin zone and localized DFT FS of CeCoIn5 and high-symmetry points. Resonance photon energy cuts at 122 eV for the two cleave directions is indicated by transparent planes. (E) Constant photon energy arcs for normal emission relative to the bulk Brillouin zone for the two different orthogonal cleave surfaces: (001), red lines; and (100), green lines.

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ARPES to comparable DMFT directly physics. are function that spectral energy-scale neces- results excitation low the single-particle the provides include of additionally 32) description screening dynamical proper (4, and for correlation DFT+DMFT electron of or ingredients sary 31) (30, band “renormalized theory” as such treatments theoretical sophisticated well-known the 3) weak and the 1) is of measurement low consequence ARPES the natural in a character itinerant energy- yet low localized by itinerant” also “small Γ-X revealed a as have component “nearly yet scale are 29), (26, systems low calculations those to down that even concluded localized” essentially have 29) cuts eV 122 of energy resonant between the midway and respectively, eV, 140 and dpnetsuy i.2A Fig. study. -dependent hoeia n xeietlsie fte3 S presented FS, 3D the of slices experimental and Theoretical CeIrIn of studies ARPES Earlier β T htcnet oadaodsae Scnee nthe on centered FS diamond-shaped a to connects that 2)o along or (27) K lcrnsetcnor n lohole-like also and contours sheet electron ytm )eprmna RE eouinlimitations, resolution ARPES experimental 2) system, k y xsi bevd hl ria n polarization and orbital while observed, is axis 0 = 5 MT( 0K)-calculated 10 = (T DMFT (A) . 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PHYSICS dependence of the matrix elements appears to suppress those A comparison of the Fig. 1D ARPES- and DMFT-derived FS X -point intensities along the vertical kx = 0 axis. More detailed sheets (α, β, γ) to itinerant DFT and localized DFT FS calcu- off-resonance high-symmetry Γ- and Z -plane FS map compar- lations, highlighting their differences, is further detailed in SI isons are given elsewhere (25). The s polarization of the incident Appendix, Fig. S3. Another recent T -dependent DFT+DMFT light used for the FS map in Fig. 2B advantageously enables dis- calculation of CeCoIn5 (13) also exhibits low T deviations from tinct enhancement of f weight at the edges of the α band along f -itinerant DFT, including the presence of the diagonal finger- X -M (cut 1), compared to p polarization. This EF enhancement shaped β’ FS along R-Γ instead of multiple shallow electron FS is also visible in the corresponding 122-eV wide-energy band dis- sheets along R-Z , but still exhibits the same incorrect DFT-like persions along M -X -M , shown in Fig. 2C, which illustrates the complete disappearance of the γZ FS sheet at low T . electron or hole character of the α, β, and γ conduction bands. Another even stronger f hotspot enabled by the s polarization is Large-to-Small Fermi Surface T Dependence Γ visible at the tip of the -centered diamond-shaped FS (cut 2). In this section we focus attention on the low energy-scale f -c k Line cuts 1 and 2 through these two points are used for the hybridization modification of the α and β bands along X -M (line T -dependent measurements presented later. cut 1) to highlight the large-to-small FS size change with temper- Γ A DMFT Fermi-energy spectral image of the orthogonal - ature. The DMFT spectral function at 10 K for this k cut, shown X Z R D Z - - plane in Fig. 2 highlights the existence of a -centered in Fig. 3A, shows the f -c hybridization interaction between two γ hole FS (labeled Z ) and its separated relation to the tubular d bands and three CEF split f levels, with a rich complexity of γ Γ X R Γ sheet along - . Diagonal features along - are associated connectivity and selectivity that arises from the close proximity β0 D with the finger-shaped FS represented in Fig. 1 and imaged of the d bands and the relative symmetries of the f and d states. in the high-symmetry 110-eV angle-dependent map of an orthog- The three 4f CEF doublets, labeled f0, f1, and f2, correspond onally cleaved (100) surface shown in Fig. 2E. The Z -centered 5/2 Γ(1) Γ(2) Γ hole FS has a theoretical “X”-shaped EF contour that outlines to 7 , 7 , and 6 orbitals, respectively, and their relative ener- a similar-shaped high-intensity spectral weight feature (Fig. 2E). gies of ∼EF, +8 meV and +40 meV, are in good agreement with Additionally the triangular lobes of the γZ FS along the diag- neutron scattering measurements of the first and second excited onal Z -A directions are imaged in (001)-cleaved ARPES in SI states at +8 and +25 meV (36, 37). Whereas the hybridized Appendix, Fig. S2. Hence with consideration of experimental outer β band connects with very heavy mass dispersion to the f0 α kz -broadening effects perpendicular to the experimental angle ground-state level, the close proximity of the band requires its maps, ARPES is consistent with the same size and shape of the hybridized dispersion to immediately connect to the first excited DMFT-predicted Z -centered hole FS represented in Fig. 2H. f1 level, thereby giving it an order-of-magnitude larger Fermi An angle-dependent map at the f -resonance energy of 122 eV velocity (vF ≈ 0.2 eV-A)˚ compared to the β band (≈0.02 eV-A).˚ for the (100) surface, shown in Fig. 2F, is then observed to be This close proximity effect, specific for this k region, con- ∗ dominated by two bright f hotspots at the BZ boundaries where tributes to the much smaller average effective mass (m < 18) the kx location is at the edge of the γZ FS where the curva- for the α-sheet orbits in dHvA compared to the β-sheet orbits ∗ ture becomes concave (electron-like). A line cut (no. 3) through (m > 48) (16). these two hotspots is used for T -dependent measurements The differences in the occupied α and β dispersions are also (see Fig. 4). visualized in Fig. 3B where the DMFT spectral function has The corresponding (100) surface high-symmetry normal emis- been multiplied by the 10-K Fermi–Dirac cutoff. In addition to sion valence band dispersion image at 110 eV, shown in Fig. 2G the very different ∆kF shifts relative to the extrapolated d-band spanning multiple c-axis BZs, also highlights the kz separation of dispersion Fermi wave-vector (kF) values, the relatively weak f the γ and γZ FS where the hole-like dispersions result in an acci- weight at kF in the α band is further diminished for the even dental band crossing at a shallow binding energy. Recently the heavier β-band dispersion. An experimental 122-eV resonance Dirac-like band crossing along Γ-Z has been identified in uncor- energy cut through the α and β bands, slightly displaced from related DFT calculations as a fourfold