I have tried to write down the boundary conditions in this case and looked into them. As conditions i) and ii) were trivial, i looked into iii) and iv) for information that I could use. But all I got was that for the transmitted wave to have an angle, the reflective wave should also have an...
There are some famous materials is determined as TI induced by SOC, like graphene and so on. But from some formula, for instance, Kane-Fu formula, they just need parities to get Z2 number. So I wonder if there is a known TI with weak soc.
I have a question (more like a curiosity) related to three-dimensional topological insulators, which support Dirac-like states at their surfaces. From the theory, it is well known that these states are immune to scattering from non-magnetic impurities, i.e. impurities that do not break...
Hello.
Do you know of any good material on topological insulators like books, review papers etc?
I would prefer something more oriented towards theoretical physics(because I know that there are reviews out there that are purely experimental).
Thank you!
I am leaning the Haldane model :
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.61.2015
Haldane imaged threading magnetic flux though a graphene sheet, and the net flux of a unit cell is zero.
He argued that since the loop integral ##\exp [ie/\hbar \oint {A \cdot dr} ]## along a path...
In the textbook "Topological Insulators and Topological Superconductors" by B. Andrei Bernevig and Taylor L. Hughes, there is a chapter titled "Hall conductance and Chern Numbers". In section 3.1.2 (page 17) they are discussing including an external field in a tight binding model, the Peierls...
Hi. I'm taking a look at some lectures by Charles Kane, and he uses this simple model of polyacetylene (1D chain of atoms with alternating bonds which give alternating hopping amplitudes) [view attached image].
There are two types of polyacetylene topologically inequivalent. They both give the...
I have been learning topological insulators recently, and I become more and more curious about the link between topological insulators and mathematical theory these days.
I know topological insulators have something to do with fiber bundles and K-theory. I have a relatively good background of...
Hi every one,
I face with a question on my works,
As you know there in many articles Physicist introduce a material that has zero gap without spin-orbit coupling (SOC). By applying the SOC, a relatively small gap (0.1 eV) is opened and it becomes topological insulator.
My question,
Is that...
I have been reading about Z2 topological invariant recently. However, after some literature survey, I still cannot understand Z2 invariant in language of time reversal polarization.
Basically, my struggle includes the following two questions:
As the ref paper says(see the picture below): On...
As we know topological phases cannot be explained using spontaneous symmetry breaking and order parameter. But can they coexist? Suppose there is a system which is undergoing quantum phase transition to a anti-ferromagnetic phase from a disordered phase. So in the anti-ferromagnetic phase...
Hi every body,
I faced a paradox. The topological insulator is robust against a potential that does not breaks the TRS.
But in the original work of Kane-Mele (PRL 95, 146802), the "staggered sublattice potential" that does not breaks the TRS,, makes zigzag ribbon trivial insulator (figure 1 in...
I have been doing a literature survey about topological insulators for some time. What surprises me is the close relation between difference of chern number and number of edge states. However, I found most review or tutorial in topological insulator avoided direct proof of the relation. So can...