7
votes
1answer
323 views

Topological insulators: why K-theory classification rather than homotopy classification?

I am reading a 2009 paper by Kitaev on K-theory classification of topological insulators. In the 4th page, 1st paragraph in the section "Classification principles", he says, Continuous ...
4
votes
1answer
149 views

Fermion zero modes under 1+1 D Higgs spacetime vortex?

Jackiw and Rossi had a classic paper Zero modes of the vortex-fermion system (1981). In that nice-written paper, they found fermionic zero modes of Dirac operator under nontrivial Higgs vortex in 2D ...
9
votes
2answers
443 views

Do topological superconductors exhibit symmetry-enriched topological order?

Gapped Hamiltonians with a ground-state having long-range entanglement (LRE), are said to have topological order (TO), while if the ground state is short-range entangled (SRE) they are in the trivial ...
6
votes
3answers
315 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 ...
3
votes
1answer
458 views

How to define the mirror symmetry operator for Kane-Mele model?

Let us take the famous Kane-Mele(KM) model as our starting point. Due to the time-reversal(TR), 2-fold rotational(or 2D space inversion), 3-fold rotational and mirror symmetries of the honeycomb ...
5
votes
1answer
296 views

A question on the doped Kitaev-Heisenberg model?

Recently, some groups have studied the effects of doping the Kitaev model on honeycomb lattice(e.g.,http://arxiv.org/abs/1109.6681 and http://arxiv.org/abs/1109.4155) and their calculations show the ...
18
votes
1answer
2k views

How Fundamental is Spin-Orbit Coupling to Topological Insulators?

I'm well aware this is a very active area of research so the best answer one can give to this question may be incomplete. Topological states in condensed matter are well-known, even if not always ...
19
votes
5answers
2k 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 ...