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Article overview
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Computation of topological invariants of disordered materials using the kernel polynomial method | | Daniel Varjas
; Michel Fruchart
; Anton R. Akhmerov
; Pablo Perez-Piskunow
; | | Date: |
6 May 2019 | | Abstract: | We present an algorithm to determine topological invariants of inhomogeneous
systems, such as alloys, disordered crystals, or amorphous systems. Our
algorithm allows for efficient analysis of three-dimensional samples with more
than $10^7$ degrees of freedom, two orders of magnitude above the previous
best. This performance gain is due to a localized approximation of the band
projector based on the kernel polynomial method combined with the stochastic
trace approximation. Our method makes it possible to study large samples and
complex compounds, where disorder plays a central role, and provides a better
resolution of disorder-driven phase transitions. As a case study we apply this
approach to Pb$_{1-x}$Sn$_{x}$Te and related alloys, and obtain the topological
phase diagram of this family of three-dimensional mirror Chern insulators. | | Source: | arXiv, 1905.2215 | | Services: | Forum | Review | PDF | Favorites | |
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