All Questions
9
questions
3
votes
0
answers
75
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Infinite stacking of integer quantum Hall systems
Let us consider a (3+1)-dimensional system $\mathcal{H}$ constructed by stacking (2+1)-dimensional integer quantum Hall systems $\mathcal{H}_\text{Hall}$, e.g., $E_8$ bosonic systems (or $\sigma_H=1$ ...
- 813
0
votes
2
answers
332
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What does "continuous transformation" mean with regard to the Hamiltonian of a system?
When dealing with topological phases of matter (topological insulators, quantum hall effect, etc...) one says that the system remains in the same phase as long as any continuous transformation of the ...
- 423
1
vote
1
answer
1k
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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
1
vote
0
answers
253
views
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
5
votes
1
answer
151
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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 ...
6
votes
3
answers
1k
views
Whis is the difference between charge fractionalization in 1D and 2D?
Both 1D Polyacetelene and 2D fractional quantum Hall state can support fractional excitations.
But as I can see, there are some differences: the ground state of Polyacetelene breaks translational ...
- 181
23
votes
3
answers
8k
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Why are there chiral edge states in the quantum hall effect?
The most popular explanation for the existence of chiral edge states is probably the following: in a magnetic field, electrons move in cyclotron orbits, and such such cyclotron orbits ensure electrons ...
- 1,055
3
votes
1
answer
387
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What is the operator for the edge current of a fracional quantum Hall state?
The edge of a fractional quantum Hall state is a chiral conformal field theory. In the Laughlin case it corresponds to the chiral boson,
$$ S = \frac{1}{4\pi} \int dt dx \left[\partial_t\phi\...
- 3,102
28
votes
5
answers
5k
views
Simple models that exhibit topological phase transitions
There are a number of physical systems with phases described by topologically protected invariants (fractional quantum Hall, topological insulators) but what are the simplest mathematical models that ...
- 5,415