arXiv:1507.01690v2 [cond-mat.supr-con] 28 Dec 2015 infiatbekhog ntecnesdmte hsc in matter years condensed recent the in breakthrough significant ytm aemc oe rtcltmeaue o example, for temperature, ( critical LaONiP lower nickel-based much the have compounds, systems iron-based the with Compared epnil o h arn ftesprodcigelectro superconducting the of pairing spin-fluctuatio the the for that responsible believed widely is it and magnetism ( vnuo doping upon even K 5 ec ugssta h ibsdssescnb understood theory be electron- can conventional evi- systems of of context Ni-based in majority the the that suggests Moreover, dence to found. proximity is in Ni with associated magnetism fluctuated even fN nsc opudi ”1.5 is compound e such the in composition, Ni stoichiometry of the in K separation phase TlNi oe3 more lcrndpdTlFe doped electron 0 eain hni t osnK cousin its in than relations n BaCo and of n BaCo and TlNi nerdfo h lcrncha n h pe rtclfiel critical upper the and heat electronic the behav electrons from heavy inferred the to explanation natural a provides iso pcrsoy(RE)measurement (ARPES) spectroscopy mission mass a oesnuaiy(H)na em nry( energy Fermi near pronounced (VHS) a to singularity rise Hove gives van point Z at band camelback-shaped er oivlehayfrinbhvo eo coher- a below behavior heavy-fermion temperature involve ent to pears 3 T . . 8 7 c h icvr fio-ae uecnutr stemost the is superconductors iron-based of discovery The eety hr iklcacgndsKNi chalcogenides nickel there Recently, Ni K K = 2 2 12,13,17 ) ) 1 Se Se 12 14 . 5 d 2 KNi , + 2 2 . lcrn nTlNi in electrons 4 eerpre,i hc uecnutvt ap- superconductivity which in reported, were opudi ooeeu ihu ivcnyor vacancy Ni without homogeneous is compound hrsauieslbn tutr ihBaFe with structure band universal a shares 2 a rpsdt nuetehaye heavy the induce to proposed was T 2 K As oee,vr eety nl-eovdphotoe- angle-resolved recently, very However, . As c 1 ) 6 h iron-pnictides The . oa utaino hredniywv CW instabilit (CDW) charge-density-wave of fluctuation local etr ntemdnrrdrnewt eraigtemperatu decreasing with range midinfrared the in feature h upeso in suppression the omdotclsetocp td nTlNi on study spectroscopy optical formed trs h vrl pia eetnesetaaesimilar are spectra reflectance optical overall The atures. ASnmes 74.70.Xa,74.70.-b,74.25.Gz,74.72.Kf numbers: PACS o existence the to due mechanism, points energy. saddle the by driven 2 BaNi , 2 2 = 4 20 S nentoa etrfrQatmMtras colo Phys of School Materials, Quantum for Center International (3 us-w-iesoa iklcacgndsTlNi chalcogenides nickel Quasi-two-dimensional 2 ihaceia oeta hfe u to due shifted potential chemical a with , T 12,14 d 3 coh 7 ( K pia rpriso TlNi of properties Optical .INTRODUCTION I. .Teeoe tcnb iwda heavily as viewed be can it Therefore, ). T 2 .B Wang, B. X. ) 2 Se ∼ osdrn h ooaetT or Tl monovalent the Considering . c 4 As 5 aNA ( LaONiAs , 0K ncnrs oK to contrast In K. 20 3 odt,n vdnefrodrdor ordered for evidence no date, To . 2 olbrtv noainCne fAvne Microstructu Advanced of Center Innovation Collaborative ≃ 2 (3 2 ( Se d T 0 6 c nttt fPyis hns cdm fSine,Beijing Sciences, of Academy Chinese Physics, of Institute 2 . . 5 x 46 2 (3 ,wt eue lcrnccor- electronic reduced with ), R = Fe eateto hsc,Zein nvriy aghu3100 Hangzhou University, Zhejiang Physics, of Department 5 olbrtv noainCne fQatmMte,Beijin Matter, Quantum of Center Innovation Collaborative ( d K 1 ω 2 0 8 / − ) n h ekiefauein feature peaklike the and ) .P Wang, P. H. hcgndsaecoeto close are chacogenides . + 1 . 