Questions tagged [berry-phase]
Questions relating to properties that depend on Berry phase-like quantities
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Gauge constraint in the definition of the Z2 invariant
Cross-posted at Physics.SE.
In Fu and Kane's paper from 2006, the authors define the $\mathbb{Z}_2$ invariant for time-reversal invariant topological insulators as an obstruction to Stoke's theorem,
$$...
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Why does VASP fail to compute Spontaneous polarization calculation through berry phase method for semiconductors?
I am trying to calculate the spontaneous polarization of a semiconducting magnetic 2d material with VASP. The Material has a band gap of 0.28 eV (indirect).
VASP warns that
"The calculation of ...
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2
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polarization jump in berry phase method using VASP
When I use VASP to compute in-plane polarization of a slab with hexagonal cell (a axis along x axis, b axis is at a(-1/2,$\sqrt{3}$/2),polarization is along diagonal direction so I got it using $p_x$/...
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How to output Berry connection and identify the gauge by changing VASP or QE source code?
Usually, the first-principles packages like VASP and QE involve many aspects to totally figure out what their subroutines do. For example, to output Berry connection $\mathcal{A}^\alpha_{nn}$ used by ...
- 14.9k
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How to transform the two-dimensional Berry curvature integral into a loop integral along Fermi circle?
The Hall conductivity is given by
$$\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 ...
- 14.9k
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1
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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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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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255
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How to plot Berry curvature flux by considering plane in momentum space? [closed]
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 ...
- 2,561
6
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1
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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-...
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6
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1
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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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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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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
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1
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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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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 ...
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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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1
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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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1
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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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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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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
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1
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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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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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212
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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 ...
- 2,281
13
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1
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877
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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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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_{...
- 2,048
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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 ...
- 4,448
6
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1
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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 ...
- 1,753
11
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1
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706
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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 ...
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12
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1
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166
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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, ...
- 1,753
10
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2
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531
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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 \...
- 1,753
6
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1
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99
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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 ...
- 1,753
17
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2
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416
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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 ...
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32
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1
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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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