degenerate quadratic the X -M line, is shown in Fig. 3C with overplotted DMFT dis- band crossing point arising from the C4v rotational symmetry persions. While quantification of the β band is limited by the of the c axis (33). Furthermore, surface state arcs connect- resolution of ∼15 meV, a relatively stronger f weight in the α ing the two crossing points per Brillouin zone (schematic lines band, similar to that of the DMFT calculation, is present for both in Fig. 2G) are theoretically predicted for the (100) surface. s and p polarization of the incident light. Closer inspection of the ARPES dispersions reveals two sep- Fig. 3D shows α-band energy dispersion images for the line arated crossing points (circles in Fig. 2G) and the absence of cut 1 for four temperatures selected out of a T series measured any surface state band. This is suggestive of the influence of from 8 K up to 86 K. The enhanced f weight near EF is observed electron correlations, in particular the effect of the spin–orbit to diminish simultaneously with the low energy kink becoming side band (SO0 in Fig. 2C), in disrupting the simple single DFT less visible. The overplotted DMFT dispersion at 86 K shows band crossing point. As further discussed in SI Appendix, sec- still a small dispersion kink at this temperature. The weak f - tion S.14, DMFT calculations provide some support for this weight enhancement and T dependence are also shown in the kF understanding. line spectra in Fig. 3E. A previous resonant ARPES analysis of The existence of complex shape of the Z -centered hole- k-integrated windows just inside and outside the α-band disper- FS with evidence of strong f participation identified here in sion at three temperatures has also reported a weakened but still DMFT and ARPES is notable in that it also exists in localized discernible low energy-scale f peak at 105 K in comparison to 20 (f -core) DFT calculations, inherently without any f contribution, and 180 K (28). and yet is completely absent in itinerant DFT calculations (34, Confident that the signatures of the large-to-small FS have 35). This highlights the artificial and sometimes misleading con- been observed experimentally with basic agreement to the clusions derived from the standard “itinerant-versus-localized” DMFT result, we go beyond the ARPES resolution and T -range DFT theory comparison. While simple postfacto energy-scale limitations and additionally analyze the DMFT spectral func- renormalization of itinerant DFT can be a sufficient correc- tions to extract the peak dispersion, Fermi velocity, and Fermi tion in the cases of isolated α or β FS band crossings, the low momentum of the α band for many intermediate and high tem- energy-scale complexity of the non-f γ-band structure along Γ-Z peratures in Fig. 3 F–H. Upon cooling from 1,000 to 200 K, in CeCoIn5 is a prime example where the itinerant DFT large Fig. 3F shows a gradual kF shift resulting from a near linear f -bandwidth disruption is too great. band velocity change extending to 100 meV below EF. Then

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K ∼90 v F eedneo the of dependence H ( momentum Fermi and (G) velocity Fermi the of analysis quantitative and ) F and F ed o li to claim not do We . hnei bevdto observed is change f and ttsfrteCeCoIn the for states -c v T k F yrdzto dis- hybridization F hra tlow at whereas , k and F v ausa high at values F T T and k -dependent -dependent F B dispersive T . >2.5 T k β F depen- ∗ α-band -band . i.3 Fig. T 5 k ∗ F 01 lae ufc.(A surface. cleaved (001) ) E F and (D) images spectral selected including crossing n fteto(0)htpt r hw nFg 4 Fig. in shown are hotspots (100) two the of one eelacniuu eraeo h ekapiuealo h way spectra the of line all the amplitude K, peak 200 the of to decrease 190 continuous at a reveal images dispersion energy the the while in cases, both In 1C. dif- Fig. the with consistent surface, (001) ferent the to compared as surface hotspot The tively. 4B. Fig. non-f a by electron-like in 3 hole-like and row at 2 lines) cuts (white of 4 line high bands surface and DMFT Fig. Overplotted cleave low K. respectively. tempera- (100) 200 2, selected and Fig. as for (001) images high for dispersion tures as energy temperatures 122-eV shows to stronger up 1C the Fig. ysis where for 3, FS and the in tion the to from attention ysis our turn we Next Hotspot dip. intensity hybridization dis- weak mass a light still linear with the observes STM-QPI above the persion K, 70 At the 3. to Fig. compared directly the be in nesting CeCoIn FS of α-sheet direction scattering (100) a band the with mass heavy along a kink observed dispersion also have surface terminated Ce-In The the of measurements (QPI) interference quasiparticle STM f egtbigple below pulled being weight f T -c f dpnetln pcr tte(001) the at spectra line -dependent -Weight yrdzto ofiuainshmtcsmltosin simulations schematic configuration hybridization T lcrnlk admnmmfrhrabove farther minimum band electron-like f d -dependent T E iprina h oebudre en induced being boundaries zone the at dispersion E bn iprini i.4A Fig. in dispersion -band F and ihu h ev asdseso ik but kink, dispersion mass heavy the without , q lutaethe illustrate T f a 0.2·(2π/ of vector pa it svsbynroe o h (100) the for narrower visibly is width -peak DMFT B) Dependence Experimental ) Z f f ln 2) ec hs eut can results those Hence (24). plane wih intrsof signatures -weight A(k f bn RE esrmnsin measurements ARPES α-band -c egtalw xeietlanal- experimental allows weight , f f ω yrdzto ofiuain 2 configurations hybridization -c pcrliaea 0Kfrct1in 1 cut for K 10 at image spectral ) ekapast esuppressed be to appears peak T E dpnetdseso anal- dispersion -dependent yrdzto configuration hybridization F and α- ). ttecne fanar- a of center the at NSLts Articles Latest PNAS ) hti ossetwith consistent is that k β F n eyshallow very a and bn rsig t8K 8 at crossings -band ieseta(E spectra line f C oso n at and hotspot and f respec- D, 5 participa- A t2 K 20 at | and .(F ). E f10 of 5 F –H in B )

PHYSICS A C

B D

Fig. 4. Temperature dependence of Ce 4f states for two hotspot locations of CeCoIn5.(A and B) Selected spectral images for the T series of (A) (001) surface central diamond-shaped f hotspot (line cut 2), and (B) (100) surface Z-hole FS f hotspot (line cut 3). Low and high T DMFT bands are overplotted in the selected spectral images illustrating the different hole and electron f-c hybridization configurations. EF momentum-dependent profiles (red) also illustrate the relative intensity decay with T and the existence of γ-band EF crossing between the two hotspots in B.(C and D) Line spectra for the complete T series for two hotspots. Low and high T Fermi–Dirac distribution profiles (dashed) for background subtraction are also shown.