5 13 y 7 ejn ainlLbrtr o odne atrPhysics, Matter Condensed for Laboratory National Beijing T hni BaFe in than ) Se .Temxdvalency mixed The ”. K n TlNi and , c ) 2 7 21 = sal oe than lower usually , utemr,the Furthermore, . 2 . ff 7 cievalance ective 18 x 1 K Fe 2 ff agogWang, Hangdong ) Se 2 eel that reveals cieband ective 5 8–11 E 2 Se 2 BaNi , − 2 F As y 2 2 2 ,which ), Se Se . Se ( ( 2 2 T T 2 2 As (3 ns c c 15,16 igecytl vrabodfeunyrnea aiu temp various at range frequency broad a over crystals single 2 2 is n d 2,3 2 bevto fpedgpformation pseudogap of Observation : ior P 19 6 ≃ ≃ d 2 ) . , 2 σ Se 1 ( 2 ω .W rps htteCWisaiiyi TlNi in instability CDW the that propose We y. sanwydsoee uecnutr ehv per- have We superconductor. discovered newly a is lysprse er20 cm 2500 near suppressed ally lsarflcac de iia oisiotutr BaNi isostructure its to similar edge, reflectance e rflcutos u esrmn niae httelo- the that indicates or- measurement CDW order Our local CDW cal the to fluctuations. attributed or is der structure gap weak 300 below The temperature any K. at appears feature pseudogap a and h vrl rqec eedn reflectivity dependent frequency overall The adsrcuewihlast h a oesnuaiyclose singularity Hove level. van Fermi in the the points to to saddle leads of which presence structure the band by driven fluctuati the is that instability suggest CDW we results, ARPES earlier the with i nKNi on sis di is which temperature, ai rpriswr led reported already were properties namic method a aarvasta TlNi that reveals data cal nesadteuiu eair ti ihydsrbet in rang to temperature K. whole desirable 300 the below highly in dynamics is charge it the vestigate behavior, unique the understand rncsse.I hswr,w rsn ealdoptical detailed a present we TlNi work, on elec- this an study In of spectroscopy probe formation to gap system. used possible tronic widely and is dynamics which carrier the resolution, energy high with ntesetauo neigteflcutn D state CDW fluctuating anomaly the any entering observe upon not spectra did the ARPES in the Moreover served. 0 u iapaso oln nte”ev-emo”state ”heavy-fermion” the in cooling below on t disappears up present but is K state 300 (CDW) wave density charge local the that PF nlssi obndhg-eouinsnhornx synchrotron high-resolution di ray combined a in analysis (PDF) measurements otoeosre nisisostructure its in observed those to ugs h rgesv omto fapseudogap a of formation progressive the suggest ) 2 e,wihmgtb rgntdfo h dynamic the from originated be might which res, iguFang, Minghu igecytl fTlNi of crystals Single pia pcrsoyi oeflbl estv techniqu sensitive bulk powerful a is spectroscopy Optical oeseily h eto pair-distribution-function neutron the specially, More c,Pkn nvriy ejn 081 China 100871, Beijing University, Peking ics, a oesnuaiyvr ls oteFermi the to close very singularity Hove van f ff T ato n eto cteigsuyi KNi in study scattering neutron and raction 14 coh hi tutr,tasot antcadthermody- and magnetic transport, structure, Their . 12,13 2 Se e,Nnig209,China 210093, Nanjing res, 14 2 h e The . / utain r ute nacda h lowest the at enhanced further are fluctuations nis”ev emo tt” nCombination In state”. fermion ”heavy its in nti ekycreae system. correlated weakly this in ,3 2, 010 China 100190, n .L Wang L. N. and I EXPERIMENT II. 7 China 27, ,China g, ff c sopst owa stpclyob- typically is what to opposite is ect ff 2 rn rmtenurnPFanaly- PDF neutron the from erent Se 2 Se 2 2 − Se 2 sago ea ihadistinct a with metal good a is 1 eegonb h self-flux the by grown were ihdcesn temperature, decreasing with 2 BaNi igecytl.Oropti- Our crystals. single ,5, 4, 2 As 14,23 ∗ 2 Both . 2 Se h frequency- The . 2 er- is R ( ω 2 Se sgradu- is ) 2 reveals 22 2 As To . ng 2 o e e - - . 2

