Magnetic Field-Tuned Fermi Liquid in a Kondo Insulator

ARTICLE

https://doi.org/10.1038/s41467-019-13421-w OPEN Magnetic ﬁeld-tuned Fermi liquid in a Kondo insulator

Satya K. Kushwaha 1,2, Mun K. Chan 1, Joonbum Park1, S.M. Thomas 2, Eric D. Bauer 2, J.D. Thompson2, F. Ronning2, Priscila F.S. Rosa2 & Neil Harrison1*

Kondo insulators are expected to transform into metals under a sufficiently strong magnetic field. The closure of the insulating gap stems from the coupling of a magnetic field to the

1234567890():,; electron spin, yet the required strength of the magnetic ﬁeld–typically of order 100 T–means

that very little is known about this insulator-metal transition. Here we show that Ce3Bi4Pd3, owing to its fortuitously small gap, provides an ideal Kondo insulator for this investigation. A ﬁ metallic Fermi liquid state is established above a critical magnetic eld of only Bc 11 T. A

peak in the strength of electronic correlations near Bc, which is evident in transport and

susceptibility measurements, suggests that Ce3Bi4Pd3 may exhibit quantum criticality analogous to that reported in Kondo insulators under pressure. Metamagnetism and the breakdown of the Kondo coupling are also discussed.

1 MPA-MAGLAB, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. 2 MPA-CMMS, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. *email: [email protected]

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ondo insulators are a class of quantum materials in which 2.0 the coupling between conduction electrons and nearly K 40 localized f -electrons may lead to properties that are dis- tinct from those of conventional band insulators1–3. Remarkable 1.5 ) properties of current interest include topologically protected –2 surface states that are predicted4–6 and reportedly conﬁrmed by – 1.0 experiments7 12, and reports of magnetic quantum oscillations .cm K Ω

– 30 originating from the insulating bulk13 16. The very same mag- ( ﬁ A netic eld that produces quantum oscillations also couples to the 0.5 f -electron magnetic moments, driving the Kondo insulator inexorably towards a metallic state17,18. The required magnetic ﬁ 17,19

elds in excess of 100 T have, however, proven to be prohi- (K) 20 0.0

T ∂ ∂ ∂ /∂ T > 0 bitive for a complete characterization of the metallic ground state. xx/ T < 0 xx Thermodynamic experiments have thus far provided evidence for the presence of electronic correlations in Kondo insulators at high-magnetic fields. Quantum oscillation experiments, for TFL example, have found moderately heavy masses within the insu- 10 lating phase in strong magnetic fields15. Furthermore, heat capacity experiments have shown that the electronic contribution TM FL undergoes an abrupt increase with increasing magnetic field20,21: in one case20 the increase occurs within the insulating phase, 22 0 suggesting the presence of in-gap states , whereas in another, it 0204060B 21 c coincides with the onset of an upturn in the magnetic B (T) susceptibility18,19 and reports of metallic behavior7,18.An Fig. 1 Magnetic field versus temperature phase diagram of Ce Bi Pd . T unambiguous signature of metallic behavior, such as electrical 3 4 3 M χ χ resistivity that increases with increasing temperature at accessible indicates the peak in the susceptibility ( ) obtained from versus T (triangles) and B (stars) from Fig. 6. Here, B ¼ BðT ! 0Þ is indicated by magnetic fields, has yet to be reported. c M a green circle. Also shown is the temperature T (circles) above which the We show here that insulating Ce Bi Pd , once polished to FL 3 4 3 resistivity departs from ρ ¼ ρ þ AT2 (i.e., Fermi liquid) behavior. Shaded remove surface contamination, exhibits properties consistent with xx 0 it being a reduced gap variant of its sister Kondo insulator regions and lines are drawn as guides to the eye. The gray dashed line ∂ρ =∂ ¼ 22,23 shows where the derivative xx T 0 (plus symbols from sample A in Ce3Bi4Pt3 , which is also a topological Kondo insulator 4,24,25 fi static fields, ´ symbols from sample A in pulsed fields and asterisk candidate . The atypically small magnetic eld of Bc 11 T symbols from sample B in static fields; see Methods). To the left of this line required to overcome the Kondo gap of insulating Ce3Bi4Pd3 (see 26 ∂ρ =∂ Fig. 1), makes this material ideal for investigating the metalli- xx T < 0, indicative of insulating behavior, while to the right of this line ∂ρ =∂ zation of a Kondo insulator in strong magnetic fields. We find a xx T > 0, indicative of metallic behavior. The right-hand-axis indicates magnetic field-induced metallic state exhibiting an electrical the magnetic field-dependence of the A coefficient (squares), with the resistivity that varies as T2 at low temperatures (where T is the values for B ≲ 20 T corresponding to the average of samples A and B in temperature), thereby revealing a Fermi liquid ground state in the Fig. 5. Error bars represent the standard error. high-magnetic field metallic phase. We also identify a magnetic fi eld-tuned collapse of the Fermi liquid temperature scale TFL fi near Bc, indicating that Ce3Bi4Pd3 may exhibit a magnetic eld- Kondo insulators have Kondo gaps of several millielectronvolts, tuned quantum critical point analogous to that observed in SmB6 accompanied by inverse residual resistivity ratios in the range 27–31 2 À1 5 as a function of pressure . The origin of the collapsing Fermi 10 Hall effect temperatures that crosses over via a maximum in the susceptibility measurements38 (see Fig. 4a), whereupon we obtain Δ ¼ 1.8 ± into a Kondo gapped state at low temperatures1,3,22,32–35. Zero 0.5 meV ( 21 K). This value is quantitatively consistent with magnetic field electrical resistivity and magnetic susceptibility estimates obtained from modeling the heat capacity and measurements reveal Ce Bi Pd to exhibit such signatures (see susceptibility (see below). An important factor in being able to 3 4 3 ρ Figs. 1 and 2 and Supplementary Fig. 1), but with a Kondo tem- extract the carrier density is that xy (shown in Fig. 4a) is linear fi fi Δ perature scale that is signi cantly reduced relative to those found in in B at low B. We therefore nd that kBTK, which is the archetypal Kondo insulators SmB6 and Ce3Bi4Pt3.Typical quantitatively consistent with the hybridized many-body band

