Two-scale theory of edge state

The edge state is considered in the spectrum region where its branch splits from the bottom of a continuous conduction band. It is shown that in this region the electron wave function demonstrates two different scale behaviours: slow and fast, that enabled us to construct some simplified procedure for the analysis of the edge state. The slow wave function part obeys a simple Schrödinger equation the parameters of which are insensitive to the peculiarities of the electron dynamics, while the fast part that describes the details of electron behaviour in the primitive cell reveals itself only at the edge. The equation for this fast part was transformed into the boundary condition for the slow part equation. The proposed method is illustrated considering the simplest continuous model for a topological insulator and a tight binding model for graphene.

Download Full-text

Edge states, band structure, and the Hall effect in two-dimensional lattice structures: quantum dot arrays and the tight-binding model

Canadian Journal of Physics ◽

10.1139/p95-022 ◽

1995 ◽

Vol 73 (3-4) ◽

pp. 147-162 ◽

Cited By ~ 5

Author(s):

R. Akis ◽

C. Barnes ◽

G. Kirczenow

Keyword(s):

Quantum Dots ◽

Tight Binding ◽

Transmission Probability ◽

Edge State ◽

Matrix Formalism ◽

Two Dimensional ◽

Tight Binding Model ◽

Edge States ◽

Binding Model ◽

Hall Conductance

Using a model that is based on a transfer matrix formalism, we study the electronic structure and transport in two dimensional periodic arrays of quantum dots in magnetic fields. The quantum dots in our model are connected to each other via ballistic constrictions. The spectrum for this system has much in common with that with the tight-binding model. In particular, q bulk bands arise if the normalized magnetic flux per unit cell is p/q, where p and q are coprime integers. Working within an edge-state picture, we investigate if these similarities translate to a correspondence in the transport properties of the two systems. As we shall show, the answer to this question depends very much on the transmission probability of the constrictions. Our analysis also shows that, under certain circumstances, the Hall conductance within the context of the tight-binding model may take on fractional values.

Download Full-text

Tight-binding model in optical waveguides: Design principle and transferability for simulation of complex photonics networks

Physical Review A ◽

10.1103/physreva.104.023501 ◽

2021 ◽

Vol 104 (2) ◽

Author(s):

Yang Chen ◽

Xiaoman Chen ◽

Xifeng Ren ◽

Ming Gong ◽

Guang-can Guo

Keyword(s):

Optical Waveguides ◽

Design Principle ◽

Tight Binding ◽

Tight Binding Model ◽

Binding Model

Download Full-text

Cobalt-based magnetic Weyl semimetals with high-thermodynamic stabilities

npj Computational Materials ◽

10.1038/s41524-020-00461-w ◽

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.

Download Full-text

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

Science Advances ◽

10.1126/sciadv.abd4248 ◽

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.

Download Full-text

Intrinsic asymmetries in spin-valves: a tight binding model study

Journal of Magnetism and Magnetic Materials ◽

10.1016/j.jmmm.2003.08.027 ◽

2004 ◽

Vol 270 (3) ◽

pp. 298-304 ◽

Cited By ~ 1

Author(s):

Jisang Hong ◽

R.Q Wu ◽

R.B Muniz

Keyword(s):

Tight Binding ◽

Spin Valves ◽

Tight Binding Model ◽

Binding Model ◽

Model Study

Download Full-text

Enabling Large-Scale Simulations of Quantum Transport with Manycore Computing

Electronics ◽

10.3390/electronics10030253 ◽

2021 ◽

Vol 10 (3) ◽

pp. 253

Author(s):

Yosang Jeong ◽

Hoon Ryu

Keyword(s):

Quantum Transport ◽

Large Scale ◽

Performance Enhancement ◽

Silicon Nanowire ◽

Matrix Multiplication ◽

Tight Binding ◽

Optimization Techniques ◽

Wide Energy Range ◽

Processing Unit ◽

Binding Model

The non-equilibrium Green’s function (NEGF) is being utilized in the field of nanoscience to predict transport behaviors of electronic devices. This work explores how much performance improvement can be driven for quantum transport simulations with the aid of manycore computing, where the core numerical operation involves a recursive process of matrix multiplication. Major techniques adopted for performance enhancement are data restructuring, matrix tiling, thread scheduling, and offload computing, and we present technical details on how they are applied to optimize the performance of simulations in computing hardware, including Intel Xeon Phi Knights Landing (KNL) systems and NVIDIA general purpose graphic processing unit (GPU) devices. With a target structure of a silicon nanowire that consists of 100,000 atoms and is described with an atomistic tight-binding model, the effects of optimization techniques on the performance of simulations are rigorously tested in a KNL node equipped with two Quadro GV100 GPU devices, and we observe that computation is accelerated by a factor of up to ∼20 against the unoptimized case. The feasibility of handling large-scale workloads in a huge computing environment is also examined with nanowire simulations in a wide energy range, where good scalability is procured up to 2048 KNL nodes.

Download Full-text