up to the highest measured temperature. A T -dependent Fermi– For theoretical comparison, DMFT k-integrated f -DOS spec- Dirac distribution (FDD) function convolved with a Gaussian tral weights were calculated from 10 to 1,000 K, shown in instrumental broadening of 15 meV, illustrated for low and high Fig. 5A for only the Kondo resonance and CEF-split states. T in Fig. 4 C and D, is used for background subtraction (39) The DMFT spectra were then multiplied by the FDD func- for the extraction of the normalized 4f amplitude T profiles in tion and convolved with a Gaussian instrumental broadening of Fig. 5C. Note that this implies a finite 4f DOS even for a flat 15 meV, to simulate the photoemission measurements, and are line spectrum that does not exhibit a visual peak. The sensitivity plotted in Fig. 5B. Using the 750-K spectrum for background to different background subtraction methods is discussed in SI subtraction, the T -dependent Fermi-edge weight is plotted in Appendix, Fig. S5. Fig. 5C with comparison to the ARPES f -peak amplitudes. The

Fig. 5. DMFT k-integrated temperature dependence of Ce 4f states for CeCoIn5.(A and B) T-dependent k-integrated DMFT 4f-DOS spectra with (B) a Fermi-edge cutoff and experimental energy broadening of 15 meV. (C) Comparison of experimental and simulated T dependences of f-peak amplitudes after background subtraction. (D and E) Spectral weight image and stack plot of the T-dependent merging of the ground state and first excited CEF peaks. (F) (left) T dependence of the DMFT total FS volume converted to electron occupation (nFS) exhibiting an ∼1-electron gain at low T and (right) the DMFT total localized-f occupation (nf ) exhibiting a tiny 0.01-electron loss at low T. Crystalline electric-field levels (CF1,2) and their crystal field sideband peaks 0 (CF1,2) are labeled.

6 of 10 | www.pnas.org/cgi/doi/10.1073/pnas.2001778117 Jang et al. Downloaded by guest on September 23, 2021 Downloaded by guest on September 23, 2021 age al. et Jang h low the f DMFT the of T normalization for found is logarithmic different approximate the and despite figurations other, each with two the for results experimental alo h E ek uhCFbodnn rgno enhanced of origin broadening CEF Such peak. E CEF the the include of CEF and then tail of peak will broadening of profiles KR that dependent the is high effect into the notable the weight of key to The subtraction 1) contribute background weight: which with effects even This enhanced generic tails. peratures, relatively peak of of the number to appearance a center(s) to peak the leads from weight spectral T higher the is to (it transfer a weight from result spectral not strong does excitations) spin–orbit and CEF (including high residual in discussed and full-range the of con- analysis that high effects various the the to delineate tribute carefully to important is It Effects CEF low the of suppression resolution amplitude. instrumental the is 2) .. 0 n 0 o CeCoIn for K 300 temperatures and splitting resistiv- 100 energy-level the e.g., CEF in the (20), hump(s) around predicted depopulation profile thermal initially ity a was as effect manifest crossover to degeneracy The the effect. to effective relative larger high regime a extended tivity an to heavy and leads Ce temperature effect of Kondo The profiles (20). resistivity compounds of fermion calculations theory turbation effective gener- will amplitudes. analyses weaker area have energy-window ally large Finally, 3) low tude. smaller a with the T Similarly calculations 2) (NCA) (41). approximation noncrossing single-impurity ftetolws E eesi bevdi the in observed is levels D function CEF spectral lowest DFT+DMFT two the of CEF the masking be possibly could crossover(s). K degeneracy 45 below downturn ence be to to estimated relative was excitations CEF CEF the both with enhanced associate An might effect. one merging addi- that apparent humps lattice no secondary with with associated tional (22), firmly studies is La-dilution downturn from whose coherence K) 45 (at imum energies. splitting peaks CEF CEF actual of the indistinguishability below to temperatures lead at general in does broadening above, lower the peak of calculations CEF much NCA and single-impurity at KR within The profile (42). mod- splittings a resistivity CEF nominal predicts the levels CEF to the ification of and broadening theory Kondo perturbation third-order including beyond going treatment cal wih aletnigt high to extending tail -weight F oheprmn n hoyaret h xsec falong a of existence the to agree theory and experiment Both . nte motn E fetcnen the concerns effect CEF important Another h aietto fsc CEF a such of manifestation The CeCoIn and eednei h Rrgo sta fpa raeigof broadening peak of that is region KR the in dependence rfieta h Rpa eas teit nteK tail KR the in exists it because peak KR the than profile f egta high at weight hl igeiprt C acltosehbtbroad- exhibit calculations NCA single-impurity While E. T f 5 T iceac n auaino h ARPES the of saturation and discrepancy eeeaya icse nteerytertclper- theoretical early the in discussed as degeneracy xeietlyehbt nyasnl eitvt max- resistivity single a only exhibits experimentally K f f T . o h iuesse,ads h coher- the so and system, dilute the for K 1.7 = 2 f nryrneaoe2e.Rte,teprimary the Rather, eV. 2 above range energy pa its esnbeareeto the of agreement reasonable A widths. -peak T eel httelarge the that reveals S4, Fig. Appendix, SI DSi h od eoac K)region (KR) resonance Kondo the in -DOS T T eedne