# Questions tagged [berry-pancharatnam-phase]

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1answer
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### Discontinuity of the geometric phase

Does the geometric phase accumulated along a closed trajectory (in some parameter space) has to be continuous?
1answer
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1answer
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### Topological invariant in 1D

In 2D, with state $\psi(k_x, k_y)$, it is common to calculate measure of topology of material: 1 - Calculate Berry connection $a = -i <\psi | \partial_{\boldsymbol{k}} | \psi>$. 2 - Calculate ...
1answer
359 views

### Dirac string and Nielsen–Ninomiya theorem

Nielsen–Ninomiya theorem states that in a lattice system one can not have just one chiral fermion. Fermions necessarily come in pairs of opposite chirality. I am wondering if one can "explain" this ...
0answers
320 views

### Massive Dirac model Chern number 1/2

Why is massive Dirac model have a Chern number as half? I know this is something related to anomalies. And for fermions we have half, for bosons we have integer. But I failed to find any good ...
0answers
44 views

### Energy magnetization in the presence of temperature and chemical potential gradient

In the following paper (Phys. Rev. Lett. 97, 026603) http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.97.026603 the energy magnetization part of the energy current is given in the presence ...
0answers
194 views

### Classical - quantum analogy of Berry phase

I am reading this webpage about Berry phase: http://materia.fisica.unimi.it/manini/berryphase.html I am happily convinced about the first "elementary geometry" example they provide. Now I am trying ...
1answer
299 views

### Sources to learn about Berry phases and Adiabatic Theorem

I recently went through Griffiths' Quantum Mechanics text and there is a chapter called the Adiabatic Theorem that includes Berry phase and the Aharonov-Bohm effect. As I found them very ...
1answer
212 views

### What is the physical meaning of an electronic system evolving adiabatically through a closed path?

I am trying to understand Physics behind the Weyl Fermion in Condensed Matter Systems. Electrons show Weyl fermionic behaviour in the vicinity of so called 'Diabolical Points' in the band structure. ...
2answers
2k views

### How to include Berry connection in Hamiltonian?

When we calculate Berry connection, $A(R)=i<\psi(x,y)|\frac{d}{dR}|\psi(x,y)>\hat{R}$ corresponding to the Berry phase of any system, the gauge potential is related to the $R$ of the parameter ...
1answer
179 views

### Phase on Aharonov-Bohm effect doubts

How I show that $$\Lambda(\textbf{x}')=\frac{q}{\hbar}\int \mathbf{A} \cdot d\mathbf{x'}$$ on $$\tilde{\psi}(\textbf{x}',t)=e^{[\frac{iq\Lambda(\textbf{x}')}{\hbar c}]}\psi(\textbf{x}',t)$$ for ...
1answer
222 views

### Why must the Berry phase in 2d parameter space be $\pi$?

I am reading a paper and it seems that the author states that the Berry phase in 2d must be $\pi$. Is this true? If so, why?
1answer
517 views

### How to calculate the ground states' Berry phases with doubly degeneracy, such as that due to the particle-hole symmetry or time reversal symmetry?

Suppose the ground states of a system are doubly degenerate due to an anti-unitary symmetry $K$, which are $|\psi>$ and $|K\psi>$. If the system is an one-dimensional Fermion system and anti-...
0answers
214 views

### Monodromy, Holonomy and Braiding Phase

In quantum Hall effect, especially in the context of CFT description, these words come up often. I think I understand the braiding phase - as the phase gained by the wave function when a quasi ...
2answers
483 views

### Local phase gauge in momentum space of Bloch state

We know Bloch state has a phase undetermined, so $\Psi_k \to \Psi_k' = e^{i\theta(k)}\Psi_k$ is still the same eigenstate. My question: Are there some restriction on $\theta(k)$ except to be a real ...
0answers
238 views

1answer
991 views

### Aharonov-Bohm Effect and Integer Quantum Hall Effect

What is the relationship between Aharonov-Bohm effect and Integer Quantum Hall effect?