scholarly journals A Unified View of Topological Phase Transition in Band Theory

Research ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Huaqing Huang ◽  
Feng Liu
Keyword(s):  
Intermediate Phase ◽  
Tight Binding ◽  
Structural Disorder ◽  
Crystalline Solid ◽  
Linear Scaling ◽  
Topological Order ◽  
Topological Phase ◽  
Binding Model ◽  
Band Theory ◽  
Unified View

We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Reevaluating the band evolution from an “atomic crystal” (a normal insulator (NI)) to a solid crystal, such as a semiconductor, we demonstrate that there exists ubiquitously an intermediate phase of topological insulator (TI), whose critical transition point displays a linear scaling between electron hopping potential and average bond length, underlined by deformation-potential theory. The validity of the scaling relation is verified in various two-dimensional (2D) lattices regardless of lattice symmetry, periodicity, and form of electron hoppings, based on a generic tight-binding model. Significantly, this linear scaling is shown to set an upper bound for the degree of structural disorder to destroy the topological order in a crystalline solid, as exemplified by formation of vacancies and thermal disorder. Our work formulates a simple framework for understanding the physical nature of TPTs with significant implications in practical applications of topological materials.

scholarly journals Robust topological phase in proximitized core–shell nanowires coupled to multiple superconductors

2018 ◽  
Vol 9 ◽  
pp. 1512-1526 ◽  
Author(s):  
Tudor D Stanescu ◽  
Anna Sitek ◽  
Andrei Manolescu
Keyword(s):  
Magnetic Field ◽  
Longitudinal Magnetic Field ◽  
Tight Binding ◽  
Core Shell ◽  
Topological Phase ◽  
Binding Model ◽  
Chemical Potentials ◽  
Topological Quantum ◽  
The Stability ◽  
Shell Nanowires

We consider core–shell nanowires with prismatic geometry contacted with two or more superconductors in the presence of a magnetic field applied parallel to the wire. In this geometry, the lowest energy states are localized on the outer edges of the shell, which strongly inhibits the orbital effects of the longitudinal magnetic field that are detrimental to Majorana physics. Using a tight-binding model of coupled parallel chains, we calculate the topological phase diagram of the hybrid system in the presence of non-vanishing transverse potentials and finite relative phases between the parent superconductors. We show that having finite relative phases strongly enhances the stability of the induced topological superconductivity over a significant range of chemical potentials and reduces the value of the critical field associated with the topological quantum phase transition.

scholarly journals External tuning of topological phase transitions induced by interaction driven mass renormalization

2021 ◽  
Author(s):  
Thies Jansen ◽  
Alexander Brinkman
Keyword(s):  
Phase Transition ◽  
Mean Field Theory ◽  
Tight Binding ◽  
Mean Field ◽  
Topological Phase ◽  
Binding Model ◽  
System A ◽  
Topological Phase Transition ◽  
Topological Phases Of Matter ◽  
Electron Interactions

Abstract Electron-electron interactions can be useful for realizing new nontrivial topological phases of matter. Here, we show by means of a tight-binding model and mean field theory how electron-electron interactions can lead to a topological phase transition. By externally adding or removing electrons from the system a band inversion between two bands with dierent parity is induced. This leads to a topological nontrivial phase if spin-orbit coupling is present. Besides the toy-model illustrating this mechanism, we also propose SmB6 as a possible playground for experimentally realizing a topological phase transition by external tuning.

Structural Disorder and Localized Gap States in Silicon Grain Boundaries from a Tight-Binding Model

1997 ◽  
Vol 491 ◽  
Author(s):  
F. Cleri ◽  
P. Keblinski ◽  
L. Colombo ◽  
S. R. Phillpot ◽  
D. Wolf
Keyword(s):  
Molecular Dynamics ◽  
Grain Boundaries ◽  
Tight Binding ◽  
Structural Disorder ◽  
High Energy ◽  
Tight Binding Model ◽  
Binding Model ◽  
Dynamics Simulations ◽  
Gap States ◽  
Forbidden Gap

ABSTRACTTight-binding molecular dynamics simulations of typical high-energy grain boundaries in silicon show that the atomic structure of the interface in thermodynamic equilibrium is similar to that of bulk amorphous silicon and contains coordination defects. The corresponding electronic structure is also amorphous-like, displaying extra states in the forbidden gap mainly localized around the coordination defects, where large changes in the bond-hybridization character are observed. It is proposed that such coordination defects in disordered high-energy grain boundaries are responsible for the experimentally observed gap states in polycrystalline Si.

scholarly journals Tight-binding model investigation of the biaxial strain induced topological phase transition in GeCH3