hnnro energy-window narrow than dependences T xeso fthe of extension E mltd n iia high similar a and amplitude F a enntdbfr 3,4)within 40) (39, before noted been has k T egtwl neetyhv weaker a have inherently will weight itgae MTseta presented spectra, DMFT -integrated eednebten4 n 0 K 200 and 40 between dependence n n obe rudsaeKondo ground-state doublet 2 = od eprtr u to due temperature Kondo 6 = T T E f F ososaevr comparable very are hotspots eednesoni i.5 Fig. in shown dependence a above far E 0)fo h Rregion KR the from <10%) nrywnos Their windows. energy F f 5 f f First, 5C. Fig. in weight oee,atheoreti- a However, . f dgnrc crossover -degeneracy T egta ihrtem- higher at weight T -c T T rfiet . tlow at 1.2 to profile K (6) eedneo the of dependence yrdzto con- hybridization T f oaihi resis- logarithmic DS discussed -DOS, ∗ ≈ esnfor reason A . T 5K(2 43) (22, K 35 T k -dependent -integrated hnthe than s T T T profile ampli- peak f T T - yCe ta.(9 a losonsimilar shown also has (19) al. et Chen by (≈3T K 150 this least of comparison at to up persisting f bulk to sensitivity which 3d (24), Ce opti- the spectroscopy (≈2T early K STM 100 in to in gap increasing and hybridization for decreases (45) a spectroscopy of cal signature CeCoIn of the measurements including scattering and spectroscopy of mental above demonstrations well DMFT effects and ARPES The Discussion (44). profiles resistivity the calculated of in on appearance humps the secondary effects and coherence, CEF scattering Fermi-edge relative reveal to related Ce tings A of downturn. study and DFT+DMFT peak resistivity the single a in the of involved separation clean a intimately that T and be effect merging may CEF maximum rapid coherence more resistivity lattice the that to gests result DFT+DMFT the in in in presented structure is band 4A, con- DMFT Fig. theoretical and overplotted excitation, the thermal with 30-K sistent by enabled specifically result, central the visualize third to a forming able is procedure recovery FDD surface (100) k the for in effect the merging CEF in A CF tail bands. and KR tion KR the the on complex of the shoulder is opportunity) weak (or challenge a as k only appear they CF the into the dis- probe as to artifacts is quantitative and in that shifts cussed approximation energy an low creating on thereby at based down is resolution- breaks a lineshape analysis by spectra data FDD the common of convolved the division the the of of Also, occupation procedure resolvable. recovery thermal most (CF lim- low and state the resolution sharpest CEF to energy due excited energy direct challenging first low to is these single it addition into its, a in into excited However, merging thermally states. meV electrons 8 of and troscopy 1 at at peaks peak two of crossover with temperature. consistent Kondo all larger are a peak to KR crossover new the the of above amplitude energy enhanced peak a higher to the The K which 10 in at width) width) 3-meV with narrow center a new (≈1-meV from peak crossover KR the acy before of K, higher suggestive 30 to merge as is decline and early broadening other as monotonic subsequent peak each the enhanced-amplitude toward single shift a to into CEF observed ground-state are and the peaks KR CEF both fixed-energy here of peaks, decline monotonic and ening rsnn ekitniyehbtn oaihi dependence logarithmic a exhibiting intensity peak -resonant dpnetcmlxt ftelws E eescmsfo the from comes levels CEF lowest the of complexity -dependent Another 5B. Fig. in shown function spectral DMFT -integrated ∗ nte eetprl xeietlAPSsuyo CeCoIn of study ARPES experimental purely recent Another h lsns fti E eeeaycosvrtemperature crossover degeneracy CEF this of closeness The degeneracy CEF this of verification experimental Direct nte xeietleapeo this of example experimental Another S9. Fig. Appendix , SI n CEF and N -e etrwt 9-meV with center (≈4-meV peak KR degeneracy 4 = 0Ki npicpepsil ypoomsinspec- photoemission by possible principle in is K ∼30 M -4f nte osbemethod possible Another S.12. section Appendix, SI 1 T ttsta rdcdteCF the produced that states f k f ∗ clsi o elzdi CeCoIn in realized not is scales rsle F+MTbn mg iwo this of view image band DFT+DMFT -resolved T 5 hr the where 4B, Fig. in probed spectrum hotspot .Smlry eoateatcXrysatrn at scattering X-ray elastic resonant Similarly, ). oso above hotspot dehsrcnl eosrtda demonstrated recently has edge dpnetbhvo ftevrulexcitations virtual the of behavior -dependent f T ttsaogte(1)drcin(6,wt the with (46), direction (110) the along states 1 T Γ rfieaepoie in provided are profile eesa hyhbiiewt h conduc- the with hybridize they as levels ∗ T 7 (1) i.S2E. Fig. Appendix, SI r upre ysvrlohrexperi- other several by supported are T nrlto oteeeg resolution, energy the to relation in and u r tl eymc rsn t70 at present much very still are but , 2 IrIn 1 and α- tlow at ) Γ E 8 E 7 (2) F sstnn fteCFsplit- CEF the of tuning uses F lsrt h CF the to closer ttsaeindistinguishable. are states lstebodrwdhand width broader the plus Γ β ∗ 7 (1) .Frhrdsuso and discussion Further ). f bn rsig sshown is crossings -band NSLts Articles Latest PNAS T obtlaiorp,the anisotropy, -orbital T k n first-excited and hr h ek are peaks the where 1 0 dpnetvariation -dependent -dependent i.S6 . Fig. Appendix, SI ieadpa,but peak, sideband 5 f N eutn nonly in resulting , -c degener- 2 = 1 T hybridization q nry This energy. -dependent -dependent f T γ T | weight ∗ bands This . f10 of 7 sug- Γ 7 (2) 5 f 5 ,

