Questions tagged [topological-insulators]

For questions about modeling topological insulators (materials which are insulating in the bulk, but have conductive surface states due to specific topology of their band structure).

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7
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35 views

The quantum spin Hall phase with Z2 = 0?

I used first principle calculations to study the thin film model. An obvious crossing was shown to appear at the gamma point when the edge state was calculated, which was originally predicted to be ...
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Z2 topological index: Is this unconventional formula summed over just filled bands, or all bands?

The $\mathbb{Z}_2$ topological index is usually defined in terms of the Pfaffian of the overlap matrix, as defined by eq. 4 of Kane and Mele's paper: $$ P(k)=\text{Pf}[\langle u_i(k) | \Theta | u_j(k) ...
7
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1answer
76 views

Help with Definitions in Numerical Calculation of Multiband Berry Phase

In the third chapter of Vanderbilt's book, they discuss the so-called multiband parallel transport and provide a scheme for numerical calculations that is similar to the single band case (where the ...
7
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50 views

Software for calculating the mirror Chern number of 2D systems?

Can anyone please explain to me how can I calculate the mirror Chern number of a 2D system? I will be very thankful if you can refer me to a package or software which can directly perform mirror Chern ...
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Help with understanding topologically-protected edge states in domain wall systems

Let's say that I have a simple domain wall system for the following Hamiltonian with added on-site potential $M(x)$: $$ H(k,M)=-t \sum_{\delta} [\cos(k\cdot\delta)\sigma_x-\sin(k\cdot\delta)\sigma_y+M(...
8
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0answers
60 views

What are some types of topologically-relevant band degeneracies in contemporary 2D condensed matter research?

Cross-posted on Physics.SE. In the study of 2D condensed matter systems, I have seen several kinds of band degeneracies. I call 'bands' the eigenvalues to the time-independent Schrodinger equation, ...
6
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72 views

Example of a standard/archetypal/simple 4-band gapped condensed matter model with analytic results?

I am looking to study Berry phase-like phenomena in a gapped 4-band material model. In particular, I want to numerically and analytically calculate the Abelian Berry curvature integral of each band ...
8
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1answer
77 views

How to calculate the parity of a band at a particular point in Brillouin zone

Some references mentioned that the calculation of $Z_2$ topological invariant of a crystal can be greatly simplified if the crystal contains inversion symmetry. But it involves the calculation of the ...
4
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0answers
47 views

Why does numerical computation of Berry curvature give me correct Berry phase when it is supposed to diverge?

I implemented the standard numerical algorithm for calculating the Berry curvature in MATLAB. For a given 2D system, I can visualize the Berry curvature over parameter space. If I sum the Berry ...
6
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0answers
72 views

Calculating the Chern number on a 2D surface of a 3D insulator

I want to calculate the Chern number of a surface of 3D time reversal insulator. I know the 3D topological insulator was characterised by the Z2 index. And the Chern number was used characterised the ...
11
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2answers
146 views

About the surface Greens function method for calculating the surface state

Currently I'm using some software package to do the data analysis from the DFT calculation so that I can study the surface state of some topological insulator. I found that the method they use is ...
9
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1answer
128 views

Topological order in Weyl Semimetal

Is the topological phase in a Weyl semimetal is intrinsic or symmetry protected? How can we realize that? If symmetry protected, which symmetry protects the topological phase of non-centrosymmetric ...
9
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1answer
195 views

Can the fermi level of a semiconductor be below the valence band?

I was looking at the data on this page for a NiWO4 calculation. I can see unoccupied bands near the fermi level that appear to be below the band gap. What does this actually mean physically or is it ...
15
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2answers
763 views

What is the difference between Ultrasoft, ONCV and PAW Pseudopotentials? Which is better for a spin-orbit coupled calculation?

I am trying to do spin-orbit coupled calculations for various topological insulators. I have found papers using Quantum Espresso with ONCV pseudopotentials and papers using VASP with PAW ...
9
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0answers
102 views

Is the non-trivial band topology in a system, caused by spin-orbit-coupling or band inversion? [closed]

How can we know that the non-trivial band topology in a system is driven by spin-orbit coupling (SOC) or by band inversion? Based on my understanding, SOC causes the band inversion and makes the ...
10
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1answer
76 views

Edge states in Topological Semimetals

Does it make any sense to calculate edge states for topological semimetals while they don't have any global gap?
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3answers
1k views

Magnetism and Topology

Can magnetism and topological insulating behavior coexist in a material? If yes, can someone refer to a recent work?
10
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3answers
161 views

How to model Topological Insulators from first-principles?

Topological insulators and quantum materials are gaining increasing interest across the physical, chemical and materials communities. Today, one can go to the Topological Materials Database and see ...
27
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1answer
2k views

What is band inversion and how to recognize it in band structure?

Band inversion is a key ingredient of a topologically nontrivial material$^1$. What is band inversion? How to recognize it in a band structure? What conclusions can I infer if I observe band inversion ...
15
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1answer
63 views

What are good resources to study crystallographic defects in different dimensional systems and their topological dimensionality?

I wonder if there are any books or resources that may address one or more of the following questions: What kinds of defects are important for topology? Especially crystallographic defects. How do ...
17
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1answer
141 views

What exactly is a topological insulator and how to recognize one from band structure?

Four years ago, the Nobel Prize in physics was awarded for "for theoretical discoveries of topological phase transitions and topological phases of matter." In line with this, I heard of topological ...