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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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How to Obtain the Zak Phase in Symmetric one-dimensional (1D) Systems?

In a symmetric 1D system, the intrinsic topological orders are characterized by the total Zak phase ($\gamma$) summed over all occupied states$$\tag{1}\gamma=\sum_{n}^{}\gamma_n$$where $n$ is the band ...
Jaafar Mehrez's user avatar
3 votes
0 answers
41 views

Z2 Topological Invariant for 2D Systems

$\mathbb{Z}_2$ topological invariant is typically calculated based on the parity of occupied bands at time-reversal invariant momenta (TRIM) in the Brillouin zone. The WannierTools docs states that we ...
Jaafar Mehrez's user avatar
3 votes
0 answers
38 views

Clarification Needed about Topological Invariants

I am seeking clarification on whether choosing the appropriate topological invariants has any relation to the dimensionality of the system. I understand that in three-dimensional (3D) materials, the ...
Jaafar Mehrez's user avatar
4 votes
1 answer
62 views

Tight binding packages for Fermi velocity of slabs

I'm studying some topological materials through first principles methods (very trendy I know) and have a question about extracting the Fermi velocity. I'd like to use a wannierised model to ...
MSteg's user avatar
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4 votes
0 answers
43 views

Gauge constraint in the definition of the Z2 invariant

Cross-posted at Physics.SE. In Fu and Kane's paper from 2006, the authors define the $\mathbb{Z}_2$ invariant for time-reversal invariant topological insulators as an obstruction to Stoke's theorem, $$...
Sounak Sinha's user avatar
5 votes
0 answers
59 views

Presence/absence of topologically protected edge states on the boundary of two topological insulators [closed]

A normal insulator is the same as vacuum because one can change the band structure from one to another without closing the gap, but for topological insulators (talking about 2D TI) like 1T'-TMDs or ...
Runnong Zhou's user avatar
7 votes
1 answer
227 views

Spin-Orbit coupling effects in topological insulator Bi2Se3

I'm currently trying to understand this paper explaining the origin of band inversion in the topological insulator Bi2Se3. In Fig. 2 (see below) they explain by means of 4 steps how certain atomic (...
Mika R.'s user avatar
  • 141
3 votes
0 answers
26 views

boundary states of higher-order topological insulators [closed]

What are the standard computational methods used in obtaining the edge and corner states of higher-order topological insulators? From my understanding, the DFT code calculates the bulk properties of a ...
user avatar
5 votes
0 answers
190 views

About the mechanism of opening of the band gap in topological insulator with the inclusion of SOC [closed]

When we work on the topological insulator (protected by time reversal symmetry ), it is often said that the SOC is the main ingredient because it is a way to open a gap when the band inversion present....
JensenPang's user avatar
  • 2,883
6 votes
0 answers
332 views

How to plot Berry curvature flux by considering plane in momentum space? [closed]

I want to plot the berry curvature flux by considering $k_x$ and $k_y$ plane in momentum space. I have experience running DFT calculations in Quantum ESPRESSO. I have tried reading the user manual of ...
UJM's user avatar
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6 votes
0 answers
87 views

What computational steps needed to characterize the Weyl points? [closed]

I am trying to learn the characterization of Weyl nodes computationally. For this, I am using Wannier90 and Z2pack codes in interface with Quantum ESPRESSO. I have done scf, nscf, bands structure, DOS,...
UJM's user avatar
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7 votes
0 answers
45 views

The quantum spin Hall phase with Z2 = 0? [closed]

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 ...
JensenPang's user avatar
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5 votes
0 answers
136 views

Z2 topological index: Is this unconventional formula summed over just filled bands, or all bands? [closed]

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) ...
TribalChief's user avatar
  • 2,361
7 votes
1 answer
316 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 ...
TribalChief's user avatar
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9 votes
0 answers
91 views

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

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 ...
Alisufyan's user avatar
  • 691
8 votes
1 answer
139 views

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 $M(x)$: $$\tag{1} H(k,M)=-t \sum_{\delta} [\cos(k\cdot\delta)\sigma_x-\sin(k\cdot\delta)\...
TribalChief's user avatar
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8 votes
0 answers
126 views

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

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, solved over 2D k-space. By '...
TribalChief's user avatar
  • 2,361
8 votes
0 answers
120 views

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

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 ...
TribalChief's user avatar
  • 2,361
10 votes
1 answer
536 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 ...
JensenPang's user avatar
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5 votes
0 answers
406 views

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

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 ...
TribalChief's user avatar
  • 2,361
16 votes
0 answers
357 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 is characterized by the Z2 index annd that the Chern number can be used to ...
JensenPang's user avatar
  • 2,883
15 votes
2 answers
1k 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 ...
JensenPang's user avatar
  • 2,883
10 votes
1 answer
201 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 ...
walber97's user avatar
  • 447
9 votes
1 answer
576 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 ...
Tristan Maxson's user avatar
21 votes
2 answers
6k 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 ...
Ashique Lal's user avatar
  • 1,621
9 votes
0 answers
169 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 ...
Alisufyan's user avatar
  • 691
10 votes
1 answer
130 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?
Alisufyan's user avatar
  • 691
15 votes
3 answers
1k views

Magnetism and Topology

Can magnetism and topological insulating behavior coexist in a material? If yes, can someone refer to a recent work?
Shahid Sattar's user avatar
11 votes
3 answers
552 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 ...
epalos's user avatar
  • 4,869
32 votes
1 answer
8k 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 ...
Thomas's user avatar
  • 9,132
16 votes
1 answer
83 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 ...
Siddhant Singh's user avatar
17 votes
1 answer
356 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 ...
Verktaj's user avatar
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