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5.0 a 6 10 1/T (K–1) Ce Pd 0.20 0.15 0.10 0.05 Sample A Bi Δ ∼ 4 meV 4.5 0 T ) 4 105 10 –2 4 K 7 –1 .cm) Ω .cm) 9 Ce Ω ( xx ( –1 xx 3 Δ ∼ 0.4 meV 4.0 10 104 Spin up 10(J mol 0 Spin down T

B = 0T 5 10 20 300 / C T (K) (meV)

3.5 E –2 Ce3Bi4Pd3 Sample A 3 10 Ce Bi Pd Sample B 3 4 3 0369 Ce3Bi4Pt3 Sample D B (T) 3.0 246810 0 50 100 150 200 250 300 T (K) b Fig. 3 Specific heat data. Low-temperature heat capacity divided by T M 450 temperature, C=T, plotted versus logarithmically scaled T (symbols). Solid 2.5 Ce Bi Pd 3 4 3 lines represent fits in which the Kondo gap is modeled using the 360 Schotte–Schotte model (see Methods). A full fit is initially made only for 270 B ¼ 0 (purple line). On extending to fittoC=T for B ¼ 4, 7, and 9 T (light 2.0 1 μ blue, green and yellow lines), only the Zeeman splitting ± 2 geff BB is 180 μ allowed to vary (where B is the Bohr magneton). The inset shows the (mol Ce per emu) 0.1 T

–1 locations of the Zeeman-split Lorentzians used in the Schotte–Schotte 1.5 90 5 T Linear fit model (see Methods). 0 0 100 200 300 ﬁ

