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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Are there topological non-trivial states in zero dimension?

The periodic table of topological insulators and superconductors suggests that there can be topological non-trivial phases in zero dimension in non-interacting system with certain symmetries. A 0D ...
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How are topological invariants constructed?

I've seen several different definitions for what are called topological invariants, for instance in the context of Majorana unpaired modes, by Kitaev: http://arxiv.org/abs/cond-mat/0010440 ...
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How does bulk-boundary correspondence works for various cases of time-invariant system?

I was pondering this question after I read this review: M. Zahid Hasan and Charles L. Kane. “Colloquium: topological insulators.” Reviews of Modern Physics 82, no. 4 (2010): 3045. (arXiv) How do ...
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37 views

Converting the Hamiltonian for the tight binding model in silicene into $k$ space

I am trying to convert the Hamiltonian from the paper "A topological insulator and helical zero mode in silicene under an inhomogeneous electric field" (also on arXiv) into $k$ space. $$H = -t\sum_{\...
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108 views

What makes a system topological?

As I understand, if the Chern number which is obtained by integrating Berry curvature over a surface with a boundary is an integer, then the Chern number is a topological invariant. So when does Chern ...
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70 views

Definition of winding numbers for Hamiltonian

In Witten's lectures at the PSSCMP/PiTP summer school, there is a use of winding number for "bad points" at sec.1.3. The formula is $$ w = \int_S\frac{d^2p}{4\pi}\left[\epsilon^{\mu\nu}\epsilon^{abc}...
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115 views

why do edge states in Graphene exist between the Valence and Conduction band?

I read in a review that there are 2 Dirac points in graphene, where the conduction band and valence band touch each other. Near these points electrons obey a linear dispersion relation. Breaking of ...
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696 views

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 C....
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167 views

What is the physics behind “Bulk-edge correspondence”?

There is a frequently mentioned concept in the field of topological insulator called "bulk-edge correspondence" or "bulk-boundary correspondence", which basically gives the relationship between the ...
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43 views

Is edge states of topological insulators superconducting?

I am told edge states of topological insulators are free from back scattering. Does this mean topological insulators have no resistance if only edge states are taken into account?
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19 views

Model of topological Kondo insulators

I read a review about topological Kondo insulators. But unfortunately I didn't really understand the theory behind it. I have to admit that my knowledge about topological condensed matter physics is ...
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119 views

Calculating the Berry curvature in case of degenerate levels (Non abelian Berry curvature): issue

The Berry phase accumulated on a path can be described by a matrix when we look at adiabatic time evolution with a Hamiltonian with degenerate energy levels. The Berry phase matrix is given by $$ \...
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20 views

Topological insulators and high symmetry points

I've been reading about topological insulators (topological systems in general) and one signature (or the defining signature?) is that an odd number of surface states cross the Fermi energy between ...
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821 views

What is a Dirac semimetal?

What is the precise definition of a Dirac semimetal? Is it sufficient for two bands to touch at a single k point with a linear crossing, or are more conditions required for a material to be called a ...
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19 views

difference between weak and strong topologiccal insulators

Does someone know what the difference is between weak and strong topological insulators? (And do both exist in any dimension?).
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499 views

Chern insulator vs topological insulator

What is the basic distinction between a Chern Insulator and a Topological Insulator? Right now I know that a Chern Insulator has "topologically non-trivial band structure" and that a Topological ...
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229 views

How does time reversal symmetry work in topological insulator?

I am doing microelectronic devices with topological insulators. Can some one explain time reversal symmetry in a topological insulator to electrical engineering student like me?
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Derivation of TKNN's main result from Kubo formula

I have a question about a small but meaningful (to me at least) step in the original TKNN paper (http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.49.405). I understand the construction of the ...
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32 views

Largest values of spin-orbit coupling

Which are some of the materials with the largest ratio spin-orbit coupling constant/hopping constant? I'm trying to compute energy bands for different values of $t$ (hopping constant) and $\lambda_{SO}...
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46 views

What is the topological number of d=1 Haldane phase?

According to the topological classification work [e.g. Chen et al. Science 338, 1604 (2012)], the 1d Haldane phase should have a topological number $Z_2$, which has close relationship with the edge ...
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55 views

why pseudo wave functions can be used to calculate berry connection

Berry connection plays a very important role in topological insulators. Berry connection $A(k)$ is defined to be $i\langle u(k)|\nabla_k|u(k)\rangle$, where $|u(k)\rangle$ is the periodic part of ...
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510 views

Jordan Wigner Transformation in 1d Majorana chain

So, I was reading the paper by Fidkowski and Kitaev on 1d fermionic phase http://arxiv.org/abs/1008.4138. It explains the classification of 1d fermionic SPT phases with $\mathbb{Z}_2^T$ symmetry for ...
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1answer
91 views

eigenvectors of tight binding Hamiltonian

I am trying to calculate berry connection using tight binding method. The most important part is to calculate $\partial_k u_k(x)$, where $u_k(x)$ is the periodic part of bloch waves, i.e. $\psi_{nk}(x)...
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77 views

Current operator in continuum model of graphene

For the graphene hamiltonian with NNN hopping, the wavefunctions are of the form: $(\psi_A ,\psi_B)^T$. The current from A(i) to B(j) site in the lattice model is given by: \begin{equation} J_{ij}=\...
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55 views

Imaginary argument in bessel function for a wavefunction

I am solving for the continuum model of haldane model with one of the site being a potential well. The Dirac equation for a topologically non trivial case gives a solution for the states in the band ...
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1answer
74 views

chern number as an obstruction to choose a smooth gauge

In condensed matter physics, I heard that if chern number of a band $n$ is non zero, it is impossible to choose a gauge such that $\psi_{nk}$ is smooth in the whole brillouin zone. However, it is ...
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When can we take the Brillouin zone to be a sphere?

