Questions tagged [berry-pancharatnam-phase]

The phase difference acquired over the course of a closed loop which results from the geometrical properties of the parameter space of the Hamiltonian.

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Why not all Berry phase just vanished?

I just learned that for any real wavefuntions, berry phase equals zero. But in Griffiths' Problem 2.1(b), he proved that any complex wavefuntion can be written as linear combination of REAL ...
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Units of Berry curvature/connection elements in Wannier90 code

If you please have a look at Eq. (25) of Vanderbilt's PRB2006 paper, the gauge transformation of the connection element $A$ results in $A^{(H)}_\alpha = \bar{A}^{(H)}_\alpha + iD^{(H)}_\alpha $, $\,\,...
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Berry curvature concentration around nodal points

It is well-known that in TI-symmetric semi-metals the Berry curvature on the Brillouin torus vanishes away from the nodal points (eg. [XCN10, III.B] [Van18, p. 105]). But even for non-TI-symmetric ...
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Numerical calculation of berry curvature of Haldane model

I'm currently trying to simulate the Haldane model of graphene and am looking into the calculation of Berry curvature of the finite lattice. I'm using a tight-binding model of graphene with nearest-...
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Understanding polarization and Zak phase

I was trying to understand the arbitrariness of polarization and Zak phase. Consider the following example, for this 1D lattice with wavefunction mostly localized at the atomic sites, the polarization ...
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Question about a step in Griffith's QM book on Berry's phase for an electron in time-varying magnetic field

Some Context I am going through David Griffith's Introduction to Quantum Mechanics (Second Edition), Chapter 10, Section 10.2 on Berry's phase. Suppose we have a system with a time-dependent ...
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Geometric Phase vs Dynamic phase

On the Wikipedia page for the Adiabatic Theorem (https://en.wikipedia.org/wiki/Adiabatic_theorem), formulas for both the dynamic and geometric phases are given. The dynamic phase is expressed as: $$\...
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Quaternion formulation for parallel transport along a curve on a 2-sphere

One image that is often used to illustrate curvature in general relativity is the triangle on a 2-sphere, made out of great circle arcs. At the end of a geodesic transport along this triangle, the ...
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Is the derivative of Berry curvature with respect to band energy possible?

The Berry curvature is one of the most important quantities for a topological material like Dirac semimetal(DSM), Weyl semimetal(WSM) etc. Berry curvature is always momentum ($\mathbf{k}$) dependent ...
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Berry flux of magnetic monopole

I am sorry if it looks stupid question. I want to ask how sin is transferred back from spherical to Cartesian and how $F_{ij}$ tells us about magnetic monopole in magnetic field. $F_{ij}$ is berry ...
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Would there be plateaus in IQHE in haldane graphene model

It's my understanding that the plateaus observed in the integer quantum hall effect are due to scattering due to impurities in the material. The haldane model for graphene does not include a model for ...
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How can i calculate the Berry Curvature for the Dirac points in Haldane graphene?

I want to calculate the berry curvature at the Dirac points in graphene with complex next nearest hopping (haldane model) in order to show that it is non-zero at the dirac points and use it to compute ...
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Numerically calculating the berry curvature for graphene

i'm trying to reproduce this density plot for the Berry curvature in the Brillouin zone of graphene from this website. In order to do this I am attempting to use this equation for the berry curvature ...
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How to derive Dirac's quantization of electric and magnetic charge from Berry's phase?

I have seen two ways of deriving Dirac's quantization of electric and magnetic charge using Berry's phase, one from Sakurai's book Modern Quantum Mechanics P354~355 and the other from David Tong's ...
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What does the toy model Hamiltonian for 3D weyl seminmetal mean?

I have been going through this Wannier tools tutorial for observation of weyl nodes in basic toy model Hamiltionan. It represents the toy model Hamiltonian as: $$H = A(k_x\sigma_x+k_y\sigma_y)+[M_0-...
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Role of Berry's curvature in nanomaterials

what is the physics behind Berry's curvature? In many papers, they are explaining topological and anomalous quantum hall effects via Berry's curvature. but what is the physics behind this curvature ...
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Deriving the Berry phase from the Schroedinger equation

Let $|n(\mathbf{R})\rangle$ be eigenstates of the snapshot Hamiltonian $H|\mathbf{R} \rangle$, of eigenvalues $E_n(\mathbf{R})$. The vector $\mathbf{R}$ contains the parameters upon which the system ...
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Why is the Chern number an integer?