dependent reflectance spectra at different temperature were 1.6 300 K )

measured by Bruker IFS 113v and 80v spectrometers in the 200 K -1 −1 100 K

∼ cm frequency range from 30 to 20 000 cm (4 meV 2.5 eV), 1 -1

− ) 1.2 1 ∼ 10 K

and then the reflectance was extended to 50 000 cm ( 6.1 -1

eV) at room temperature with a grating-type spectrometer. An ( cm in situ gold and aluminum overcoating technique was used -1

0.8

to obtain the reflectivity R(ω). Considering the small size of 4 0.1 −1 our samples, the data below 100 cm are cut off for reliabil- 100 1000 10000

-1

(cm ) (10 ity. The real part of conductivity σ1(ω) is obtained by the 1

0.4

Kramers-Kronig transformation of R(ω). The Hagen-Rubens TlNi Se relation was used for low frequency extrapolation; at high fre- 2 2 quencyside, an extrapolationmethod using X-ray atomic scat-

tering functions was applied to generate the high-frequency 0 3000 6000 9000 12000 24 reflectivity . -1

(cm )

FIG. 2: (Color online). Frequency dependence of the optical conduc- III. RESULTS AND DISCUSSION tivity below 12 000 cm−1 at different temperatures. The inset shows −1 σ1(ω) over broad frequencies up to 50 000 cm on a logarithm scale. Figure 1 shows the reflectance spectra of TlNi2Se2 single crystals over a broad energy scale at various temperatures. The value of R(ω) approaches unity towards zero energy and eral temperature-independent interband transitions could be shows an increase with decreasing temperature, indicating a also well resolved, as shown in the inset of Figure 2. The op- −1 good metallic behavior. By lowering the temperature, we do tical conductivity between 500 and 10 000 cm is gradually not see any sharp changes in the optical spectra but rather suppressed and a broad peak-like feature becomes more and −1 weak suppression of R(ω) near 2500 cm−1 , signaling the more obvious at 2800 cm as the temperature decreases. The 26 opening of a partial gap (pseudogap). With increasing ω, spectral line shape is similar to that of BaFe2As2 across the R(ω) drops quickly near 7000 cm−1 , known as the screened SDW transition though the feature is much weaker. It seems plasma edge. The relativity high edge position reveals a high to suggest that there should also be a density-wave gap open- carrier density, which is similar to isostructural compound, ing in TlNi2Se2 . Furthermore, this pseudogap feature is most 25 BaNi2As2 . There is another edge structure at about 15 000 prominent at low temperature and can be resolved even in the cm−1 which is caused by an interband transition. The reflec- 300 K data. tivity becomes roughly temperature independent at higher fre- To quantify the temperature evolution of optical conductiv- quencies. The inset of Fig. 1 shows R(ω) data up to 50 000 ity, especially the low frequency components, we use a sim- cm−1 in a logarithmic scale at 300 K. ple Drude-Lorentz model to decompose optical conductivity 27 Figure 2 shows the real part of conductivity spectra below spectra : 12 000 cm−1 at different temperatures. The Drude-type con- 2 2 2 ωpi Γ S j Γ jω ductivity is observed for all spectra at low frequency and sev- σ (ω) = Di + (1) 1 X 4π 2 + Γ2 X 4π 2 − 2 2 + 2Γ2 i ω Di j (ω j ω ) ω j

