Questions tagged [berry-phase]

Questions relating to properties that depend on Berry phase-like quantities

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How to output Berry connection and identify the gauge by changing VASP or QE source code?

Usually, the first-principles packages like VASP and QE involve many aspects to totally figure out what their subroutines do. For example, to output Berry connection $\mathcal{A}^\alpha_{nn}$ used by ...
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6 votes
1 answer
83 views

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

The Hall conductivity is given by $$\sigma_{xy}^{2D}=\frac{e^2}{\hbar} \int \frac{d\vec{k}}{(2\pi)^d} f(\epsilon(\vec{k}))\Omega_{k_xk_y} \tag{1} $$ in which $f$ is the Fermi distribution function and ...
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8 votes
1 answer
453 views

Berry Curvature with VASP+WANNIER90

I searched in the tutorials in WANNIER90 and example 18 says that the calculation of the Berry curvature requires the "recent version of the pw2wannier90 ...
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5 votes
0 answers
130 views

What's the role of Berry curvature in quantized Hall effects? [closed]

Cross-posted and answered at Physics.SE. The quantized versions of the Hall effect include (ignoring fractional quantum Hall effect): Quantum Hall effect; Quantum anomalous Hall effect; Quantum spin ...
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6 votes
0 answers
120 views

How to plot Berry curvature flux by considering plane in momentum space?

I want to plot the berry curvature flux by considering $k_x$ and $k_y$ plane in momentum space. I have experience running DFT calculations in Quantum ESPRESSO. I have tried reading the user manual of ...
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6 votes
1 answer
53 views

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

I had a question about Haldane's wormhole interpretation (picture below). I believe he first proposed it in his paper Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-...
  • 2,091
6 votes
1 answer
109 views

Help with definitions in k-space twisted bilayer graphene model

I am trying to numerically do calculations using Eq. 8 of MacDonald's simple model for twisted Bilayer graphene. I only want to calculate the Berry phase. However, I don't think I have my definitions ...
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6 votes
0 answers
37 views

Example of 2D k-space models allowing interband transitions after a closed-loop trajectory? [closed]

I have been mainly exposed to 2D momentum-space condensed matter models in the context of Berry-related topology. I now want to study models where, if I take a closed loop in momentum space, I will ...
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9 votes
0 answers
58 views

What is special about valley-focused Hamiltonians that make them give quantized/rational (valley) Chern numbers? [closed]

I have been thinking about so-called valley Chern numbers $C_v$ and associated topological phenomena. To my knowledge, they are usually applicable when inter-valley scattering is suppressed, leaving ...
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6 votes
1 answer
82 views

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

EDIT: Please see my first comment on this question first. In this paper, Fukui and Hatsugai present a numerical scheme for the calculation of the $\mathbb{Z}_2$ index that uses the following ...
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7 votes
0 answers
40 views

Can the anomalous Hall effect only be applied to magnetic materials? [closed]

As I understand the anomalous Hall effect, in materials with a strong spin-orbit coupling, the intrinsic deflection effect is dominant over the side jump and skew scattering effects. In the intrinsic ...
5 votes
0 answers
79 views

Z2 topological index: Is this unconventional formula summed over just filled bands, or all bands? [closed]

The $\mathbb{Z}_2$ topological index is usually defined in terms of the Pfaffian of the overlap matrix, as defined by eq. 4 of Kane and Mele's paper: $$ P(k)=\text{Pf}[\langle u_i(k) | \Theta | u_j(k) ...
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7 votes
1 answer
181 views

Help with Definitions in Numerical Calculation of Multiband Berry Phase

In the third chapter of Vanderbilt's book, they discuss the so-called multiband parallel transport and provide a scheme for numerical calculations that is similar to the single band case (where the ...
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8 votes
1 answer
90 views

Help with understanding topologically-protected edge states in domain wall systems

Let's say that I have a simple domain wall system for the following Hamiltonian with added on-site potential $M(x)$: $$\tag{1} H(k,M)=-t \sum_{\delta} [\cos(k\cdot\delta)\sigma_x-\sin(k\cdot\delta)\...
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8 votes
0 answers
97 views

