All Questions
Tagged with topological-insulators quantum-hall-effect
52
questions
6
votes
2
answers
1k
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A simple conjecture on the Chern number of a 2-level Hamiltonian $H(\mathbf{k})$?
For example, let's consider a quadratic fermionic Hamiltonian on a 2D lattice with translation symmetry, and assume that the Fourier transformed Hamiltonian is described by a $2\times2$ Hermitian ...
- 3,744
18
votes
1
answer
1k
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Hall conductivity from Kubo: Bulk or edge?
Using the Kubo formula, Thouless, Kohmoto, Nightingale, and den Nijs (TKNN, PRL 49 405-408 (1982)), proved that upon summing all the contributions of the filled states of an insulator, the Hall ...
- 271
6
votes
3
answers
1k
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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
0
answers
911
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Simple model of edge states for a two-dimensional topological insulator
Quantum spin Hall states or, topological insulators are novel states of matter that have insulating bulk and gapless edge states. Are there any simple models that show these features?
See e.g. the ...
3
votes
1
answer
387
views
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