1.0 where ωpi and ΓDi are the plasma frequency and the relax- 0.8 ation rate of each conduction band, while ω j, Γ j and S j are

0.6

the resonance frequency, the damping and the mode strength R

0.8

300 K of each Lorentz oscillator, respectively. This model includes 0.4 Drude and Lorentz terms, which approximately capture the

100 1000 10000 contribution by free carriers and interband transitions. Both TlNi Se

-1

2 2 (cm ) 14,23 18

transport and ARPES results suggest the multiband 0.6 R character of TlNi2Se2 , therefore we applied two Drude com- 300 K ponents analysis here, similar to the other members of ”122” 200 K 25–27

100 K system . Even though the Drude-Lorentz fit is somewhat

0.4

10 K arbitrary and the accuracy of the derived fit parameters is un- certain, it will not modify the key outcomes of the analysis. Figure 3 illustrates the conductivity spectra at 300 K and 10 0 5000 10000 15000 20000 K together with the Drude-Lorentz fitting components at 10 K -1 (cm ) for TlNi2Se2 . In order to reproduce the optical conductivity below 50 000 cm−1 at 300 K, two Drude components, a nar- FIG. 1: (Color online). The temperature dependent R(ω) in the fre- row and a broad one, and four Lorentz components have to −1 quency range from 100 to 20 000 cm . The inset shows R(ω) data be used. Furthermore, an additional midinfrared peak is nec- −1 up to 50 000 cm on a logarithmic scale at 300 K. essary near about 2800 cm−1 at any temperature below 300 3

8 high to low energy at low temperature. We should remark that −1

300 K most of the SW below 6000 cm (the minimum of optical

10 K conductivity) would come from the intraband transitions. As Drude 1

6

) the temperature decreases, the SW transformation from high D-L fit -1 to low energy is induced by the Drude components narrow-

TlNi Se

2 2 cm ing. This is the typical optical response of a metallic mate-

Drude 2 -1

4 rial. On the other hand, the pseudogap develops below 2000 − 3 cm 1 at low temperature. However, we note that the effects of

Lorentz 3

Lorentz 1 Lorentz 5 the pseudogap formation to the SW transfer are minimal. It (10 1 2 is the metallic response that leads to the SW transfer to low

Lorentz 4 energy. In other words, the pseudogap is too weak to change Lorentz 2 the SW evolution in such a good metal. Notably, the SW of the mid-infrared peak could not fully compensate for the loss 0 5000 10000 15000 20000 of the low-energy Drude component, and the recovery of SW

-1

(cm ) extends to fairly high energy scale. Furthermore, the high en- ergy SW transfer above 8000 cm−1 is almost undistinguish- FIG. 3: (Color online). The experimental data of σ1(ω) at 300 and able in TlNi2Se2 . This may be related to the weaker corre- 10 K with the Drude-Lorentz fits shown at the bottom. lation or Hund’s coupling effect in TlNi2Se2 as compared to 18,22 BaFe2As2, in agreement with the ARPES results . In order to make the pseudogap-like suppression more K. We are mainly concerned about the evolution of the low clear, we also plot a model ratio of the low-temperature in- energy conductivity, therefore the fitting parameters for the tegrated SW to the model integrated spectral weight at 10 K. the two Drude components are shown in the Table 1 for dif- Assuming that TlNi2Se2 is a puremetal withoutthe pseudogap ferent temperatures. We also show the error bars of the fit- feature, the model optical conductivity at 10 K could be ob- ting parameters corresponding to an absolute error of 0.5% tained according to the Drude-Lorentz model with two Drude in reflectivity. We find that the two Drude components narrow components and four Lorentz components, as the situation at with decreasing temperature due to the metallic response. The 300 K . The parameters of the model optical conductivity are −1 listed in Table 1, where ΓD1 is set to 217cm in order to keep plasma frequency ωp1 keeps roughly unchanged, while ωp2 decreases suggesting that the gapping of the Fermi surfaces the same DC optical conductivity as the real data and ωp2 is −1 mainly appears in the broad Drude component. The Lorentz 5 set to 30100 cm to conserve the total spectral weight at 10 K. We then normalize the integrated SW at low temperature oscillator strength S 5 increases continuously with decreasing temperature, indicating the progressive formation of the ab- SW(10 K) to the model value MSW(10 K). As shown in the ≈ −1 sorption peaks just above the pseudogap. We use the formula inset of Fig. 4, the ratio decrease below 1700 cm , suggest- ing that the SW is depleted due to opening of the pseudogap, ω = ω2 + ω2 to estimate the overall plasma frequency, p q p1 p2 and the suppressed SW is transferred to higher energy, lead- −1 −1 then we get ωp ≈ 36360 cm at 300 K, and 32400 cm at ing to the gradually recovery of the SW above the pseudogap. 10 K, respectively. Therefore, the ratio of the square of the plasma frequency at 10 K to that of 300 K is about 0.80. It is 2 2 ∗ 2.0 well known that ωp = 4πne /m , where n is the carrier density 1.00 and m∗ is the effective mass. If we assume that the effective

