Formation Mechanism of Hybridization Gap in Kondo Insulators based on a Realistic Band Model and Application to YbB₁₂

Abstract

A new LDA+U band calculation is performed on the Kondo insulator material YbB 12 and an energy gap of about 0.001Ryd is obtained. Based on this, a simple tight-binding model with 5dε and 4f Γ 8 orbitals on Yb atoms and the nearest neighbor σ-bonds between them is constructed with a good agreement to the above the LDA+U calculation near the gap. The density of states is also calculated and the shape is found to be very asymmetric with respect to the gap. A formation mechanism of the gap is clarified for the first time in a realistic situation with the orbital degeneracies in both conduction bands and the f states. This model can be a useful starting point for incorporating the strong correlation effect, and for understanding all the thermal, thermoelectric, transport and magnetic properties of YbB 12 .KEYWORDS: hybridization gap, Kondo insulator, mixing, tight-binding model, LDA+U §1. Introduction Among the rare-earth compounds which include the strongly correlated f electrons, SmB 6 , 1) YbB 12 , 2) Ce 3 Bi 4 Pt 3 , 3) CeRhSb, 4) CeFe 4 P 12 , 5) CeNiSn, 6) TmSe 7) etc. exhibit insulating behavior at low temperatures whereas the Kondo-like behaviors (the enhanced electric specific heat and the enhanced paramagnetic susceptibility, etc.) are often observed at higher temperatures. These materials are called Kondo insulators, Kondo semiconductors or heavy fermion semiconductors. 8)Recent studies on CeNiSn uncovered that this material is a semimetal with a pseudogap. 9) TmSe orders antiferromagnetically below T N =5K, so that the insulating behavior seems to be due to the gap caused by this order. Sm has a complicated f shell with five to six f electrons (although the ground state of f 6 has vanishing total angular momentum, so that the treatment of Sm ions might not be so difficult than expected 10) ). We exclude these three materials from the following discussions. 1The Kondo effect usually occurs in metals, so that the existence of an energy gap at the Fermi energy in insulators may seem contradictory to the occurence of the Kondo effect in these materials.However, it is already clarified that the Kondo effect can occur if the Kondo temperature T K exceeds the gap size E g . 11) Even in the compounds with the periodic array of rare-earth ions, the effect of the strong correlation is mainly to renormalize the gap size if the band calculation does yield an energy gap. 12) Thus, we can understand that the Kondo insulator is a band insulator with a strong correlation. 13,14) In fact, all the known Kondo insulators have even number of electrons which fill the bands below the gap. (TmSe has odd number of electrons, so that it may not be classified into the Kondo insulators also in the present sense.) In this context, the concept of the Kondo insulator may be extended beyond the rare-earth compounds. FeSi 15) is considered to be such an example among the transition metal compounds with 3d electrons 16) although the correlation may not be so strong as in rare-earth compounds.Recently, some of the Kondo insulator compound...

Optical Conductivity of Ce-based Filled Skutterudites

“…This scheme was performed in ref. 16 for YbB 12 and we follow the same procedure here. The resulting f bands, which will be shown in the next section, are rather similar to those above the Fermi level obtained by the LDA band calculation.…”

Pressure-Driven Topological Phase Transition in the Yb Chalcogenides YbO and YbS

“…20 Very recently, Weng et al have predicted that the simple cubic YbB 6 is a candidate topological insulator, while YbB 12 with a rock-salt structure is a potential candidate topological crystalline insulator with a nontrivial mirror Chern number protected by mirror symmetry. 21,22 Angle-resolved photoemission spectroscopy (ARPES) also suggested YbB 6 as a candidate TKI. 23 In fact, there are hundreds of rare-earth compounds RX with a rock-salt structure, with R referring to the rare-earth Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu, and X standing for the pnictide atoms N, P, As, Sb, Bi and the chalcogenide atoms O, S, Se, Te, Po.…”

Comparison of Semimetallic Ce-Skutterudites and the Kondo Insulator YbB12–Field-Induced Insulator-to-Metal and Metal-to-Insulator Transitions

“…4 The indirect gap is about 0.007 Ry (∼ 1100 K) between X and L points and the direct gap is 0.02 Ry (∼ 0.25 eV). The former is about six times larger than the best estimated value of the indirect gap in the optical experiment, E g =174 K. However, in the present realistic band model, we use the larger value mentioned above simply because of the technical reason in numerical calculation.…”

“…Based on the LDA+U band calculation, we previously constructed a tight-binding band composed of the 5d and 4f Γ 8 orbitals both on Yb atoms, where B 12 orbitals were eliminated. 4 Some of the dconduction bands are doubly degenerate (four-fold if spin degeneracy is included). A gap opens by the hybridization with the four-fold degenerate Γ 8 states with the dconduction bands with degeneracy.…”

“…It was pointed out that the gap can not open if the crystal-field groud state of 4f were Γ 7 doublet. Therefore, proper consideration of the degeneracy is a key to understanding the opening 4 and closing of a gap in the Kondo insulators.…”