PHYSICS above T ∗. Differences in the results, methods, and interpre- level of detail would be greatly aided by a future full theoret- tations with the current study are discussed below and in SI ical calculation of the separate T dependences of each of the Appendix, section S.7. Also a recent angle-integrated photoemis- five FS sheets. However, in our opinion, at the moment there sion study of YbNiSn reports a T -linear behavior of a <35% is no experimental reason to doubt the DMFT result in Fig. 5F variation of the Yb 4f intensity, in the range of 1 to 100 K, or the validity of the Luttinger theorem at sufficiently low T that also extends far above its transport signature of coherence for CeCoIn5. below ∼10 K (47). In that case, the occupied Yb 4f spectral Theoretical efforts to compute the lattice coherence scale (4, peak inherently contains multiple CEF levels which contribute 5, 38, 49–52) rely on a variety of definitions including onset to its broad ∼80-meV width. This T-linear dependence, differ- of Fermi-liquid transport coefficients, comparison of single- ent from the T -logarithmic behavior observed here for CeCoIn5, impurity Anderson model and periodic Anderson model proper- was described there by a non-Fermi liquid-like T -linear damp- ties (51), effective mass scaling (4, 38), and others, with unclear ∗ ing in the self-energy of the periodic Anderson model, proposed relation to the experimental CeCoIn5 resistivity maximum T . as accounting phenomenologically for effects of feedback from In addition, while the proposed two-fluid model universal scal- closely spaced CEF-split bands. ing formula for the f -DOS (14) contains a logarithmic term that The small to large FS crossover can be additionally visualized extends out to ≈2.7 T ∗, a multiplying “order parameter” term from the DMFT calculation by the total FS volume as a function defines a sharp termination of the f -DOS at T ∗, as illustrated of temperature, as plotted in Fig. 5f with conversion to electron in SI Appendix, Fig. S7. CEF effects are not discussed within the occupation, nFS , e.g., 2 electrons per Brillouin Zone volume. It two-fluid model. is observed that nFS ∼3 at high T increases to nFS = 4 at 15 K The low T discrepancy between the ARPES and DMFT f where one f electron fully participates in the FS. In this case, T ∗ spectral weight profiles in Fig. 5C, ascribed to instrumental res- appears to be associated with the onset of a more rapid change olution limitations, is also in the T regime of the T -linear in FS size, while surprisingly ∼0.5 electron are already gradu- resistivity below 20 K and thus is suggestive of a possible role ally incorporated from high T down to T ∗. Similarly, the small of quantum criticality in this discrepancy. Hence this motivates to large FS transition of the α and β sheets can be analyzed by an exploration of the power law T dependences of the ampli- the cross-sectional FS area, provided in SI Appendix, Fig. S11, tude, width, and peak energy of our (100) and (001) f -hotspot with comparison to Ce versus La dHvA orbits (34). Note that the lineshapes in SI Appendix, section S.13, to look for possible large FS volume f -occupation increase to low T should be distin- E/T scaling behavior, similar to that of the previous ARPES guished from the few percent decrease of the local f occupation T -dependent study (19). What we discover instead is that, inti- from nf ∼ 1, also plotted in Fig. 5F, which is consistent with mately related to the f -weight analyses leading to Fig. 5C, the recent analysis of Ce 3d hard X-ray core-level photoemission instrumental resolution and choice of background also play key obtaining nf = 0.97 at 20 K (48). roles in deviations at low and high T from uniform power law In their ARPES study of CeCoIn5, Chen et al. (19) have scaling of the f lineshape and provide a natural explanation for estimated that the net FS volume change from 145 to 17 K the “intermittent” scaling behavior previously reported (19). is rather small, corresponding to only 0.2 f -electrons incorpo- In summary, we have presented a detailed view of the exper- ration. In their discussion this estimate is contrasted with an imental 3D FS of CeCoIn5, including the complex-shaped hole- expected change of 1 electron, i.e., a discrepancy as large as 0.8 like Z sheet, using ARPES measurements from two orthogonal electrons, and it is speculated that the presence of CEF levels (001) and (100) cleave surfaces. We have used an f -resonant may be responsible in some way for such a large discrepancy. photon energy to highlight the k locations of the enhanced f Our Fig. 5F shows what is actually expected quantitatively in a weight corresponding to three different f -c hybridization con- DMFT calculation that includes the CEF splittings. As we have figurations, including the well-known α-band crossing, and have already seen, their major effect is to extend the Kondo regime measured the T dependence of these f weights. We find declin- to much higher temperature than would be obtained considering ing, but finite f weight extending up to ∼200 K, surprisingly far only the lowest level. Thus we see that 0.3 electrons are already above the transport coherence temperature of ∼45 K. incorporated in the FS from the highest T down to 200 K (out- Theoretical k-resolved DFT+DMFT calculations confirm the side the scope of the experiment) via kF shifts originating from experimental 3D FS topology and provide T -dependent f - high energy vF slope changes (Fig. 3F). The f -electron