0.95

TlNi Se

mass of itinerant carriers would not change with temperature, 2 2

Model ratio BaFe As the optical data reveals that roughly 20% of the itinerant carri- 0.90 1.5 2 2 ers is lost due to the pseudogap opening at the Fermi surface. K) SW(10 K)/MSW(10

0 2000 4000 6000 8000

-1

(cm )

To further characterize the spectral evolution, we plot the integrated spectral weight of TlNi2Se2 at 10 K, as shown in Figure 4, where the low-temperature integrated spectral 1.0 weight has been normalized to the integrated spectral weight at room temperature. The optical spectral weight is defined as Ω SW(10 K)/SW(300 K) K)/SW(300 SW(10

= σ ω ω 0.5 S W 0 1( )d . For the convenience of comparison, we also presentR the low-temperature integrated spectral weight 26 of BaFe2As2 . For BaFe2As2, the strong dip below 1000 0 2500 5000 7500 10000 −1 -1 cm represents the formation of SDW gap in the magnetic (cm ) ordered state26, while the second dip near 3000 cm−1 reflects the unconventionalSW transfer at high energy which seems to FIG. 4: (Color online). Ratio of the integrated spectral weight be a common feature in iron-pnictides/chacogenides28. Nev- SW(10K)/SW(300K) as a function of cutoff frequency Ω in ertheless, for TlNi2Se2 , the temperature-dependent spectral TlNi2Se2 and BaFe2As2. The inset shows the model ratio of the low change are very different. The SW ratio exceeds 1 before it temperature integrated SW over that of the model optical conductiv- recovers to unity suggesting that the SW is transferred from ity at 10 K. 4

TABLE I: The fitting parameters of two Drude components for TlNi2Se2 at different temperatures. ωp1 and ωp2 are the plasma frequencies of the narrow Drude term and the broad Drude term, respectively, ΓD1 and ΓD2 are the scattering rages of the narrow Drude term and the broad Drude term, respectively. S 5 is the mode strength of Lorentz 5 oscillator. The parameters of the model optical conductivity as discussed in the context is also given. The shown error bars correspond to an absolute error of 0.5% in reflectivity. The unit of these quantities is cm−1 .

