Systematic construction of tight-binding Hamiltonians for topological insulators and superconductors

Topological insulators are a new class of materials characterized by fully spin-polarized surface states, a linear dispersion, imperviousness to external non-magnetic perturbations, and a helical character arising out of the perpendicular spin-momentum locking. This article answers in a pedagogical way the distinction between a topological and normal insulator, the role of topology in band theory of solids, and the origin of these surface states. Numerical techniques including diagonalization of the TI Hamiltonians are described to quantitatively evaluate the behaviour of topological insulator states. The Hamiltonians based on continuum and tight binding approaches are contrasted. The application of TIs as components of a fast switching environment or channel material for transistors is examined through I-V curves. The potential pitfall of such devices is presented along with techniques that could potentially circumvent the problem. Additionally, it is demonstrated that a strong internal electric field can also induce topological insulator behaviour with wurtzite nitride quantum wells as representative materials.

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Tight-binding model for topological insulators: Analysis of helical surface modes over the whole Brillouin zone

Physical Review B ◽

10.1103/physrevb.84.115413 ◽

2011 ◽

Vol 84 (11) ◽

Cited By ~ 13

Author(s):

Shijun Mao ◽

Ai Yamakage ◽

Yoshio Kuramoto

Keyword(s):

Brillouin Zone ◽

Topological Insulators ◽

Tight Binding ◽

Tight Binding Model ◽

Helical Surface ◽

Binding Model ◽

Surface Modes

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Theoretical studies of single magnetic impurities on the surface of semiconductors and topological insulators

MRS Proceedings ◽

10.1557/opl.2013.1088 ◽

2013 ◽

Vol 1564 ◽

Author(s):

M. R. Mahani ◽

A. Pertsova ◽

C.M. Canali ◽

M. F. Islam ◽

A.H. MacDonald

Keyword(s):

Topological Insulators ◽

Tight Binding ◽

Three Dimensional ◽

Magnetic Coupling ◽

Magnetic Impurities ◽

Theoretical Studies ◽

Acceptor State ◽

Binding Model ◽

Deep Acceptor ◽

Antisite Defects

ABSTRACTWe present results of theoretical studies of transition metal dopants in GaAs, based on microscopic tight-binding model and ab-initio calculations. We focus in particular on how the vicinity of surface affects the properties of the hole-acceptor state, its magnetic anisotropy and its magnetic coupling to the magnetic dopant. In agreement with STM experiments, Mn substitutional dopants on the (110) GaAs surface give rise to a deep acceptor state, whose wavefunction is localized around the Mn center. We discuss a refinement of the theory that introduces explicitly the d-levels for the TM dopant. The explicit inclusion of d-levels is particularly important for addressing recent STM experiments on substitutional Fe in GaAs. In the second part of the paper we discuss an analogous investigation of single dopants in Bi2Se3 three-dimensional topological insulators, focusing in particular on how substitutional impurities positioned on the surface affect the electronic structure in the gap. We present explicit results for BiSe antisite defects and compare with STM experiments.

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Discovery of higher-order topological insulators using the spin Hall conductivity as a topology signature

npj Computational Materials ◽

10.1038/s41524-021-00518-4 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Marcio Costa ◽

Gabriel R. Schleder ◽

Carlos Mera Acosta ◽

Antonio C. M. Padilha ◽

Frank Cerasoli ◽

...

Keyword(s):

Density Functional ◽

Topological Insulators ◽

Tight Binding ◽

Density Functional Theory Calculations ◽

Higher Order ◽

Hall Conductivity ◽

Two Dimensional ◽

Boundary States ◽

Potential Applications ◽

Spin Hall Conductivity

AbstractThe discovery and realization of topological insulators, a phase of matter which hosts metallic boundary states when the d-dimension insulating bulk is confined to (d − 1)-dimensions, led to several potential applications. Recently, it was shown that protected topological states can manifest in (d − 2)-dimensions, such as hinge and corner states for three- and two-dimensional systems, respectively. These nontrivial materials are named higher-order topological insulators (HOTIs). Here we show a connection between spin Hall effect and HOTIs using a combination of ab initio calculations and tight-binding modeling. The model demonstrates how a non-zero bulk midgap spin Hall conductivity (SHC) emerges within the HOTI phase. Following this, we performed high-throughput density functional theory calculations to find unknown HOTIs, using the SHC as a criterion. We calculated the SHC of 693 insulators resulting in seven stable two-dimensional HOTIs. Our work guides novel experimental and theoretical advances towards higher-order topological insulator realization and applications.

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Edge singularity in tight binding approximation

Journal de Physique ◽

10.1051/jphys:019720033011-120108100 ◽

1972 ◽

Vol 33 (11-12) ◽

pp. 1081-1088 ◽

Cited By ~ 2

Author(s):

P. Joyes

Keyword(s):

Tight Binding ◽

Tight Binding Approximation ◽

Edge Singularity

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Understanding surface states of topological insulators

Uspekhi Fizicheskih Nauk ◽

10.3367/ufnr.2017.12.038307 ◽

2017 ◽

Vol 188 (11) ◽

pp. 1226-1237 ◽

Cited By ~ 1

Author(s):

O.A. Pankratov

Keyword(s):

Topological Insulators ◽

Surface States

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Vapour Pressure Isotope Eﬀect on Evaporation from Pure Organic Phases - a PIMD Approach

10.26434/chemrxiv.12003186.v1 ◽

2020 ◽

Author(s):

Luis Vasquez ◽

Agnieszka Dybala-Defratyka

Keyword(s):

Path Integral ◽

Vapour Pressure ◽

Density Functional ◽

Isotope Effects ◽

Tight Binding ◽

Decomposition Analysis ◽

Energy Decomposition Analysis ◽

Special Importance ◽

Non Covalent Interactions ◽

Covalent Interactions

Very often in order to understand physical and chemical processes taking place among several phases fractionation of naturally abundant isotopes is monitored. Its measurement can be accompanied by theoretical determination to provide a more insightful interpretation of observed phenomena. Predictions are challenging due to the complexity of the effects involved in fractionation such as solvent effects and non-covalent interactions governing the behavior of the system which results in the necessity of using large models of those systems. This is sometimes a bottleneck and limits the theoretical description to only a few methods. In this work vapour pressure isotope effects on evaporation from various organic solvents (ethanol, bromobenzene, dibromomethane, and trichloromethane) in the pure phase are estimated by combining force field or self-consistent charge density-functional tight-binding (SCC-DFTB) atomistic simulations with path integral principle. Furthermore, the recently developed Suzuki-Chin path integral is tested. In general, isotope effects are predicted qualitatively for most of the cases, however, the distinction between position-specific isotope effects observed for ethanol was only reproduced by SCC-DFTB, which indicates the importance of using non-harmonic bond approximations. Energy decomposition analysis performed using the symmetry-adapted perturbation theory (SAPT) revealed sometimes quite substantial differences in interaction energy depending on whether the studied system was treated classically or quantum mechanically. Those observed differences might be the source of different magnitudes of isotope effects predicted using these two different levels of theory which is of special importance for the systems governed by non-covalent interactions.

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