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What is band inversion and how to recognize it in band structure?

Topological materials form a broad family including insulators, semimetals, and superconductors, of which perhaps the best known are topological insulators. For concreteness, I will focus on ...
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11 votes

Magnetism and Topology

Not a very thorough answer, but it should get the ball rolling. Spontaneous magnetization or extrinsically magnetic TIs have been achieved through defect engineering in non-magnetic Topological ...
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11 votes

What is the difference between Ultrasoft, ONCV and PAW Pseudopotentials? Which is better for a spin-orbit coupled calculation?

Pseudopotentials (PPs) describe the effective interaction between the valence electrons and a nuclei screened by frozen core electrons. This approximation makes DFT calculations less computationally ...
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10 votes
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Topological order in Weyl Semimetal

A Weyl point is a crossing of two bands. A two-band crossing can be described using the general Hamiltonian: $$ \hat{H}(\mathbf{k})=d_0(\mathbf{k})+d_1(\mathbf{k})\sigma_1+d_2(\mathbf{k})\sigma_2+d_3(\...
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How to model Topological Insulators from first-principles?

There is a whole zoo of topological phases, and hopefully someone will provide a more complete answer, but here are some thoughts. Symmetry and dimension. The topological classification of a material ...
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10 votes

Magnetism and Topology

Magnetic order and topological order can exist simultaneously. In fact, what one may call the very first proposal of an instrinsic topological material was Haldane's model from 1988, which is an ...
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9 votes

What exactly is a topological insulator and how to recognize one from band structure?

The bulk band structure of a topological insulator would look just like any other insulator, with the Fermi level in the gap between the valence and conduction bands. If your band structure includes ...
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Can the fermi level of a semiconductor be below the valence band?

There are two different questions in your post: The band structure that you are reproducing is not that of a semiconductor. There are bands crossing the Fermi level, so the material is metallic. ...
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7 votes

Magnetism and Topology

Topological magnon band structures Another way of combining topology and magnetism is to consider a magnetic insulator with non-trivial magnon band structure. This setting is somewhat different from ...
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Help with Definitions in Numerical Calculation of Multiband Berry Phase

Question 1. eq. 3.102 defines a matrix in "band-space", e.g. it's NxN where N = number of bands being considered. The right hand side is a regular vector inner product for fixed m,n. The ...
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About the surface Greens function method for calculating the surface state

The surface Green's function method is described in detail here, but here is a summary. Principal Layers: Block Tridiagonal Form We consider a semi-infinite system (a surface with an infinite bulk ...
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6 votes

About the surface Greens function method for calculating the surface state

You can see the open-source package WannierTools: https://github.com/quanshengwu/wannier_tools A brief description: We present an open-source software package WannierTools, a software for the ...
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How to model Topological Insulators from first-principles?

As a first step, you can use the WannierTools. There are five typical examples in there. Bi2Se3 (3D strong TI) MoS2 (2D QSHE) WTe2 (Type II Weyl semimetal) IrF4 (Nodal Chain metals) FeSi (Weyl point ...
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How to model Topological Insulators from first-principles?

Finding topological invariant number(called Z$_2$ number) can give information about topological invariance. Different codes are available for such calculations such as Z2pack or wanniertools and ...
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What are good resources to study crystallographic defects in different dimensional systems and their topological dimensionality?

Arkadiy Simonov and Andrew Goodwin have a nice review out on the arXiv regarding designing disorder into materials, that can elicit unique topological states [1], and there is are some older reviews ...
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Help with understanding topologically-protected edge states in domain wall systems

I think my understanding on this problem has improved somewhat. Let me try to clarify my confusions. If anyone sees issues with this reasoning, please let me know. The idea of phases in this context ...
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How to calculate the parity of a band at a particular point in Brillouin zone

Consider the energy eigenstate $|\psi_{n\mathbf{k}}\rangle$, where $n$ is the band you are interested in and $\mathbf{k}$ is wave vector of the TRIM point. Then, if the system has inversion symmetry, ...
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4 votes

What is the difference between Ultrasoft, ONCV and PAW Pseudopotentials? Which is better for a spin-orbit coupled calculation?

Spin-orbit coupling is an effect that is dependent on the relativistic effect. So you should use fully relativistic PP(pseudopotentials) whatever you use. Another thing is that PP often varies from ...
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4 votes

Edge states in Topological Semimetals

Topological semimetals do have interesting edge states. Here I give two examples: Weyl semimetals. The edge states are called "Fermi arcs", which are constant-energy states that connect the ...
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