Topological insulator are materials formed by a insulator bulk and metallic surfaces with topological origin. These materials may be important for developments in Quantum Computing and Spintronics.

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Intuition on topologically nontrivial 2D-band structures?

I want to get more intuition on topologically nontrivial band structures. There's this popular 2D two-band model for a topological insulator where $H=\sum_{k}h(\boldsymbol{k})$ (see Qi, Hughes, and ...
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How to derive the spin-orbit term in Kane Mele model?

The Kane mele model is a famous quantum spin hall model on honeycomb lattice (C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005)). The Hamiltonian is $$H = - t\sum\limits_{\left\langle ...
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Where does the Berry phase of $\pi$ come from in a topological insulator?

The Berry connection and the Berry phase should be related. Now for a topological insulator (TI) (or to be more precise, for a quantum spin hall state, but I think the Chern parities are calculated in ...
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Descent equation and anomaly polynomial

I am just reading Ryu, Moore and Ludwig's paper on classifications of topological insulators and quantum anomaly. They are trying to relate the quantum anomaly as a signal of the presence of a ...
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How can one localize the massless fermions in Dirac materials?

I noticed that finite electric potential cannot localize the low energy excitations in a graphene sheet. Is it possible to localize the massless fermions in the surface band of topological insulators ...
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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 ...
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Significance of Dirac cones in condensed matter physics

In condensed matter physics, Dirac cones can be found in graphene, topological insulators, cuprates, and iron-pnictides. This means that electrons behave as massless particles near the Dirac points. ...
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Defects in 3+1 TFTs/2+1 CFTs

I would like to know of good pedagogic references to learn about the notion of "defects" in TFTs and CFTs. I am specially interested in 3+1 TFTs (.and probably about their relation to 2+1 CFTs..) In ...
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Hamiltonian of the surface states of a 3D topological insulator

The surface states of a 3D topological insulator (let's say in the (x-y) plane) are sometimes described by the following Hamiltonian : $$H(k)=\hbar v_F (p_x \sigma_x + p_y \sigma_y)$$ or sometimes by ...
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Why p-wave superconductors are rare in nature?

I have the basic question that why so many superconducting materials are s-wave and d-wave pairing, but the p-wave superconductors are so rare in nature? An equivalent question may be that why ...
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How much merit is there in the heuristic argument of bulk-edge relation for topological insulators?

Take 2D quantum hall insulator for example. The typical argument goes like this: We have a Hamiltonian that has translation symmetry in both directions on a infinite lattice, and we assign a integer ...
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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 ...
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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 ...
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Finding parity eigenvalues from a character table

The all-electron code Wien2K will optionally calculate the character tables for a specified list of $k$-points. I'd like to know the parity eigenvalue for a given $k$-point and band index. Is there ...
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Parity of the surface state in a Topological Insulator (TI)?

Please bear with this experimentalist trying to understand the subtleties of TIs in what may well be imprecise language. I appreciate that one can deduce the topological trivial or non-trivial nature ...
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Some questions about the edge states for time-reversal invariant topological superconductors?

Stimulated by my some recent calculations on edge states(ES) for time-reversal invariant(TRI) topological superconductors(TS) as well as many questions concerning the "edge states" in Physics ...
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331 views

1D Topological insulator with PT symmetry

Assume I have the Hamiltonian for a 1D topological insulators as: $H=sin(P_x) \sigma_x+i \Delta \sigma_{y}+(1-m-cos(P_x)) \sigma_z $ where $m$ is the mass term, $P_x$ is the momentum and $\Delta$ is ...
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Phase factor for nearest neighbor hopping in the Haldane Model

In Haldane's model, he imagines a staggered magnetic field in graphene where the net flux through a unit cell is zero. To model this, he has a phase factor in next nearest neighbor hopping on the ...
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how to determine the parity eigenvalues of time-reversal invariant momenta point from first principle calculation when we judge topological insulator?

This is a question of topological insulator. Liang Fu and C. L. Kane proposed a method to judge whether an inversion symmetric insulator is a topological insulator or not in their article(L. Fu and ...