An implementation of spin-orbit coupling for band structure calculations with Gaussian basis sets: Two-dimensional topological crystals of Sb and Bi

We present an implementation of spin-orbit coupling (SOC) for density functional theory band structure calculations that makes use of Gaussian basis sets. It is based on the explicit evaluation of SOC matrix elements, both the radial and angular parts. For all-electron basis sets, where the full nod...

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Bibliographic Details
Published in:Beilstein journal of nanotechnology 2018-03, Vol.9 (1), p.1015-1023
Main Authors: Pakdel, Sahar, Pourfath, Mahdi, Palacios, J J
Format: Article
Language:English
Subjects:
antimonene
Antimony
Band structure
Band structure of solids
Bismuth
Codes
Coupling
Density functional theory
electronic structure
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Mathematical analysis
Multilayers
Nanoscience
Nanotechnology
Nuclear capture
Nuclear potential
Parameter estimation
Quantum theory
Relativism
Relativistic effects
Sb few-layers
spin–orbit coupling (SOC)
topological material
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Summary:We present an implementation of spin-orbit coupling (SOC) for density functional theory band structure calculations that makes use of Gaussian basis sets. It is based on the explicit evaluation of SOC matrix elements, both the radial and angular parts. For all-electron basis sets, where the full nodal structure is present in the basis elements, the results are in good agreement with well-established implementations such as VASP. For more practical pseudopotential basis sets, which lack nodal structure, an ad-hoc increase of the effective nuclear potential helps to capture all relevant band structure variations induced by SOC. In this work, the non-relativistic or scalar-relativistic Kohn-Sham Hamiltonian is obtained from the CRYSTAL code and the SOC term is added a posteriori. As an example, we apply this method to the Bi(111) monolayer, a paradigmatic 2D topological insulator, and to mono- and multilayer Sb(111) (also known as antimonene), the former being a trivial semiconductor and the latter a topological semimetal featuring topologically protected surface states.
ISSN:2190-4286
2190-4286
DOI:10.3762/bjnano.9.94