(emu per mol Ce) The atypically small Kondo gap and nite concentration of in-

1.0 T (K) –2 gap states in Ce3Bi4Pd3 imply that this system lies closer to the 10 40

Ce Bi Pd (0.1 T) 3 4 3 insulator-metal threshold than archetypal Kondo insulators, TM Ce Bi Pd (5 T) 0.5 3 4 3 leaving open the possibility that its Kondo insulating behavior is Ce Bi Pt (0.1 T) 3 4 3 tuned by impurities and defects, as has been found to be the case in CeNiSn41,42. Although subsequent samples of CeNiSn 0.0 prepared with fewer impurities were found to exhibit increased 0 50 100 150 200 250 300 metallic behavior, the opposite has thus far been found in T (K) Ce Bi Pd 40,43. Further, in nominally pure CeNiSn, a residual 3 4 3 Ã ρ ¼ carrier density quantitatively similar to n0 in the inset to Fig. 4a Fig. 2 Sample characterization. a Comparison of xx versus T at B 0 for two Ce Bi Pd samples (labeled A and B) with Ce Bi Pt (sample D). The yields a coherent metallic state with an a-axis resistivity of 3 4 3 3 4 3 between 20 and 50 μΩcm or less42,44, whereas this same value of inset graph shows Arrhenius plots. Whereas Ce3Bi4Pt3 exhibits activated ÀΔ=k T residual carrier density in Ce Bi Pd yields an insulating behavior (ρ / e B ) behavior for 5 ≲ T ≲ 30 K, Ce Bi Pd appears to exhibit 3 4 3 xx 3 4 3 such behavior over a range 6 ≲ T ≲ 35 K (with a smaller slope) that lies with an electrical resistivity that is 20 to 50 times higher. outside the fitting range, suggesting that Δ cannot be estimated reliably Indications are therefore that the residual carriers in Ce3Bi4Pd3 ρ are incoherent or extrinsic in contrast to CeNiSn (see Methods). from xx in the case of Ce3Bi4Pd3. The shallow slope and departure from Here, we consistently prepare samples of Ce3Bi4Pd3 with activated behavior at low T is suggestive of a temperature-dependent ¼ scattering rate or residual in-gap states associated either with bulk insulating behavior at B 0 (two examples of which are shown in Fig. 2) by polishing away surface oxidation (see Methods) and defects, inclusions of other phases or the sample surface (see Methods). fl Also shown is a schematic of the crystal structure (see Methods). by avoiding superconducting binaries inherent to the ux χ ¼ technique used to grow these materials (see Supplementary b Susceptibility versus T for Ce3Bi4Pd3 (at B 0.1 and 5 T in gray and ¼ Fig. 3). All samples prepared in such a manner have a thermally blue, respectively) compared with that for Ce3Bi4Pt3 (at B 0.1 T) from 35 =χ activated carrier density at low-magnetic fields (see Fig. 4a) of ref. , with TM indicating the maxima. The inset shows 1 versus T for – similar magnitude to that in Ce3Bi4Pt3, and have an electrical Ce3Bi4Pd3, evidencing Curie Weiss behavior (indicated by red dashed ≲ fitted line) over a broad range of T and a Curie constant C 0.8 mol Ce resistivity that increases with decreasing T for all T 250 K (see per emu K. Fig. 2a), which includes the absence of saturating behavior at low temperatures (see Methods and Supplementary Fig. 4)45. The above observations are consistent with the finding made by way picture4. The activated behavior can also be approximately of electronic structure calculations performed in the non- 39 interacting limit (in which the f -electrons are regarded as rescaled against that measured in Ce3Bi4Pt3 (see inset of Fig. 4a) —the only significant difference being that Ce Bi Pd has a itinerant) that Ce3Bi4Pt3 and Ce3Bi4Pd3 both similarly exhibit a 3 4 3 37,46 several times smaller gap and a higher concentration of in-gap charge gap , with the robustness of the Kondo gap being Ã largely contingent upon the strength of TK. states, n0 (corresponding to 0.2% holes per Ce), than Ce3Bi4Pt3. Consistent with Ce3Bi4Pd3 having a several times smaller gap, the insulating state is found to be suppressed by magnetic fields that Magnetic field-induced metallization. Metallization of the are several times weaker in strength than those required in Kondo insulating Ce3Bi4Pd3 samples beyond Bc 11 T (in the ! Ce3Bi4Pt3 (see Fig. 4b). limit T 0) is evidenced in Figs. 1, 4b and 5 by the crossover

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ρ a the reduced gap. The nonlinearity of xy above Bc indicates the T (K) 60 0 40 80 presence of multiple bands and a possible anomalous Hall con- 2 47 4 tribution from skew scattering (see Methods). In the absence of ) ) Ce3Bi4Pd3 –3 –3 a dominant anomalous Hall component from skew scattering, the Ce3Bi4Pt3 · m · m positive Hall coefﬁcient implies either that the hole carriers have 26 26 1 2 numerical supremacy over electron carriers, as would be expected 37

/Ce (10 on the basis of band structure calculations , or that the hole /Ce (10 40 * * n

n 38 B = 2T 0 carriers are of higher mobility . 0 .cm)

Ω 01020 ( T (K) Fermi liquid behavior. On entering the high-magnetic field xy regime, we find the low-temperature electrical resistivity to dis- ρ ¼ ρ þ 2 ρ 20 play the Fermi liquid form xx 0 AT , where 0 is a constant 20 K and A is a coefficient proportional to the square of the quasi- 12.5 particle effective mass. The quadratic-in-temperature form is 7.5 demonstrated by plotting the electrical resistivity versus T2 in 4.12 Sample A 1.8 Fig. 5, yielding linear behavior at the lowest temperatures. The fi 0 Fermi liquid temperature scale TFL, which we de ne as the point 0 15304560beyond which the resistivity is observed to exhibit a downward b curvature from T2 behavior on increasing the temperature, is 1600 1.5 found to collapse on approaching B in Fig. 1. At the same time, A 40 K 50 K c 35 9.0 is observed to undergo a steep upturn on approaching Bc from 30 7.0 high-magnetic fields in Fig. 1. Both the upturn in A and collapse 1.0 5.0 25 of TFL are indicative of a collapsing Fermi liquid energy scale in 1200 .cm) 4.0

20 Ω

the vicinity of B , which is one of the primary signatures of

( c

3.4 15 5 48,49 2.5 quantum criticality in Fermi liquid systems . However, rather 12.5 10 0.5 xx 1.5

than peaking precisely at B , A is observed to peak at B 15 T. 10 c

.cm) 0.5

Ω This is a likely consequence of the metallic contribution to the

800 7.5 (

xx 4.12 0.0 conductivity vanishing due to the collapse of the sizes of the Ce Bi Pt Sample E ! 1.8 3 4 3 Fermi surface pockets in the limit B Bc. Other possible factors 0.74 20 40 60 include sample inhomogeneities causing Bc to be non-uniform 400 B (T) throughout the sample or an anisotropic gap causing the gap closure ﬁeld to be momentum-space-dependent.