partici- spectral functions that predict both dispersion and f -weight pation in the FS becomes >0.9 electrons by 20 K, i.e., at most changes that extend even higher than the ARPES measurements. a net 0.6 electron change from 145 to 17 K. So the difference The inclusion of CEF states in the DMFT provides a glimpse between the 0.2 estimate of Chen et al. (19) and the DMFT of the complexity of k-resolved f -c hybridization interactions prediction is actually no more than 0.4 electrons, and this much above EF, origins of the disparity in effective masses of α- and smaller difference could easily be within the large uncertainties β-band crossings, and an explicit spectral function view of a involved in their estimate. That estimate is based on a single T -dependent crossover of the Kondo resonance effective degen- Γ-M cut for the α and γ sheets only, coupled with the assumption eracy involving the two lowest CEF f states. These CEF effects that the kF changes along this single line can be used to com- may explain much of the long high T tail of KR f weight, but the pute the volume changes of both of the sheets. In contrast to role of CEF states in the observed DMFT high T onset of the the situation for the roughly cylindrical α sheet, this assumption effective mass and large-to-small FS size T evolution still needs is very questionable for the complex shape of the γ sheet. It is to be elucidated. A mismatch between the transport-defined also assumed that the volume change of the β sheet is approxi- coherence temperature and the higher T onset of signatures of mately equal to the sum of the α and γ contributions. However, f -c hybridization and coherence-related effective mass changes, its ≈2× larger total FS size and its significantly heavier effective as observed here for CeCoIn5, is also the framework put forth mass likely make this a considerable underestimation of the β- (16) to account for the absence thus far of an observation of the sheet contribution to the f occupation at low T (see additional small FS in high T ARPES studies of YbRh2Si2. discussions in SI Appendix, sections S.8 and S.10). Finally, the 0 β and the γZ sheets, newly identified and characterized here, Materials and Methods are not included in this estimate. Unfortunately we also do not Experimental. Temperature-dependent ARPES measurements were per- have sufficiently detailed experimental knowledge to specify the formed at the MERLIN beamline 4.0.3 of the Advanced Light Source (ALS) T dependences of these complex volumes well enough to test employing both linear horizontal and linear vertical polarizations from the theory quantitatively. A future experimental effort with this an elliptically polarized undulator. A Scienta R8000 electron spectrometer

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Si, Q. 10. age al. et Jang fteC 4f Ce the of used. is Ce NCA the the of step, occupation DMFT the which in (32), respectively eV, 4f param- 0.68 and interaction 5.0 exchange of temperature. and eters low Coulomb at determined splitting previously is field matrix used crystal We the interaction describe atomic to full account the into where taken self-energy, local DMFT the for with 4f employed Ce is (56). potential (PBE-GGA) exchange-correlation Perdew–Burke– approximation augmented The gradient linearized (55). generalized potential Ernzerhof full method the (FP-LAPW+lo) on used based orbitals was is plane-wave+local which package part, WIEN2k DFT The the 54). for (53, method DFT+DMFT self-consistent Theory. C” “type (24). third STM the by to observed corresponds surface (28) state surface the observed of previously details This termination emission In from normal originating the state obscures surface that which (001) common selected a were avoid spot to given beam 50-µm 4f a Fermi-edge by maximal top- exhibit excited surfaces the cleaved using the side narrow of using vacuum with fractured samples in similarly platelet were cleaved of mounting surfaces was (100) Orthogonal surface method. (001) post the The to (23). cooling technique brief to K, 40 to 20 at lowest optimization and alignment sample from progressed typically hν procedures Temperature-dependent at 4d cross-section. measurements Ce the for to used sponding was meV 15 approximately ncmiainwt i-xshlu rottgnoee ih6Kbase K 6 with used goniometer was cryostat angle helium and six-axis and energy temperature a kinetic with electron combination of in detection parallel 2D with .P eewr,Q i .Selc,Qatmciiaiyi ev-emo metals. heavy-fermion in criticality heavy- Quantum Steglich, of F. Si, properties Q. Transport Gegenwart, P. Pruschke, T. 9. Czycholl, G. Anders, B. F. Grenzebach, C. 8. .S aasj,D ie,Z ik w uddsrpino h od lattice. Kondo doped the the of of description fluid scales Two Energy Fisk, Shim, Z. Pines, H. J. D. Nakatsuji, Coleman, P. S. Kotliar, 7. G. Haule, K. Temperature-dependent Kang, Kotliar, H. G. 6. Haule, K. Zlati V. Burdin, Shim, S. H. 5. J. Min, I. B. Choi, C. H. 4. in magnetism” of edge the at Electrons fermions: “Heavy Coleman, P. systems. Heavy-fermion 3. Stewart, R. G. compounds. Mixed-valence 2. Varma, M. C. 1. ntedsrpino h pnobtitrcin(O n E splittings CEF and (SO) interaction spin–orbit the of description the In CeCoIn of samples crystal Single CeCoIn (1964). impurities. cerium with compounds and Lett. Rev. silto nbt h omladsprodcigmxdsae fCeCoIn of states mixed superconducting Matter and Condens. normal the both in oscillation YbRh opudYbRh compound 944(2008). 