All Questions
Tagged with topological-insulators quantum-hall-effect
52
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How to calculate Edge states of Topological insulators
Topological insulators are novel state of matter in which bulk is insulator and edges are gapless. How do we calculate these gapless states? I am reading the following PRL
Feng Liu and Katsunori ...
- 831
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0
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Laughlin's topological argument
I have a confusion about understanding the Laughlin's topological argument on Hall conductivity quantization.
This argument states that the Hall conductivity is
$$
\sigma_{xy}=\frac{e}{h}Q,
$$
where $...
- 2,333
2
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Why is disorder essential for the Integer Quantum Hall effect IQHE?
The title already gives away the question. I see that disorder effects that the Landau levels are broadened out. They allow states to be either extended through the whole solid or localized to a ...
- 808
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Hall Conductance and Chern Number Sign Convention
I have a simple question regarding sign conventions pertaining to the Chern number and Hall conductance (and what seems to be inconsistencies in the literature).
In a 2D band insulator, the Chern ...
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How to show that Chern number gives the amount of edge states?
When talking about topological insulator and talking about bulk-edge correspondence, it seems to be widely accepted conclusion that the band Chern number (winding number) is equal to, when the ...
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Derivation of Kubo Formula for Hall Conductance
I am trying to derive the result of the TKNN formula but am experiencing difficulty in deriving the Kubo formula. The Kubo formula used in the TKNN paper is,
$$ \sigma_{xy}= \frac{ie^2}{\hbar} \sum_{E^...
- 369
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Does any Hamiltonian that breaks time-reversal symmetry is isomorphic to a IQHE
The bulk Hamiltonian of the 2D Chern insulator in is given by
\begin{equation}
H=\sin k_{x}\sigma^{x}+\sin k_{y}\sigma^{y}+(2-m-\cos k_{x}-\cos k_{y})\sigma^{z}
\end{equation}
This Hamiltonian breaks ...
- 177
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why Hall conductance quantized
When I am studying quantum Hall effect, the quantum Hall conductance can be represented by Green function $\left(\text{up to}\ \frac{e^2}{h}\large \right)$:
I cannot understand why it is an integer?
...
- 41
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Why bulk states in quantum hall effect do not contribute to electric conductivity
Most reviews and textbooks explain quantum hall effect as insulating bulk states and conducting edge states, as is shown in the following picture.
My question is: why bulk states are insulating in ...
- 1,431
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Problem with quantum Hall effect and Berry curvature
I am having trouble proving that the Hall conductivity is equal to the integral over the Berry curvature in momentum space. In the TKNN (1982) paper, using the Kubo formula
$$
\sigma_{xy} = \frac{ ie^...
- 81
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Does Hall plateus require the existence of impurity in the sample?
While studying Hall conductivity with The Quantum Hall effect written by S.M.Girvin, I read a sentence
"We have shown that the random impurity potential (and by implication Anderson localization) ...
- 31
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Equivalence classes of mappings from $T^{2}$ to an arbitrary space $X$
I was reading the paper "Homotopy and quantization in condensed matter physics", by J.E Avron et al. ( http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.51.51). There they have classified the ...
3
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1
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How to determine the orientation of the massive Dirac Hamiltonian?
In the calculation of the Chern number within a 2D lattice model, let's take the Haldane model for example, the Chern number$=\pm1$ has 2 contributions coming from 2 Dirac points described by
$$h_1(\...
- 3,744
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TKNN invariant changes due to continuous deformation of parameter space
Naively, I would assume that a topological invariant remains invariant under continuous deformations of whatever space the invariant belongs to. In the case of topological insulators, this space is ...
- 949
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Determining spectra of edge states numerically
Normally we write a Bloch Hamiltonian $H(\mathbf{k})$ for the bulk and determine the spectrum which gives us various bands i.e we basically obtain $E=E(\mathbf{k})$ for the bulk only.
Also in the ...
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