I have relatively limited knowledge on the Chern number, and I know that there exists high-level math proofs that the Chern number is an integer, but let me try to focus on the case I have in mind. $\...
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What is the physical meaning of adiabatically varying the wavevector $k$ as a parameter to calculate the Chern number for topological effects?

Could it mean something like applying a weak electric field and perturbing the band structure? Or some other weak perturbation? Or is that the wrong idea?
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‘Proof’ that non-Abelian Berry phase vanishes identically

For a degenerate system with Hamiltonian $H =H(\mathbf{R})$ and eigenstates $\left|n(\mathbf{R})\right\rangle$ the non-Abelian Berry connection is $$A^{(mn)}_i=\mathrm{i}\left\langle m|\partial_in\...
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Is the local Berry connection difference gauge invariant?

The Berry connection in terms of the cell-periodic Bloch states $u_{n\mathbf{k}}=e^{-i\mathbf{k \cdot r}}\psi_{n\mathbf{k}}$ with band index $n$ and crystal momentum $\mathbf{k}$ is defined as $$ A_{n}...
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Noncontractable loops in the 2D Brilluoin zone and the Chern number

I'm getting quite twisted around trying to figure out what all is quantized exactly in IQH looking at it from the Chern number perspective. Let's suppose quantum hall on a torus -- I can apply a large ...
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Quantization of the Berry Phase

Let's consider the Aharanov-Bohm effect. Following Girvin & Yang, an infinitely long, very thin flux tube running along the $\hat z$ axis is surrounded by a strong potential barrier preventing ...
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How to understand degeneracy and singularity of field

In the online lecure given by Professor Wu Yongshi https://www.koushare.com/video/videodetail/4619 1:30‘, he says: Suppose we have a state $|m,R(t)\rangle$, where $R(t)$ is controlled parameters ...
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What definition of integral is implied when expressing nonzero Chern number as the integral of Berry curvature?

In defining a nonzero Chern number as the integral of Berry curvature over the parameter manifold: $$n=\frac{1}{2\pi}\int_{S}{\mathcal{F}}{dS}$$ does the integral exist in a general Riemann sense, or ...
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Berry Phase, Chern Number, Topological Insulators

I would like to understand the Berry phase and Chern number a bit better. For this, consider the SSH model, where it turns out that the Berry phase $\gamma_{+}$ of the upper band is given by $$\gamma_{...
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Numerical calculation of berry curvature of Alpha t3 lattice

https://doi.org/10.1143/JPSJ.74.1674 by this paper of Fukui how can I deduce numerical calculation of berry curvature of Alpha t3 lattice?
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Adiabatic evolution of superposition of states

I am supposed to find a specific superposition of eigenstates of a time-dependent hamiltonian $H(t)$. The hamiltonian is of the form : $H(t) =\sum_i \left(J\vec{\sigma}_i\cdot \vec{\sigma}_{i+1} + h(t)...
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Phase in Quantum Theory

Can somebody please give the most general answer to: "what is a Phase of a wavefunction in quantum theory?" I have understandings and doubts so far as follows: The non-relativistic quantum ...
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Haldane definition of Berry connection

In Haldane's article about Anomalous hall effect (arXiv:cond-mat/0408417) berry connection, curvature and phase are defined from Bloch state. From my previous knowledge about Berry phase I thought ...
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How to prove Berry Curvature is a pseudo-vector?

I know the definition of a pseudo-vector, it is a vector that changes sign under improper rotation. Is there any semiclassical way to understand it for the context of Berry Curvature?
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Berry Phase in Graphene

I am trying to understand the a) Concept of Berry Phase b) its effects/ observation in graphene. I am an experimental physicist and I want to understand these concepts without getting awed by ...
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How to calculate the integral of a loop? [closed]

A certain field has a singularity at the origin, and the divergence of its curl is zero at any point outside the origin, but surface integral of the curl is not zero in the area of any closed surface ...
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Berry Curvature

Can I ask two questions about the Berry curvature? The formula for the berry curvature is written below. $$\Omega_n (k) = -Im \langle \bigtriangledown_k u_{nk} | \times | \bigtriangledown_k u_{nk} \...
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Berry curvature and parallel transport gauge

As I understand it, the Berry connection in the parallel transport gauge is null. The Berry curvature however is gauge-invariant and we can compute it in any gauge we wish, including the parallel ...
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Why does the Berry Phase of π cause anti localisation in Dirac fermions?