2017 ◽  
Vol 96 (8) ◽  
Author(s):  
Mohsen Rezaei ◽  
Esmaeil Taghizadeh Sisakht ◽  
Farhad Fazileh ◽  
Zahra Aslani ◽  
F. M. Peeters
Keyword(s):  
Phase Transition ◽  
Tight Binding ◽  
Model Investigation ◽  
Topological Phase ◽  
Tight Binding Model ◽  
Biaxial Strain ◽  
Binding Model ◽  
Topological Phase Transition

The band theory of solids

2018 ◽  
Author(s):  
L. Solymar ◽  
D. Walsh ◽  
R. R. A. Syms
Keyword(s):  
Band Structure ◽  
Bragg Reflection ◽  
Tight Binding ◽  
Binding Model ◽  
Band Theory ◽  
Potential Wells ◽  
Coupled Equations ◽  
Model Based ◽  
Dirac Function ◽  
The Difference

The solution of Schrodinger’s equation is discussed for a model in which atoms are represented by potential wells, from which the band structure follows. Three further models are discussed, the Ziman model (which is based on the effect of Bragg reflection upon the wave functions), and the Feynman model (based on coupled equations), and the tight binding model (based on a more realistic solution of the Schrödinger equation). The concept of effective mass is introduced, followed by the effective number of electrons. The difference between metals and insulators based on their band structure is discussed. The concept of holes is introduced. The band structure of divalent metals is explained. For finite temperatures the Fermi–Dirac function is combined with band theory whence the distinction between insulators and semiconductors is derived.

scholarly journals Cobalt-based magnetic Weyl semimetals with high-thermodynamic stabilities

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Wei Luo ◽  
Yuma Nakamura ◽  
Jinseon Park ◽  
Mina Yoon
Keyword(s):  
Tight Binding ◽  
Three Dimensional ◽  
Interlayer Coupling ◽  
First Principles Calculation ◽  
Optimization Approach ◽  
Binding Model ◽  
Nodal Lines ◽  
Weyl Semimetal ◽  
Topological Quantum ◽  
First Time

AbstractRecent experiments identified Co3Sn2S2 as the first magnetic Weyl semimetal (MWSM). Using first-principles calculation with a global optimization approach, we explore the structural stabilities and topological electronic properties of cobalt (Co)-based shandite and alloys, Co3MM’X2 (M/M’ = Ge, Sn, Pb, X = S, Se, Te), and identify stable structures with different Weyl phases. Using a tight-binding model, for the first time, we reveal that the physical origin of the nodal lines of a Co-based shandite structure is the interlayer coupling between Co atoms in different Kagome layers, while the number of Weyl points and their types are mainly governed by the interaction between Co and the metal atoms, Sn, Ge, and Pb. The Co3SnPbS2 alloy exhibits two distinguished topological phases, depending on the relative positions of the Sn and Pb atoms: a three-dimensional quantum anomalous Hall metal, and a MWSM phase with anomalous Hall conductivity (~1290 Ω−1 cm−1) that is larger than that of Co2Sn2S2. Our work reveals the physical mechanism of the origination of Weyl fermions in Co-based shandite structures and proposes topological quantum states with high thermal stability.

scholarly journals Single-crystalline epitaxial TiO film: A metal and superconductor, similar to Ti metal

2021 ◽  
Vol 7 (2) ◽  
pp. eabd4248
Author(s):  
Fengmiao Li ◽  
Yuting Zou ◽  
Myung-Geun Han ◽  
Kateryna Foyevtsova ◽  
Hyungki Shin ◽  
...  
Keyword(s):  
Transition Metal ◽  
Density Functional ◽  
Tight Binding ◽  
Crystal Form ◽  
Titanium Monoxide ◽  
Binding Model ◽  
Functional Theory ◽  
Single Crystalline ◽  
First Time ◽  
Lattice Matched

Titanium monoxide (TiO), an important member of the rock salt 3d transition-metal monoxides, has not been studied in the stoichiometric single-crystal form. It has been challenging to prepare stoichiometric TiO due to the highly reactive Ti2+. We adapt a closely lattice-matched MgO(001) substrate and report the successful growth of single-crystalline TiO(001) film using molecular beam epitaxy. This enables a first-time study of stoichiometric TiO thin films, showing that TiO is metal but in proximity to Mott insulating state. We observe a transition to the superconducting phase below 0.5 K close to that of Ti metal. Density functional theory (DFT) and a DFT-based tight-binding model demonstrate the extreme importance of direct Ti–Ti bonding in TiO, suggesting that similar superconductivity exists in TiO and Ti metal. Our work introduces the new concept that TiO behaves more similar to its metal counterpart, distinguishing it from other 3d transition-metal monoxides.

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