Tuning valley degeneracy with band inversion

Michael Y. Toriyama,Lídia C. Gomes,Ferdaushi A. Bipasha,Elif Ertekin,G. Jeffrey Snyder,Badih A. Assaf,Madison K. Brod

doi:10.1039/d1ta08379a

Abstract

Valley degeneracy in materials with inverted bands can be increased by strengthening the band inversion. One method to tune the band inversion is by controlling the chemical interactions between cation and anion atomic orbitals.

Highlights

We show that mere band inversion is an aDepartment of Materials Science and Engineering, Northwestern University, Evanston, IL 60208. bDepartment of Mechanical Science and Engineering, University of Illinois at UrbanaChampaign, Urbana, IL 61801. cDepartment of Physics, University of Notre Dame, Notre Dame, IN 46556. ∗E-mail: MichaelToriyama2024@u.northwestern.edu, jeff.snyder@northwestern.edu insufficient condition to obtain a valley degeneracy higher than NV = 4 in rock-salt IV-VI compounds, and that the degree to which the bands are inverted instead determines whether NV > 4 can be achieved
Our analysis of the electronic structures of rock-salt IV-VI compounds shows that the mere existence of inverted bands is an insufficient condition for high valley degeneracy near the band edges
Our model predicts that a 6× increase in the valley degeneracy, from NV = 4 to Nv = 24, can be achieved in rock-salt IV-VI compounds with inverted bands by tuning nearest-neighbor chemical interactions

Summary

Introduction

7 Improving zT by increasing the valley degeneracy has been a focus of many studies; for example, converging the valence bands of PbTe at the L-point (NV = 4) and along the Σ-line (NV = 12) has been shown to improve the thermoelectric performance of p-type PbTe. 8–13. Nontrivial electronic structure topologies have attracted interest as a strategy for increasing the valley degeneracy in materials such as rock-salt SnSe, 14,15 PbTe-SnTe-GeTe alloys, 16 and Bi2Te3. It is curious that band inversion leads to high valley degeneracy in some materials while it does not in others; for example, Bi2Te3 has inverted bands and exhibits high valley degeneracy (NV = 6), 20 whereas the chemically similar Bi2Se3 has inverted bands but exhibits a single carrier pocket at the Γ-point (NV = 1).

Electronic Structure Topologies of RockSalt IV-VI Compounds

When Does Band Inversion Lead to High Valley Degeneracy?

Chemical Origins of Band Inversion

Conclusion

Methods