Ce Bi Pd 3 4 3 Sample A Magnetic susceptibility measurements. Thermodynamic evi- 0 0 15304560dence linking Bc to the breakdown of the Kondo coupling B (T) accompanying the closing of the gap is provided by measurements of magnetization and magnetic susceptibility in Fig. 6.A fi Fig. 4 Magnetic eld-dependent electrical transport measurements. a The strong argument for the reduction in Kondo screening is pro- ρ Hall resistivity xy of Ce3Bi4Pd3 plotted versus B measured at several Ã vided by the approach of the magnetization towards saturation in temperatures. The inset shows the carrier density n (green circles) plotted the inset to Fig. 6a, which is indicative of a state in which the ¼ versus T for Ce3Bi4Pd3 at B 2 T (left-hand and bottom axes), estimated f -electron moments are to a large extent polarized and subject to using nÃ B=eρ (not corrected for the anomalous Hall component), with xy reduced fluctuations. More directly, we find the insulator-to- the magenta line representing a fittonÃ ¼ nÃ þ nÃ ðÀΔ=k TÞ, where 0 1 exp B metal transition or crossover near B to be accompanied by a low- nÃ ¼ 0.2 ´ 1026 m–3, and nÃ ¼ 3.7 ´ 1026 m–3 and Δ ¼ 1.8 0.5 meV. The c 0 1 ± temperature peak in the magnetic susceptibility χ in Fig. 6a, Ã residual value of n0 (equivalent to 2% of the Brillouin zone or 0.2% per χ which we trace back to the peak in at TM along the temperature Ce) is smaller than the concentration of uncompensated Ce moments and axis. On performing magnetic susceptibility measurements over a magnetic impurities inferred from the susceptibility (see Methods), range of temperatures and magnetic fields, we construct a pseudo suggesting that the latter contribute only partly to the residual in-gap Ã phase boundary from the locus of the peak that continuously states. For comparison, the dotted line shows n plotted versus T for ; ¼ 39 connects Bc with TM within the B T plane (see Fig. 1), revealing Ce3Bi4Pt3 at B 5 T (right-hand and top axes) from ref. . b Measured that B ¼ BðT ! 0Þ. In the low-magnetic field limit, the magnetoresistivity ρ of Ce Bi Pd sample A (for B kh100i) at different c M xx 3 4 3 broadness of the peak is indicative of a crossover, yet it becomes temperatures (as indicated in different colors) plotted versus B. For increasingly sharp on increasing the magnetic field and reducing comparison, the inset shows the magnetoresistance of Ce3Bi4Pt3 at the temperature. different temperatures. Specific heat measurements. Further thermodynamic evidence from insulating behavior for BBc. We identify metallic behavior as an electrical resistivity vided by the finding of a Schotte–Schotte anomaly in the specific having a value that decreases with decreasing temperature in the heat in Fig. 3 (see also Supplementary Fig. 5), which undergoes a ! ∂ρ =∂ limit T 0 (i.e., xx T>0). Further evidence for the transi- continuous change in shape in an applied magnetic field. A tion or crossover from insulating to metallic behavior with the Schotte–Schotte50,51 anomaly occurs under circumstances in closure of the Kondo insulating gap in Ce3Bi4Pd3 is provided by which a peak in the electronic density-of-states in the shape of a Hall effect measurements at high-magnetic fields. The Hall Lorentzian is offset from the chemical potential by a gap (see ρ resistivity xy begins to drop on the approach to Bc, which indi- Supplementary Fig. 6 and Methods). Fits (see Fig. 3a) to the cates an increase in carrier density in advance of the closing of the heat capacity measured at B ¼ 0 yield Δ ¼ 1.7 ± 0.2 meV, which Kondo gap, likely caused by thermal excitations of carriers across is in excellent agreement with Δ estimated from Hall effect

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a 1400 400 b 0 T 20 T Sample 2.5 25 1200 A 5.0 30 350 7.5 35 1000 10 40

12.5 45 .cm) Ω .cm) 2 300 ( Ω T 800 15 50 FL xx ( xx 17.5 55 59 600 250

400

200 200 0 102030400 100 200 c d 450 700 0 T Sample 10 A 11 2 T FL 600 12 13 .cm) Ω

400

14 ( xx

.cm) 15 Ω

500 ( 16 xx 17 18 400 350

300 0 6 12 18 24 0 5 10 15 20 25 30 e f 0 T 550 Sample 400 B 10 11 2 T FL 12 500 13 375 14 .cm) Ω .cm) 450 15 ( Ω xx (

