All Questions
7
questions
2
votes
0
answers
168
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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 ...
3
votes
3
answers
672
views
‘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
$$A^{(mn)}_i=\mathrm{i}\left\langle m|\partial_in\...
- 2,157
0
votes
2
answers
738
views
Berry Curvature
Can I ask two questions about the Berry curvature? The formula for the berry curvature is written below.
$$\Omega_n (k) = -Im \langle \bigtriangledown_k u_{nk} | \times | \bigtriangledown_k u_{nk} \...
- 173
0
votes
0
answers
177
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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-...
- 1
8
votes
2
answers
607
views
Numerical Berry curvature for bosons
I am trying to numerically compute the Berry Curvature for a generic quadratic Bosonic Hamiltonian of the form $$H = \sum_{ij} A_{ij} b_{i}^\dagger b_j + \frac{1}{2} \sum_{ij}\left( B_{ij} b_i b_j + \...
user138458
3
votes
1
answer
4k
views
Numerical Calculation of Berry Curvature
I am trying to calculate some berry curvature (BC) in a 2D lattice and I have some things I am getting lost with.
In the 2D lattice, we set up the eigenvalue problem $H|u_1\rangle = \epsilon_i|u_i\...
- 1,788
3
votes
2
answers
1k
views
Derivation of the Berry Curvature and Bloch Magnetic Moment in Graphene
(I found a workable solution, skip to the "Solution" part to see it) I am attempting to derive equations 2 and 6 from Xiao et al. paper "Valley contrasting physics in graphene" (...
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