When reading some literatures on topological insulators, I've seen authors taking Brillouin zone(BZ) to be a sphere sometimes, especially when it comes to strong topological insulators. Also I've seen ...
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68 views

Are the edge states of a topological insulator only zero energy states?

For non-trivial topological insulators, are the edge states only zero energy states? Or are boundary states of different energies also available?
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63 views

does Hall plateus require the existence of impurity in the sample?

While studying Hall conductivity with The Qantum Hall effect written by S.M.Girvin, I read a sentence "We have shown that the random impurity potential(and by implication Anderson localization) ...
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1answer
349 views

Berry phase in 1D materials

The Berry phase $\phi_B$ is the phase that an eigenstate acquires after its momentum vector goes around a circle at constant energy around the Dirac point. It is defined as $\phi_B = -i \int \langle\...
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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 ...
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About the $Z_2$ topological invariant

In Kitaev 2001 it is shown that the topological invariant $Z_2$ in a topological superconductor (Class D or BDI, one dimensional) can be defined as $$ (-1)^\nu={\rm sign\, Pf} [ A ]={\rm sign\, Pf}[ \...
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Topological invariant for interacting systems using single particle green functions?

Why Single particle green's function is (preferred) used to find topological for interacting systems? $N_1 =\frac{\epsilon_{ijk}}{24 \Pi ^2} \int dw d^3k G \partial_i G^{-1}G\partial_jG^{-1}G\...
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How to describe spin-orbital coupling in Weyl semi-metal

In three dimensional Weyl semi-metal, the Hamiltonian that describes low excitation quasi-particle is well-know Weyl Hamiltonian: +/- $k\cdot\sigma$. But if I want to add spin-orbital coupling in that ...
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About Weyl superconductors and fractionalized Weyl semimetals

Recently, the experimental observations of Weyl fermion semi-metal have been made. Weyl fermion becomes very hot in condensed matter physics. I am confused about the Weyl superconductors and ...
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Quantum spin Hall effect and the edge states

In quantum spin Hall effect or Kane-Mele model, how can one get rid off the edge states without affecting the bulk?
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362 views

Topological invariant in 1D

In 2D, with state $\psi(k_x, k_y)$, it is common to calculate measure of topology of material: 1 - Calculate Berry connection $a = -i <\psi | \partial_{\boldsymbol{k}} | \psi>$. 2 - Calculate ...
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110 views

$Z_2$ invariant and Wannier states switching partner

I have been reading about $Z_2$ topological invariant recently. However, after some literature survey, I still cannot understand $Z_2$ invariant in language of time reversal polarization. Basically, ...
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Is spin-orbit coupling really necessary for topological insulators

I have heard that for an insulator to be non-trivial, large spin-orbit coupling is necessary. However, I have read the definition of $Z_2$ topological invariant and chern number. In no way can I ...
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56 views

Will all linear band inversions of non-degenerate bands change chern number by one?

I have learned from literature that band touching is the source of chern number.In three dimensional material, any non-degenerate linear band crossing will form a weyl point which is a monopole of ...
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Majorana fermions in s wave superconductor

I need some help to understand the majorana fermions in $s-$ wave superconductor and to check whether following method is correct For $s-$ wave superconductor we can write the Hamiltonian as $$H=-t\...
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Superconductivity and time-reversal symmetry

Let us consider a system of a 1D edge of a 2D topological insulator in proximity to an s-wave superconductor. The system is described by the Hamiltonian: $$ H =\frac{1}{2} \int \mathrm{d}x \ \Psi^{\...
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What are the conditions to observe gapless modes at the boundary for 1D case?

We observe gapless modes at the boundary for the case of SSH model or Polyacetylene The Hamiltonian for SSH model has particle hole and time reversal symmetries, it also has a Dirac like spectrum. It ...
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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? ...
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1/m Laughlin state and $U(1)_M$ chiral CFT

I am a little confused that people claim that the edge theory of a 1/m Laughlin state corresponds to a $U(1)_m$ chiral CFT. This indicates there should be $m$ primary field operators in $U(1)_m$ ...
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70 views

Magnetism in Topological Insulator?

I have read many papers with the statement that on the introduction of the magnetic impurity, the gap at the Dirac point opens in the surface states. I am little confused about it. If the gap is ...
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2answers
133 views

Exact Diagonalization of a BdG Hamiltonian on a Finite Lattice

I would like to numerically find the edge modes of a $p_x$ + $i p_y$ BdG Hamiltonian. The lattice version is given by H = $\sum\left[-t \left(c_{m+1,n}^{\dagger} c_{m,n} + \text{h.c} \right) - t\left(...
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How to perform stroboscopic measurements for Floquet topological insulators?

Floquet topological insulators (arXiv:1008.1792, arXiv:1211.5623) have attracted much research interests in condensed matter physics. The goal is to realize topological insulators from trivial ...
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Can a nondegenerate fermionic topological Mott insulator (TMI) state support an emergent bosonic topological order?

Based on my recent study and motivated by a recent paper, I have a naive question. Consider a 2d Hubbard model for electrons at half filling $H=\sum c_k^\dagger h_k c_k+U\sum n_{i\uparrow }n_{i\...