Tunable Electronic Structure and Topological Properties of $LnPn$ ($Ln$=Ce, Pr, Gd, Sm, Yb; $Pn$=Sb, Bi)

Abstract

Recently, the rare-earth monopnictide compounds LnPn have attracted considerable attention in condensed matter physics studies due to their possible topological properties. We have performed systematic first principles study of the electronic structure and band topology properties of LnPn (Ln=Ce, Pr, Sm, Gd, Yb; Pn=Sb, Bi). Assuming the f -electrons are well localized in these materials, both hybrid functional and modified Becke-Johnson calculations yield electronic structure in good agreement with experimental observations, while generalized gradient approximation calculations severely overestimate the band inversions. From Ce to Yb, a systematic reduction of band inversion with respect to the increasing Ln atomic number is observed, and Z 2 for CePn and YbPn are [1;000] and [0;000], respectively. In both hybrid functional and modified Becke-Johns calculations, a topologically nontrivial to trivial transition is expected around SmSb for the antimonides and around DyBi for the bismuthides. Such variation is related with lanthanide contraction, but is different from simple pressure effects.

Quantum transport in a compensated semimetal W2As3 with nontrivial Z2 indices

“…The product of parities at all these TRIMs up to the 27th band is -1, suggesting a strong topological property of this compound. In addition, we also performed the PBE calculations and obtained the same topological properties as the mBJ calculations, in contrast to the divergence between the PBE and mBJ calculations in LnPn (Ln = Ce, Pr, Gd, Sm, Yb; Pn = Sb, Bi) [42] and LaSb [43], in which the PBE calculations underestimate the band gap between conduction band and valance band. Compared with the bulk band structure along X 1 − Y in Fig.…”

Tunable electronic structure and surface states in rare-earth monobismuthides with partially filled f shell

“…Note that the observed SSs are not real TSSs, since they are apparently gapped and connect to valence band or conduction band separately, different from intrinsic TSSs that form a continuous connection between valence and conduction bands. Nevertheless, these SSs are thought to be intimately linked to nontrivial band inversion near the X point, as no SS could be seen in the calculations of heavy REBi where no band inversion occurs [46]. A possible explanation is that a direct projection of two symmetryinequivalent X points give rise to two sets of originally gapless TSSs, which then interact and open up a gap, rendering two sets of trivial gapped SSs.…”

“…Although the definition of Z2-topological invariant was intended for topological insulator with an absolute band gap, such concept can be extended to semi-metallic REBi, where a momentum-dependent partial band gap exists, separating the valence and conduction bands [12]. Detailed numerical calculations predict that REBi (with RE ranging from Ce to Gd) could possess nontrivial Z2 index and hence TSSs [46]. Since there are three X points in this calculation, the Z2 index is dependent on the product of the parity of all occupied bands at X: if there is band inversion along the ГX direction, the Z2-topological invariant is nontrivial; otherwise, the system will be topologically trivial.…”

“…Interestingly, both experiments and calculations indicate that GdBi possesses a very small inverted gap and highly linear bulk bands, suggesting a possible topologically nontrivial-trivial phase transition when replacing Gd with a slightly heavier RE element. Specifically, DFT calculations have predicted that no bulk band inversion occurs for REBi with RE heavier than Dy [46], resulting in a topologically trivial phase. The large tunability of both bulk bands and SSs in REBi is quite different to the case of RESb, where the change of the electronic structure with RE replacement is much less pronounced [31].…”

Heavy fermions in high magnetic fields

“…On the other hand, other RSb compounds such as PrSb show evidence for a trivial Berry phase from the Landau index analysis, [104] suggesting that substituting for different rare earth elements can tune the band topology. [105,106] Another important probe for looking for Weyl fermions is from the presence of the chiral anomaly, which can be inferred from a negative longitudinal magnetoresistance. Weyl semimetals host Weyl points with different chiralities, and the chiral anomaly arises due to the parallel magnetic and electric fields pumping charges from one Weyl point to another of opposite chirality, which in turn leads to a population imbalance.…”