16 xx 17 400 350 18

350

325 0 6 12 18 24 0 5 10 15 20 25 30 T (K) T 2 (K2) ρ fi Fig. 5 Temperature-dependent electrical resistivity measurements of Ce3Bi4Pd3. a Electrical resistivity xx versus T at various values of the magnetic eld ρ 2 fi (as indicated) extracted from Fig. 4a. Connecting lines are a guide to the eye. b xx versus T at various values of the magnetic eld (as indicated) extracted ρ fi ρ 2 from Fig. 4a. c xx versus T for the same sample measured at various steady static magnetic elds (as indicated). d The same xx as in c versus T . e and f 2 Same as for c and d but measured on a different sample (as indicated). Dashed lines indicate the linearity in T while arrows indicate TFL (the temperature ρ 2 2 above which xx appears to deviate from T behavior). The slopes of the lines versus T provide an estimate of A (plotted in Fig. 1). A small departure from T2 behavior in the limit T2 ! 0 is sample-dependent, suggesting it to be of extrinsic origin.

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a B (T) of increased tendency for magnetism accompanying a continuous increase in the valence towards a trivalent value27–31.In 0 15304560 3.6 1.2 Ce3Bi4Pd3, the polarization of the f -electron moments by a 0.63 K magnetic field causes the magnetic field to behave like an effective 1.5 0.9 4.2 negative pressure; the lattice volume invariably increases under a 52,53 10 magnetic field in Ce compounds , causing a reduction in the 20 0.6 per Ce) valence towards a trivalent value. The relative ease by which 30 B 2.4 fi 40 ( f -electron moments are polarized by a magnetic eld in

0.3 M 54 Ce3Bi4Pd3 (see inset to Fig. 6a) compared to Ce3Bi4Pt3 suggests

(emu per mol Ce) that the smaller Kondo temperature and gap in the former is a Bc –2 0.0 likely consequence of it lying closer to integer valence than the 0153045 10 latter37. B B (T)

∂ 1.2 While a peak in the magnetic susceptibility at Bc has been M/

∂ 55

= predicted to occur on closing the gap in a Kondo insulator , along with signatures of quantum criticality, other scenarios are

B possible at Bc, including the case found in itinerant electron c 56–58 0.0 metamagnets . Here, quantum criticality may occur in the absence of broken symmetry due to the tuning of the highest b ﬁ 2.45 temperature end point of a notional line of rst order phase B (T) 56 ﬁ 13 transitions to absolute zero . Our nding of a peak in the sus- T M 11 ceptibility that becomes increasingly sharp on lowering the 10 temperature suggests that Ce Bi Pd remains in the crossover 2.40 8 3 4 3 6 regime, however, with the end point remaining inaccessible in the 5 limit T ! 0. It has yet to be determined whether this is an 4 2.35 intrinsic property of the metal-insulator transition in Ce3Bi4Pd3 2 or whether it is caused by the broadening of the quasiparticle (emu per mol Ce) bands by defects and impurities. –2