096404 100, CeCoIn quasiparticles. heavy coherent to B electrons Rev. light From lattices: Kondo in ference approach. approximation cluster (2010). Dynamical 245105 model: lattice Kondo (2010). 1166 8–9 (2008). 186–197 4, systems. fermion Lett. model. lattice Anderson approach. boson CeIrIn fermion heavy in (2012). evolution surface Fermi 148. Theory and ria a siae ob .6a 0K o h muiysle nthe in solver impurity the For K. 20 at 0.96 be to estimated was orbital T 141(2004). 016401 92, 2 h orlto feto h e4f Ce the of effect correlation The Si ofl ag amn otehighest the to warming range full to , 911(2011). 195141 84, 5 5 . 2 nlssbsdo D MTmethod. DMFT + LDA on based Analysis : us-w-iesoa em ufcsadted asvnAlphen Haas-van de the and surfaces Fermi Quasi-two-dimensional al., et . hs e.B Rev. Phys. 325(2008). 237205 101, hs e.X Rev. Phys. acher ¨ .Kr H. , ietosraino o h ev-emo tt eeosin develops state heavy-fermion the how of observation Direct al., et eprtr-needn em ufc nteKnolattice Kondo the in surface Fermi Temperature-independent al., et ttsudrtettaoa ymty ohtediagonal the both symmetry, tetragonal the under states antcfil eedneo h YbRh the of dependence Magnetic-field al., et ,Mlil eprtr clso h eidcAdro oe:Slave model: Anderson periodic the of scales temperature Multiple c, 2 ´ <5 hs e.B Rev. Phys. hs e.B Rev. Phys. nih nothe into Insight al., et 67L3 (2001). L627–L634 13, Si nulr .Pri,Es Jh ie os 07,vl ,p.95– pp. 1, vol. 2007), Sons, & Wiley (John Eds. Parkin, S. onmuller, ¨ 2 . × 417(2017). 045107 96, hs e.Lett. Rev. Phys. 108(2015). 011028 5, -4f 10 hs e.B Rev. Phys. −11 eoatehneeto the of enhancement resonant 119(2009). 115139 79, 919(2006). 195119 74, orbs rsue oa nryrslto of resolution energy Total pressure. base torr egta 2 V lo pca teto was attention special Also, eV. 122 at weight 615(2019). 165115 99, 5 661(2011). 267601 107, e.Md Phys. Mod. Rev. eegonwt otnidu flux indium molten a with grown were f hs e.B Rev. Phys. drvdFrisraeo h heavy-fermion the of surface Fermi -derived e.Md Phys. Mod. Rev. lcrn r rae dynamically treated are electrons c ria stetdb h charge the by treated is orbital ai hcns.Otmlregions Optimal thickness. -axis hs e.B Rev. Phys. 5 T 5146 (1972). 4541–4561 5, . γ i.S5). Fig. Appendix, (SI Z hs e.Lett. Rev. Phys. 5–8 (1984). 755–787 56, d ). S2 Fig. Appendix , (SI FS wv uecnutvt in superconductivity -wave rg ho.Phys. Theor. Prog. 1–3 (1976). 219–238 48, 2 Si 217(2014). 125147 90, f 2 em surface. Fermi photoionization Science 2 Vcorre- eV 122 = hs e.B Rev. Phys. hs e.Lett. Rev. Phys. Fundamentals 016402 108, 1161– 329, hs Rev. Phys. a.Phys. Nat. 5 37–49 32, . .Phys. J. Phys. Phys. 82, 8 .C hi .Hue .Ktir .I i,J .Si,Osraino ikdrn the during kink a Reinert F. of Observation 39. Shim, H. J. Min, I. B. Kotliar, G. Haule, K. Choi, C. H. 38. Willers T. 37. electronic localized-to-itinerant Shishido H. the 34. Modeling Shirer Kotliar, G. R. K. Haule, 33. K. Shim, YbRh in H. state J. heavy-fermion 32. the of suppression systems. Field-induced Zwicknagl, fermion G. heavy 31. in Quasi-particles Zwicknagl, G. 30. Koitzsch A. 29. Koitzsch A. 28. Fujimori I. S. 27. Fujimori I. S. 26. Dudy L. 25. Aynajian P. 24. Zapf S. V. 23. Nakatsuji S. 22. 1 .E ikr,D .Cx .W ikn,Sl-ossetlreNepninfor expansion large-N Self-consistent Wilkins, W. J. Cox, L. D. Bickers, E. N. 41. Ehm D. 40. superconductor fermion heavy the in excitations field electric Crystalline Bauer, D. E. 36. Oppeneer M. P. 35. a ut ml f-ignlcmoet,i a sdisd h impu- the degenerate inside they doubly used then three and was state are part) atomic it ground DFT There the components, the solver. Because off-diagonal in rity solver. small (i.e., impurity quite lattice the the has calculated inside of first renormalized level are the splittings are energy-level on CEF initio The ab results. similar give atomic and simple the and basis Γ = .5 au ssmlrt -a bopinrslsta eotahg portion high a report that results absorption of X-ray to similar is value (∼0.25) onaino oe rn uddb h oenMnsr fScience, of Ministry Korean (MSIP) Planning the Research Future by and National (physical Technology (2020R1A5A1019141). funded a DMR-1810310 Communications grant and Grant of by Information Korea was under Division supported NSF of Diego was Sciences, US Foundation J.H.S. San Energy the measurements). Basic California (sin- and properties DEFG02-04-ER46105 of growth) of Grant Office crystal under University gle Engineering, DOE, Founda- at and US Science Sciences Research Florida, Materials the National of DOE. by US State US the the supported DMR-1157490, by the National Grant funded The under Cooperative and is through DE-FG02-07ER46379. Facility (NSF) Lab Contract a User tion under Field is DOE Science Magnetic sup- which US of High was the Source, Michigan Office of by Light University (DOE), ported cross- at Advanced Research Energy Dirac-like the for DE-AC02-05CH11231. of Contract the Sun of Kai Department of resources thank US implications used and topological Research Matho Konrad ing. the and concerning Varma, M. insights Chandra Assaad, F. ACKNOWLEDGMENTS. Appendix Availability. Data CeM be other to estimated are splittings 7 (2) |5/2, |5/2, photoemission. study. spectroscopy photoemission resolved B Rev. properties. lattice. CeRh (2002). 