T(K) ω Γ ω Γ S ω2 + ω2 p1 D1 p2 D2 5 q p1 p2 300 18500 390 31300 2600 0 36360 200 18500 310 29400 2200 9500 34740 100 18500 270 27700 1900 12000 33310 10 18500 200 26600 1500 14100 32400 Model 18500 217 30100 1500 0 35300 error bars ±300 ±15 ±400 ±50 ±300 -

This is a typical behavior of gap opening induced SW trans- optical measurement on TlNi2Se2 indicates that the partial gap formation. feature is further enhanced at the lowest temperature. Now we can summarize the main finding of our optical An earlier angle-resolved photoemission spectroscopy data: the overall optical spectra are similar to those observed measurement on KNi2Se2 crystals suggested the quasi-two- in its isostructure BaNi2As2. Corresponding to the weak sup- dimensional nature of the Fermi surface and that the par- pression of R(ω), the real part of the conductivity σ1(ω) shows tial nested Fermi surface might be responsible for the local a suppression roughly below 2000 cm−1 , which leads to a CDW fluctuations22. However, a more recent ARPES mea- peak above this energy. The mid-infrared peak is present at all surements on TlNi2Se2 revealed more complicated and three measurement temperatures below 300 K, and becomes more dimensional Fermi surface shape. Thus, a naive picture for a and more obvious with decreasing temperature, indicating the FS nesting scenario is not applicable here on TlNi2Se2 . Fur- gradual formation of pseudogap. At the same time, irrespec- thermore, a camelback-shaped band near Fermi energy at Z tive of the uncertainly, the overall plasma frequency decreases, point was identified, in particular, the existence of four flat implying the partial gap opening on the Fermi surface, which part of the dispersion very close to EF would give rise to gives a further proof of the pseudogap formation. In particu- a pronounced van Hove singularity (VHS)18. On this basis, lar, the SW transformation to higher energy induced by pseu- the CDW instability can be naturally understood in the frame dogap could be clearly observed in the model ratio, where we of ”saddle-point” CDW mechanism, proposed by Rice and 30 use the metallic response at 10 K as a reference. Scott . The four saddle points near Z point in TlNi2Se2 gives As we have mentioned above, for KNi2Se2 or KNi2S2, the a divergent contribution to Lindhard response function χ(q), neutron PDF analysis suggested that the local CDW fluctua- where q is a wave vector connecting two saddle points, lead- tions are present at high temperature but disappear upon fur- ing to a CDW instability. 12,13 ther cooling . However, our optical data of TlNi2Se2 single crystals reveals the progressive formation of pseudogap in the midinfrared range, especially below Tcoh. To understand IV. SUMMARY the origin of pseudogap in TlNi2Se2 crystals, there are also a few other experimental facts which should be taken into ac- We have performed optical spectroscopy study on count. First, to date no evidence for magnetic transition was TlNi Se over a broad frequency range at various tempera- found on such nickel chalcogenides. Second, no static den- 2 2 tures. Both the suppression in R(ω) and the peaklike feature in sity wave, such as CDW or SDW, has been observed. Third, σ (ω) suggest the progressive formation of a pseudogap fea- the anisotropy in TlNi Se is rather small, although the com- 1 2 2 ture in the midinfrared range with decreasing temperatures, pound has a layer structure. It looks like that the pseudo- which might be originated from the dynamic local fluctuation gap in TlNi Se might be originated from local CDW fluc- 2 2 of charge-density-wave (CDW) instability. The CDW insta- tuations, in agreement with earlier neutron measurement on bility in TlNi Se may not be driven by Fermi surface nesting, KNi Se and KNi S 12,13. Moreover, the local CDW fluctu- 2 2 2 2 2 2 but by the saddle points mechanism, due to the exitance of van ation was suggested to be entirely dynamic and/or spatially Hove singularity very close to the Fermi energy. incoherent12,13, in contrast to the coherence CDWs observed in structurally related compounds such as 2H-typed transi- tion metal dichalcogenides29. With such CDW fluctuation, there could be a partial gap-opening in k-space on the Fermi Acknowledgments surface, which could be related to the pseudogap feature in TlNi2Se2 . However, different from KNi2Se2 and KNi2S2 This work is supported by the National Science Founda- where the fluctuated CDW order tends to disappear upon en- tion of China (Grants No. 11120101003, 11327806, and tering the heavy electron state at very low temperature, the 11374261), and by the Ministry of Science and Technology 5 of China (Grant No. 2012CB821403).

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