10 2.30 An alternative possibility, given the suppression of the Kondo coupling in strong magnetic fields, is that the Kondo coupling 59,60— vanishes completely at Bc in effect causing the f -electrons 2.25 to behave in a more localized fashion for B>Bc. Indeed, one of the predicted consequences of a localization of the f -electrons in 37 Ce3Bi4Pd3 (and Ce3Bi4Pt3) is a metallic state . The metallic state 246810 induced by the localization of the f -electrons has also recently T (K) been identified by way of dynamical mean field-theory as a strong 46 Fig. 6 Magnetization and susceptibility measurements of Ce3Bi4Pd3. candidate for a line-node semimetal , in which case Bc would a Magnetic susceptibility χ ¼ ∂M=∂B versus B of Ce Bi Pd (for B kh100i) correspond to a insulator-to-line-node semimetal transition or, 3 4 3 61 at different temperatures (as indicated; see Methods). Vertical bars potentially, a topological quantum critical point . The collapse of ≳ indicate the T-dependent maximum. The inset shows the magnetization M the Hall resistivity to a small value for B Bc is indeed consistent versus B. b χ versus T at different static magnetic fields (as indicated), with with the Fermi liquid regime also being semimetallic. vertical bars indicating the maxima in the temperature dependence. Note The contiguity between a vanishing carrier density for BB has the potential to that at B 2 T, a shoulder rather than a peak is observed due to a low T fi c contribution from magnetic impurities (or defects) at low B and T (see make the nature of the magnetic eld-tuned transition somewhat unique compared to that in other d- and f -electron systems. Methods). A similar low T contribution is observed in Ce3Bi4Pt3 in Fig. 2b, although, in that case, it is farther from T . Whether the strong correlations are caused by proximity to a M metamagnetic end point or a magnetic field-induced localization of the f -electrons, in both cases the reduction in electronic cor- ≠ fi measurements (see Fig. 4a). On considering B 0 and xing all relations beyond Bc is generally expected to result in a gradual fi reduction in the effective mass mÃ57,62, or equivalently the A parameters except geff ,we nd that the evolution of the Schotte–Schotte anomaly under a magnetic field can be explained coefficient56,63, with increasing magnetic field. The reduction in A with increasing field in Ce Bi Pd is indeed qualitatively similar solely in terms of Zeeman splitting, where geff 2.9 ± 0.3 is an 3 4 3 1 to that previously observed in d- and f -electron metamagnets (for effective g-factor for pseudospins of ± 2. The critical magnetic 56,62,63 field B therefore roughly corresponds to g μ B Δ k T .As example, Sr3Ru2O7 and CeRu2Si2) . c eff B B K Finally, there is the question of whether strong electronic a further consistency check, a similar value of the gap (Δ ¼ 1.5 ± correlations in proximity to a magnetic field-tuned quantum 0.2 meV) qualitatively accounts for the maximum in the magnetic critical point contribute to the growth of the electronic con- susceptibility as a function of temperature (see Methods and tribution to the heat capacity in the vicinity of the field-induced Supplementary Fig. 7) and its shifting to lower temperatures fi transitions into the metallic states of the Kondo insulators under a magnetic eld. 20,21 Ce3Bi4Pt3 and YbB12 , or to the temperature dependence of the quantum oscillation amplitudes within the insulating phases 13,15 fi Discussion of SmB6 and YbB12 . Our ndings suggest, at the very least, The signatures of strongly enhanced electronic correlations in the that a growth of electronic interactions at the expense of a fi declining hybridization needs to be taken into consideration in vicinity of the critical magnetic eld Bc 11 T in Figs. 1, 4, 5 and 6, and their association with an insulator-to-metal transition, are future more complete models of the insulating state in strong fi magnetic fields. A further possibility is that the Kondo insulator strikingly similar to those recently identi ed in SmB6 as a func- 28,31 gradually transforms into an excitonic insulator64 in advance of tion of pressure . In SmB6, the entry into the metallic phase with increasing pressure can be qualitatively understood in terms metallization.