106402 nCeCu in system. heavy-fermion a in (2013). band 125111 resonance Kondo the of formation study. scattering neutron (2010). inelastic 195114 and 81, absorption x-ray combined A Rh): Ce(Co,Rh,Ir)In CeIrIn system fermion heavy the in transition Matter Condens. Phys. (1992). spectroscopy. omlsaepoete fdlt antcalloys. magnetic dilute (1987). of properties normal-state dependence. temperature (2007). their 045117 and 76, structures, field crystal resonance, CeCoIn compounds. (2007). Pu-115 and Ce-115 in transitions CeTIn and = p 1−x ±1/2 ±3/2 457(2003). 144507 67, 5 Nature 2 1 . . ihrslto hteiso td nlow-T on study photoemission High-resolution al. , et tal. et Si In Co .Ap.Phys. Appl. J. − rsa-edadKnosaeivsiain fCeMIn of investigations Kondo-scale and Crystal-field al., et 5 eprtr eedneo h od eoac n t satellites its and resonance Kondo the of dependence Temperature al., et 2 5 hs e.B Rev. Phys. em ufc,mgei n uecnutn rpriso LaRhIn of properties superconducting and magnetic surface, Fermi al., et oxsec fsprodciiyadatfroants in antiferromagnetism and superconductivity of Coexistence al., et lcrncsrcueo CeCoIn of structure Electronic al., et . iulzn ev emoseegn naqatmciia Kondo critical quantum a in emerging fermions heavy Visualizing al., et T:C,R n Ir). and Rh Co, : (T x using i, α i Γ nest opigefcsi od lattice. Kondo a in effects coupling Intersite al., et hs e.Lett. Rev. Phys. In yrdzto fet nCeCoIn in effects Hybridization al., et (M erylclzdntr of nature localized Nearly al., et ietosraino uspril adi CeIrIn in band quasiparticle a of observation Direct al., et 5 hs e.B Rev. Phys. ttsfor states 2 bvlnecag nCe in change valence Yb , 7 (1) ia emosi h ev-emo superconductors heavy-fermion the in fermions Dirac al., et 5 ri:88043( uut2018). August (1 arXiv:1808.00403 . 0–0 (2012). 201–206 486, |5/2, hs e.B Rev. Phys. . em ufc hne u olocalized-delocalized to due changes surface Fermi al., et hadI)cmons(37). compounds Ir) and Rh = hs e.B Rev. Phys. = l td aaaeicue nti ril and article this in included are data study All α|5/2, ±5/2 |J 925(2011). 094215 23, 2170 (2004). 7201–7203 95, 618(2013). 165118 88, , eakoldeueu icsin ihFakher with discussions useful acknowledge We Γ J 714(2009). 075104 79, z 7 (1) i i ±5/2 518(2008). 155128 77, 041(2001). 106401 87, 156(2001). 014506 65, + tt oain nCeCoIn In notation. state and .Py.Sc Jpn. Soc. Phys. J. jj and ∼8 α|5/2, ai fteitrcinmti eetested, were matrix interaction the of basis − i |5/2, p ∓3/2 1−x 1 ±5/2 0mV hc r ossetwith consistent are which meV, ∼40 − hs e.B Rev. Phys. 5 Yb .Mg.Mg.Mater. Magn. Magn. J. . α n eodectdstate excited second and i, f 7–7 (2002). 276–278 71, Science 5 i 2 x lcrn nCeTIn in electrons |5/2, rmagersle photoemission angle-resolved from CoIn ttsfor states NSLts Articles Latest PNAS 5 5 hs e.B Rev. Phys. 6511 (2007). 1615–1617 318, ∓3/2 J rmsetocp n bulk and spectroscopy from bevdb angle-resolved by observed 257(2006). 224517 73, / E ttswith states CEF 5/2 = d.Phys. Adv. 5 Γ h calculated the , rtectdstate excited first i, 7 (2) K hs e.Lett. Rev. Phys. esses Kondo systems: Ce 5,5) h CEF The 57). (53, 5 5 TR,Ir). (T=Rh, hs e.B Rev. Phys. 1684–1690 310, 2036–2079 36, MC,I,and Ir, (M=Co, 5 203–302 41, hs e.B Rev. Phys. hs e.B Rev. Phys. nangle- An : | jj f10 of 9 2 f Si -state basis Phys. 2 α 89, 88, Γ . SI J. 6 2 5

PHYSICS 42. S. Kashiba, S. Maekawa, S. Takahashi, M. Tachiki, Effect of crystal field on Kondo 50. S. Burdin, A. Georges, D. R. Grempel, Coherence scale of the Kondo lattice. Phys. Rev. resistivity in Ce compounds. J. Phys. Soc. Jpn. 55, 1341–1349 (1986). Lett. 85, 1048–1051 (2000). 43. K. Hanzawa, K. Yamada, K. Yosida, Orbital degeneracy effect on the dense Kondo 51. N. S. Vidhyadhiraja, A. N. Tahvildar-Zadeh, M. Jarrell, H. R. Krishnamurthy, “Exhaus- state in real systems. J. Magn. Magn. Mater. 47-48, 357–359 (1985). tion physics” in the periodic Anderson model from iterated perturbation theory. 44. B. G. Jang et al., Temperature-evolution of spectral function and optical conductivity Europhys. Lett. 49, 459–465 (2000). in heavy fermion compound Ce2IrIn8 under crystalline electric field. arXiv:2007.10641 52. F. F. Assaad, Coherence scale of the two-dimensional Kondo lattice model. Phys. Rev. (21 July 2020). B 70, 020402(R) (2004). 45. E. J. Singley, D. N. Basov, E. D. Bauer, M. B. Maple, Optical conductivity of the heavy 53. K. Haule, C. H. Yee, K. Kim, Dynamical mean-field theory within the full-potential fermion superconductor CeCoIn5. Phys. Rev. B 65, 161101 (2002). methods: Electronic structure of CeIrIn5, CeCoIn5, and CeRhIn5. Phys. Rev. B 81, 46. A. Gyenis et al., Quasiparticle interference of heavy fermions in resonant X-ray 195107 (2010). scattering. Sci. Adv. 2, e1601086 (2016). 54. G. Kotliar et al., Electronic structure calculations with dynamical mean-field theory. 47. A. Generalov et al., Insight into the temperature dependent properties of the Rev. Mod. Phys. 78, 865–951 (2006). ferromagnetic kondo lattice YbNiSn. Phys. Rev. B 95, 184433 (2017). 55. P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, J. Luitz, WIEN2k (Karlheinz 48. M. Sundermann et al., Quantitative study of the f occupation in CeMIn5 and other Schwarz, Techn. Universitat Wien, Vienna, Austria, 2001). cerium compounds with hard x-rays. J. Electron. Spectrosc. Relat. Phenom. 209, 1 56. J. P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made (2016). simple. Phys. Rev. Lett. 77, 3865–3868 (1996). 49. T. Pruschke, R. Bulla, M. Jarrell, Low-energy scale of the periodic Anderson model. 57. T. Willers et al., Correlation between ground state and orbital anisotropy in heavy Phys. Rev. B 61, 12799–12809 (2000). fermion materials. Proc. Natl. Acad. Sci. U.S.A. 112, 2384–2388 (2015).

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