30 votes
Accepted

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 ...
ProfM's user avatar
  • 11k
16 votes
Accepted

Berry's curvature and magnetic moment in TMDCs

The Berry curvature is defined as: $$ \Omega_{\mu\nu}(\mathbf{k})=\partial_{\mu}A_{\nu}(\mathbf{k})-\partial_{\nu}A_{\mu}(\mathbf{k}), \tag{1} $$ where $A_{\mu}(\mathbf{k})=\langle u_{\mathbf{k}}|i\...
ProfM's user avatar
  • 11k
12 votes

Berry's curvature and magnetic moment in TMDCs

Resolution for the time reversal symmetry: I need to demonstrate: $\Omega(-\mathbf{k})=-\Omega(\mathbf{k})$ (Berry's curvature is a odd function under time reversal symmetry) Berry's curvature: $$\...
Carmen González's user avatar
10 votes
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Anomalous Quantum Hall Effect

What is the quantum anomalous Hall effect? Figure from C-X. Liu, S-C. Zhang, and X-L. Qi. "The Quantum Anomalous Hall Effect: Theory and Experiment," Annual Review of Condensed Matter ...
Anyon's user avatar
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9 votes
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Dynamic phase in an adiabatic system

The exponential comes from solving a linear differential equation: \begin{align} \frac{\textrm{d}|\psi(t)\rangle}{\textrm{d}t} &= -\frac{\textrm{i}}{\hbar}H|\psi(t)\rangle\tag{1}\\ |\psi(t)\rangle ...
Nike Dattani - No Free Time's user avatar
7 votes
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Property related with Berry curvature: $\Omega_{n,\mu\nu}=-\Omega_{n,\nu\mu}$

You can just exchange the $\mu,\nu$ indices to verify the antisymmetry: $$ \Omega_{n,\mu\nu}(\mathbf{k})=\partial_{\mu}A_{n\nu}(\mathbf{k})-\partial_{\nu}A_{n\mu}(\mathbf{k})\\ \Rightarrow \Omega_{n,\...
Anyon's user avatar
  • 4,741
7 votes

Dynamic phase in an adiabatic system

Here are some basic comments: I don't think you should call Eq(1) as the Schrödinger equation. It's just defining the energy eigen states/values, or in other words, establishing the relation of those ...
Jun_Gitef17's user avatar
7 votes
Accepted

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 ...
Slenderman's user avatar
6 votes
Accepted

Create an image from scratch with the vectors that represent the Berry phase for parallel transport (classic system)

The figure you are showing can be made in Adobe Illustrator or Gimp I've recreated a crude rendition (very quickly) using adobe illustrator The steps to get this far are: create a sphere cut the ...
Cody Aldaz's user avatar
  • 8,017
5 votes

Berry Curvature with VASP+WANNIER90

Yes, one can do the similar calculations with VASP. TL;DR. Check out my example 🔗here. There are two steps involved here, one is obtaining well localized Wannier functions and the other is using ...
Chengcheng Xiao's user avatar
5 votes

How can I prove that a material is ferroelectric using DFT?

As a good starting, you may take a look at this classical paper and its supplementary material: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.097601 Here I just show some general steps:...
Jack's user avatar
  • 15.1k
5 votes

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 ...
5 votes

polarization jump in berry phase method using VASP

This is quite a peculiar scenario and I think more information is needed in order to find the root casue of it. With the information at hand, I think this might be caused by different k-samplings used ...
Chengcheng Xiao's user avatar
4 votes
Accepted

How to transform the two-dimensional Berry curvature integral into a loop integral along Fermi circle?

If the distribution function has a step discontinuity at the Fermi surface, its derivatives are Dirac delta functions which reduce the integral to one over the Fermi surface. I will illustrate this ...
Anyon's user avatar
  • 4,741
4 votes
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Example of a standard/archetypal/simple 4-band un-gapped condensed matter model with analytic results?

The Bernevig-Hughes-Zhang (BHZ) model for topological insulators comes to mind, see e.g. this pedagogical introduction or the review by Qi and Zhang (arXiv link here). It's often justified to set the ...
Anyon's user avatar
  • 4,741
4 votes

How to choose half-Brillouin-zone (HBZ) in Fukui & Hatsugai's numerical scheme for the Z2 invariant?

I think I figured this out. For most practical purposes, I think it is fine to just choose $-\pi\leq k_x\leq \pi$ and $0\leq k_y\leq \pi$ (half-BZ, with exact ranges depending on the model). I think ...
3 votes
Accepted

Adiabatic equation related to the Berry phase for lambda with first order terms

The TD-Schrodinger equation is $$H(\lambda)|\psi(t)\rangle=i\hbar\frac{\partial}{\partial t}|\psi(t)\rangle$$ So, we just need to plug in \eqref{4} and remove all terms that aren't first-order in $\...
Tyberius's user avatar
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3 votes
Accepted

Help with definitions in k-space twisted bilayer graphene model

I don't think I can use this Hamiltonian to recover the band structure. The band structure should use a tight-binding Hamiltonian with several unit cells. A colleague told me that this Hamiltonian is ...
2 votes

polarization jump in berry phase method using VASP

The problem is a bug in old version VASP that can occur in that unit cell because the non-polar phase polarization is not symmetric around 0. The jump happens where ionic contribution to dipole moment ...
mollen's user avatar
  • 101
2 votes

Confusions in interpreting Dirac strings (wormholes) in Haldane's Hilbert space picture ft. two tori joined by strings at gapless points

I found the following slides helpful: https://physics.princeton.edu//~haldane/talks/dirac.pdf Here are my answers: Yes. From what I understood, the above is not necessarily a 3D effect. The wormholes ...

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