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Methods with respect to the chemical potential (at ε ¼ 0)20, band structure calculations of fl Sample preparation.Ce3Bi4Pd3 crystallizes in a cubic structure of space group Ce3Bi4Pt3 and Ce3Bi4Pd3 have indicated an asymmetric gap with at bands I43d with a noncentrosymmetric unit cell that contains four formula units and a situated just below the chemical potential37. Flat bands are also situated above the lattice parameter of a ¼ 10.05 Å26. The crystals are grown by the Bi-flux technique chemical potential, but are considerably further away in energy. Given what is with starting composition Ce:Pd:Bi = 1:1:1.8. The reagents are put in an alumina known about the electronic structure, we model the Schotte–Schotte anomaly using crucible placed inside an evacuated quartz tube. The quartz tube is then heated to an electronic density of states of the form 1050 °C at 100 °C/h and is kept there for 8 h. The solution is then cooled down to X 450 °C at 2 °C/h. The excess of Bi is removed by spinning the tube in a centrifuge. W DðεÞ¼D ; ð Þ The crystallographic structure is verified by single-crystal diffraction at room 0 πð 2 þðε þ Δ þ σ μ Þ2Þ 1 σ¼ ± 1 W geff BB temperature using Mo radiation in a Bruker D8 Venture diffractometer. 2 The upturn in the magnetic susceptibility at low temperature indicates the where σg μ B represents Zeeman splitting. Here, σ represents pseudospins of ± 1 presence of uncompensated Ce moments and magnetic impurities (such as other eff B 2 – ¼ rare earths)1,3,32 34, which are frequently seen in Kondo insulators. However, while Rgeff is an effective g-factor. The free energy given by F À 1 ðεÞ ½ þ ðÀε= Þ ε inclusions of other crystalline phases such as CePdBi2, which has a sharp kBT À1D ln 1 exp kBT d while the heat capacity given by 65 ¼ ∂2 =∂ 2j 67 fi antiferromagnetic transition at TN 6K , and superconducting Bi-Pd binary Cp Cv T F T v, which we calculate numerically and t to the compounds, which have a variety of different transition temperatures Tc, can also experimental data over the temperature range 1.5 ≲ T ≲ 10 K. During fitting, we ¼ ¼ – – – be present. The latter include tetragonal PdBi2 (Tc 4.25 K), BiPd (Tc 3.7 K) assume a phonon contribution C =T ¼ βT2 where β ¼ 1 mJ mol 1 Ce 1 K 4.Itis ¼ ph and monoclinic PdBi2 (Tc 1.73 K). The absence of a sharp feature in the heat fi – fi fi important to note, that on tting to the Schotte Schotte model, one cannot capacity at 6 K rules out a signi cant presence of CePdBi2.On tting the Δ – distinguish whether is positive (corresponding to a peak below the chemical magnetic susceptibility to a Kondo gap plus a low-temperature Curie Weiss term potential) or whether it is negative (corresponding to a peak above the chemical to model uncompensated Ce moments and isolated magnetic impurities (see potential), or whether there are peaks located at both ±Δ as has sometimes been simulations of the magnetic susceptibility below), we estimate their concentration 20 assumed . to be equivalent to 2% per Ce. In the case of Tb impurities, which are determined We initially fit the data only at B ¼ 0, from which we obtain Δ ¼ 1.7 ± 0.2 from a chemical analysis of Ce to be the leading impurity, the larger moment would meV, which is comparable to the value estimated from Hall effect measurements imply a significantly lower concentration of 0.1%. In samples that have been ¼ ≠ Δ fi (see Fig. 4a), and W 1.1 ± 0.2 meV. For B 0, we hold D0, W, and constant polished, no signi cant negative contribution to the susceptibility is found that and allow only g to vary. Zeeman splitting alone, with g ¼ 2.9 ± 0.3, is able to would indicate a significant presence of superconducting impurity phases within eff eff explain the evolution of the Schotte–Schotte peak under a magnetic field. the bulk, suggesting that superconductivity seen in electrical transport Δ À W 0.6 meV (7 K) is of comparable order to the reduced gap estimated measurements occurs mostly on the surface (see electrical transport experimental from the slope of the Arrhenius plot in the inset to Fig. 2a. details below). A distinguishing feature of the Schotte–Schotte anomaly that appears to be At this early stage of sample growth, the electrical resistivity becomes higher present in the experimental data (see Fig. 3 and ref. 40) is an electronic contribution with improved sample quality (see e.g., the difference between early work on these to the heat capacity of the form samples40, this work and more recent work by another group43). = γ þðβ0 À βÞ 2 ð Þ Cel T 0 T 2 Electrical transport experimental details. Samples of Ce Bi Pd are cut into 3 4 3 0 rectangular shapes and polished for electrical transport measurements. All resis- (see Supplementary Fig. 5b) in the limit T ! 0, where ðβ À βÞT2 exceeds the fi β 2 γ fi tivity measurements, including those in static and pulsed magnetic elds are per- contribution T from phonons and where 0 is the Sommerfeld coef cient formed using the four wire technique. Whereas freshly polished samples (green line characterizing in-gap states (that also depends on the strength of the magnetic fi 67 in Supplementary Fig. 4) exhibit insulating behavior down to 2 K, thermally eld) . Supplementary Fig. 5b shows that Ce3Bi4Pd3 exhibits the form given by ! γ À1 À2 cycled samples exhibit additional superconductivity (red line in Supplementary Eq. (2) in the limit T 0, with 0 increasing by 30 mJmol K on increasing Fig. 3). After re-polishing, most of the additional superconductivity is removed fi the magnetic eld from 0 to 4 T. A comparable increase was reported in Ce3Bi4Pt3 (blue line in Supplementary Fig. 3). on increasing the magnetic field from 0 to 40 T20. Despite the opening of a gap in the energy spectrum, Kondo insulators are The observed consistency with the Schotte–Schotte model therefore includes (i) prone to in-gap states that can reside either at the surface or the bulk and generally γ fi a peak at 5 T, (ii) a residual electronic contribution 0 and (iii) a magnetic eld- fi ! 0 cause the electrical resistivity to acquire a nite value in the limit T 0. In a dependent low- temperature behavior of the form C =T γ þðβ À βÞT2 (see 45 ρÀ1 el 0 similar manner to SmB6 ,Ce3Bi4Pd3 is found to have an inverse resistivity xx Supplementary Fig. 5 and Methods). It remains to be determined to what extent the that varies linearly in T at low temperatures (see Supplementary Fig. 4), suggesting Lorentzian line-shape (of halfwidth W ¼ 1.1 ± 0.2 meV) is intrinsic (e.g., related that scattering from defects may be responsible for the departure from activated to the Kondo coupling and electronic bandwidths) or affected by quasiparticles 45 behavior at the lowest temperatures (at least down to 2K) . scattering from defects and impurities. ∂ρ =∂ To delineate regions of the phase diagram where insulating xx T<0 and metallic ∂ρ =∂T<0 are observed, the data in Fig. 5 are differentiated (see xx Simulations of the magnetic susceptibility Supplementary Fig. 1) and the points where ∂ρ =∂T ¼ 0 are plotted in Fig. 1. . As a further consistency check, we xx show that similar parameters as used in the modeling of the heat capacity also provide a qualitative explanation for the approximate location of the peak in the Magnetic susceptibility experimental details. Magnetic susceptibility measure- susceptibility as a function of temperature and its suppression to lower tempera- ments in pulsed magnetic fields are performed using an extraction magnet- tures as the magnetic field is increased. We calculate the susceptibility using 66 fi ometer . Magnetic susceptibility measurements in static magnetic elds are Z 1 performed using a Quantum Design vibrating sample magnetometer. Owing to χ ¼ ðεÞ 0 ðεÞ ε; ð Þ C D f FD d 3 isolated impurities giving rise to an upturn in the susceptibility at low À1 temperatures1,3,32–34, and the small energy scale associated with the Kondo gap in fi ≳ fi 0 ðεÞ Ce3Bi4Pd3, a steady magnetic eld of B 4 T is required to uncover the maximum (valid for low-magnetic elds) where f FD is the derivative of the Fermi-Dirac in the susceptibility. Only a shoulder is observed at lower magnetic fields (see distribution function and C is a constant renormalized to the experimental sus- simulations of the magnetic susceptibility below). In a similar manner to ceptibility at 300 K, the results of which are plotted in Supplementary Fig. 7. 54 Ce3Bi4Pt3 , the magnetic susceptibility of Ce3Bi4Pd3 continues to remain large as Equation (3) does not include the low-temperature Curie–Weiss-like contribution the magnetic field is increased, which is suggestive of a band Van Vleck para- from impurities and defects. Partly for this reason, it overestimates the the initial magnetism effect23. growth in the susceptibility with increasing field. The model performs poorly once B Bc, however, which is likely a consequence of electronic correlations not being included. Electrical transport measurements indicate electronic correlations to be Heat capacity experimental and modeling details. Heat capacity measurements important in the vicinity of Bc. On comparing the calculated peaks in the sus- on Ce3Bi4Pd3, made using a Quantum Design Physical Properties Measuring Δ ¼ ceptibility (B