What are some types of topologically-relevant band degeneracies in contemporary 2D condensed matter research? [closed]

In the study of 2D condensed matter systems, I have seen several kinds of band degeneracies. I call 'bands' the eigenvalues to the time-independent Schrodinger equation, solved over 2D k-space. By '...
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8 votes
0 answers
102 views

Example of a standard/archetypal/simple 4-band gapped condensed matter model with analytic results? [closed]

I am looking to study Berry phase-like phenomena in a gapped 4-band material model. In particular, I want to numerically and analytically calculate the Abelian Berry curvature integral of each band ...
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6 votes
1 answer
64 views

Example of a standard/archetypal/simple 4-band un-gapped condensed matter model with analytic results?

I am looking to study Berry phase-like phenomena in an un-gapped material model. However, I am having trouble finding a widely-used 4-band model with analytic expressions for wavefunctions and ...
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5 votes
0 answers
211 views

Why does numerical computation of Berry curvature give me a correct Berry phase when it is supposed to diverge? [closed]

I implemented the standard numerical algorithm for calculating the Berry curvature in MATLAB. For a given 2D system, I can visualize the Berry curvature over parameter space. If I sum the Berry ...
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7 votes
0 answers
173 views

How to fix gauge in Quantum ESPRESSO? [closed]

I am trying to use Quantum ESPRESSO to manually calculate the Berry phase using the Berry connection, due to evolution along a closed loop in k-space. I want to do this manually instead of using ...
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12 votes
1 answer
515 views

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

I would like to prove that a 2D material (Say ZnO) is ferroelectric. Since Ferroelectric materials are a subset of piezoelectric materials. How should I proceed to prove that the polarization is ...
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12 votes
0 answers
196 views

Orbital magnetization in periodic solids

The orbital magnetization in periodic solids has been nicely described by the so-called modern theory of magnetization [1,2,3,4]. $$\tag{1} \mathcal{M}_{orb} = -\frac{1}{2} \Im \sum_{n,\mathbf{k}} f_{...
6 votes
0 answers
233 views

Is there any way to simulate the Polarization vs Electric Field loop of BaTiO3 using Quantum ESPRESSO? [closed]

I'm new to the Quantum ESPRESSO package. There are articles outlining the procedure of indirectly simulating the P-E loop of piezo-electric materials via Berry phase calculations.One procedure is ...
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6 votes
1 answer
59 views

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

I want to represent parallel transport as in the following figure, but next to this figure I would like to place a diagram with the two arrows (of the initial state and of the final state that are ...
11 votes
1 answer
414 views

Anomalous Quantum Hall Effect

I am studying the transition metal dichalcogenides (TMDs) and I have seen webinars and articles that said that these materials exhibited the anomalous quantum Hall effect related to the curvature of ...
12 votes
1 answer
147 views

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

Consider the following derivation in David Vanderbilt's book "Berry Phases in Electronic Structure Theory - Electric Polarization, Orbital Magnetization and Topological Insulators" (2018, ...
9 votes
2 answers
386 views

Dynamic phase in an adiabatic system

I am trying to understand the Berry phase through the evolution of a system that evolves adiabatically. Schrodinger's equation is: \begin{equation} H(\lambda)|n(\lambda)\rangle=E_n|n(\lambda)\rangle \...
5 votes
1 answer
76 views

Property related with Berry curvature: $\Omega_{n,\mu\nu}=-\Omega_{n,\nu\mu}$

I read in David Vanderbilt's book named "Berry Phases in Electronic Structure Theory - Electric Polarization, Orbital Magnetization and Topological Insulators" the definition of Berry ...
17 votes
2 answers
354 views

Berry's curvature and magnetic moment in TMDCs

I am studying the transition metal dichalcogenides (TMDCs) and one of the applications that these materials have is their use in valleytronics. Valleytronics is related to the magnetic moment, Berry ...
31 votes
1 answer
5k views

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

Band inversion is a key ingredient of a topologically nontrivial material$^1$. What is band inversion? How to recognize it in a band structure? What conclusions can I infer if I observe band inversion ...
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