All Questions
6
questions
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
1
vote
1
answer
234
views
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 $\gamma_{n}(t)$ ...
- 13
1
vote
1
answer
93
views
What is the logic connection between these two statements?
What is the connection between these two statements:
the berry curvature change sign under time-reversal operation
If the system has the time-reversal symmetry, then berry curvature is odd in k.
...
- 6,095
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" (...
- 63
8
votes
1
answer
2k
views
Derivation of expression for Berry curvature
Many texts quote the expression for the Berry curvature for a two-level system, with Hamiltonian $\mathbf{h}(\mathbf{k})=(h_x,h_y,h_z)$ in terms of $\mathbf{k}=(k_x,k_y)$, as something like
\begin{...
- 419