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63. Daou, R., Bergemann, C. & Julian, S. R. Continuous evolution of the Fermi Competing interests surface of CeRu2Si2 across the metamagnetic transition. Phys. Rev. Lett. 96, There are no competing interests. 026401 (2006). 64. Knolle, J. & Cooper, N. R. Excitons in topological Kondo insulators: theory of thermodynamic and transport anomalies in SmB6. Phys. Rev. Lett. 118, Additional information 096604 (2017). Supplementary information is available for this paper at https://doi.org/10.1038/s41467- 65. Han, F. et al. Antiferromagnetic Kondo lattice in the layered compound 019-13421-w. CePd1ÀxBi2 and comparison to the superconductor LaPd1ÀxBi2. Phys. Rev. B 92, 045112 (2015). Correspondence and requests for materials should be addressed to N.H. 66. Detwiler, J. A. et al. Magnetization of UBe13 to 60 T. Phys. Rev. B 61, 402 (2000). 67. Silhanek, A. V. et al. Quantum critical 5f electrons avoid singularities in U(Ru, Peer review information Nature Communications thanks Andrea Bianchi, Toshiro Rh)2Si2. Phys. Rev. Lett. 95, 026403 (2005). Takabatake and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Acknowledgements Reprints and permission information is available at http://www.nature.com/reprints This high-magnetic field work was supported by the US Department of Energy “Science ” of 100 tesla BES program. S.K.K. acknowledges support of the LANL Directors Post- Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in doctoral Funding LDRD program. Sample characterization at Los Alamos National published maps and institutional affiliations. Laboratory was performed under the auspices of the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, “Quantum Fluctuations in Narrow Band Systems” project. The high-magnetic field facilities of the Open Access This article is licensed under a Creative Commons National High-Magnetic Field Laboratory—PFF facility and related technical support are funded by the National Science Foundation Cooperative Agreement Number DMR- Attribution 4.0 International License, which permits use, sharing, 1157490 and DMR-1644779, the State of Florida and the U.S. Department of Energy. We adaptation, distribution and reproduction in any medium or format, as long as you give acknowledge helpful discussions with Mucio Continentino, Peter Riseborough, Chao appropriate credit to the original author(s) and the source, provide a link to the Creative Cao, Jianxin Zhu, Qimiao Si. and Peter Wölfle. M.K.C. acknowledges support by the Commons license, and indicate if changes were made. The images or other third party ’ Laboratory Directed Research and Development program of Los Alamos National material in this article are included in the article s Creative Commons license, unless Laboratory under project number 20180137ER in conducting experiments on Kondo indicated otherwise in a credit line to the material. If material is not included in the ’ insulators. N.H. acknowledges support from the Los Alamos National Laboratory LDRD article s Creative Commons license and your intended use is not permitted by statutory program: project number 20180025DR. regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/. Author contributions S.K.K., M.K.C., J.P., S.M.T., and N.H. performed the measurements. P.F.S.R. and E.D.B. grew and characterized the samples. S.K.K., N.H., and P.F.S.R. wrote the manuscript. This is a U.S. government work and not under copyright protection in the U.S.; foreign J.D.T. and F.R. assisted with the interpretation of the experimental data. copyright protection may apply 2019

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