I am learning about the theory of topological insulators and one point that puzzles me is the following: The Berry Phase aqcuired by forming a closed loop on a Dirac cones is π. The argument that I do ...
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Does a Berry phase operator exist?

The closed-path Berry phase can have measurable effects and, if I am understanding correctly, is a measurable quantity in and of itself. If that is so, is there a Hermitian operator with Berry phases ...
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How the wave vector $k$ change slowly and travel a loop in Brillouin zone when we calculate the Berry phase?

According to the definition of the Berry phase, there must have a slowly changing parameter that travel a loop. when we discuss topology in energy band, the slowly changing parameter seems the $k$. my ...
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Numerically calculating non-Abelian Berry curvature: Definition of multiplet in explicit $4\times 4$ system with 2-fold degeneracy?

I am trying to use eq 16 of the following paper to calculate the Chern number of a 4x4 degenerate system: https://arxiv.org/abs/cond-mat/0503172 [1]. I believe this is the standard scheme used by many....
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Does the fiber bundle approach for Berry connection contradict adiabatic theorem?

In Ref [1], the authors show how the Berry connection is a geometric quantity using the fiber bundle approach. My question is about the idea of taking a local section of a fiber bundle (corresponding ...
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Gradient of a line integral of a vector field

I need some advice on how to perform the gradient of a line integral of a vector field. My problem refers to the Aharonov-Bohm Effect as it is discussed in the QM book from David Griffiths, as it ...
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Curl of Berry connection

If $|n\rangle=|n( \textbf{R}(t) ) \rangle $ satisfies the equation $$H(\textbf{R}(t))|n(\textbf{R}(t)) \rangle = E_{n}(\textbf{R}(t))|n(\textbf{R}(t))\rangle$$ then the berry phase $\gamma_{n}(t)$ ...
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Aharonov-Bohm effect of doubly localized wavepacket

I want to imagine an exotic situation regarding Aharonov-Bohm effect. The wavefunction $\psi$ of the electron is even ($\psi(\mathbf r) = \psi(-\mathbf r)$) and localized in two spatially separated ...
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Berry's phase for non-normalized wave functions

Let $\hat{H}(t)$ be the Hamiltonian of a quantum system depending on time $t$ through $k$ parameters $R(t) = (R_1(t), R_2(t), \dots, R_k(t))$: $$ \hat{H}(t) = \hat{H}(R_1(t),R_2(t),\dots,R_k(t)). $$ ...
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In fiber bundle picture of Berry connection, what is the vertical basis if the horizontal basis is the underlying parameter space?

In Ref. [1], the authors show how The geometric (Berry) phase is shown to have its origin in the nontrivial geometry of the fiber bundle: Hilbert space --—> space of states. The nontrivial ...
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Berry Connection Calculation for a 2-Level System [closed]

Suppose we start with a state on the Bloch sphere given by: $$|\psi\rangle = \begin{pmatrix}\cos\left(\frac{\theta}{2}\right)\\e^{i\varphi} \sin\left(\frac{\theta}{2}\right)\end{pmatrix}$$ The Berry ...
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Numerically calculating Berry curvature in >2-band 2D systems?

The standard method for numerically calculating the Berry curvature of a 2D condensed matter system is given by Fukui-Hatsugai-Suzuki in this paper. They discretize $k$-space into a grid with tiny ...
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Deriving the non-abelian Aharonov-Bohm effect as a Berry phase

I am trying to derive the non-abelian Aharonov-Bohm effect by generalising Michael Berry's derivation to the case of non-abelian gauge field $A$. My derivation so far We require a degenerate ...
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Berry curvature vanishes in TRS system

In spin 1/2 system with TR symmetry , the Berry curvature must vanish. Because Berry curvature is odd. How to prove it? \begin{equation} \langle\partial_{-k_x}u^{I}(-k)|\partial_{-k_y}u^{I}(-k)\rangle-...
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Examples of Chern number calculations where more than two $U(1)$ gauge of wavefunction has been used

While computing the Chern number of electronic wave functions \begin{align} \left|\psi\right\rangle = \begin{pmatrix}\cos\left(\frac{\theta}{2}\right) \\ \sin\left(\frac{\theta}{2}\right)e^{i \phi} \...
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