Questions tagged [symmetry]

Questions relating to symmetries and symmetry groups encountered in materials modeling.

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Space group will not change in vesta

I have one unit cell of 16 atoms (4 formula unit cells) 2x2x2 unit cells. I want to construct the supercell with 32 and 64 atoms. I went in the transform and I changed the rotation matrix 4x2x2 and ...
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33 views

Constructing the symmetry operator from k.p Hamiltonian

I have a question regarding to how to construct an operator from k.p Hamiltonian. Maybe there are some problems in my understanding, I hope you can point me out and correct my description if I made ...
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1answer
67 views

How to do a proper relaxation of the multicomponent structure?

I have a beta Ti (Space Group 229) structure with 16 atoms, I prepared 15 disordered TiNb structures with 5 atoms of Nb. I did it using VASPKIT. However, before the ...
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1answer
54 views

Hubbard model SU(2) symmetry: manifest invariance

Could someone explain, is it possible to make Hubbard Hamiltonian manifestly SU(2) invariant? I know about the interaction term, but how would kinetic (hopping effect) term have to look like? Here I'm ...
10
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1answer
85 views

Quantum ESPRESSO ph.x output

I wanted to calculate the normal modes of some particular material using the Quantum ESPRESSO. Everything went fairly well, but there is a couple of lines in the output that I do not understand. In ...
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Crystallography: How to sample *unique* structures from configuration space? (binary alloy supercell)

I'm working with a binary alloy system (call it 'AB'), and I'd like to generate a few unique configurations for DFT purposes. My primitive cubic unit cell consists of 4 atoms; i.e. 4 positions. Thus, ...
9
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How to generate a complete set of doped (substituted) structures?

I'm trying to analyse doping in a certain material in low concentrations. I'm approaching the problem by taking crystallographic unit cell of that material, then expanding that to a 2x2x2 supercell ...
11
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1answer
303 views

Does the spin polarised DFT calculation mean broken time reversal symmetry?

Recently, I have got to learn that if time-reversal symmetry and inversion symmetry are present simultaneously in the system we have the following conditions on energy of Bloch's states: $$E_{n,\chi }(...
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2answers
541 views

What are good tools for visualizing glide planes and screw axes?

While there are a few tools for visualizing crystal structures, I'm particularly curious to know tools for visualizing space group symmetry, including: screw axes glide planes I teach a class on ...
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59 views

Construct a parity operator at a TRIM point?

I want to calculate the band parity at some TRIM (time-reversal invariant momentum) point in Brillouin zone. Parity was defined as the eigenvalue of the inversion operator. My question is how to ...
5
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1answer
109 views

How do I extract the wave function from a VASP calculation?

We can obtain a energy band structure of a crystal from a DFT calculation in Vasp. Each point in each band represents an energy eigenvalue with a corresponding wave function from the Schrödinger ...
5
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118 views

What's the information contained in a character table of a group? [closed]

This question has an answer on the Chemistry Stack Exchange: Understanding group theory easily and quickly. Anyone wishing to add alternative or additional perspectives that aren't already covered in ...
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3answers
758 views

How to build a nanocluster?

What are the software tools (if possible open source) or methods we can use for constructing a nanocluster, most preferably with high symmetry such as icosahedron, octahedron, cuboctahedron etc. ?
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What will break the time-reversal symmetry?

Specifically, I am interested in the time-reversal symmetry $(\mathcal{T})$ in quantum mechanics. The $\mathcal{T}$ is considered as an anti-unitary operator, namely: $$\mathcal{T}\psi(\vec{r},t)=\psi^...
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3answers
128 views

Rotation of crystal structure to match another structure of the same compound/polymorph

Say, I have two crystal structures of a particular organic molecule, the crystal structures are basically identical, apart from a rotation and redefinition of the lattice vectors/angles, a simple ...
9
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1answer
166 views

PT-symmetry leading to spin-degenerate band structures

I am trying to understand the fundamental physics of a kind of problem. I will introduce a specific example and then list some of the broader qualms I hold. I have observed many band structures, be it ...
10
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1answer
173 views

Nematicity in superconductors

It seems to me that the definition of "nematic phase" is quite chamaleonic. Quoting from its first definition [Nature 393, 550 (1998)] for a 2-dimensional square lattice "The nematic ...
9
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1answer
132 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 ...
12
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1answer
148 views

Why linear response is absent in a non-centrosymmetric system with time reversal symmetry?

In this paper, it is mentioned that a non-centrosymmetric system with time-reversal symmetry doesn't have a linear response. It is actually a consequence of the Onsager reciprocal theorem. But I didn'...
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1answer
198 views

How to analyze the band symmetry with Quantum ESPRESSO?

This question is related to this paper: J. Phys. Chem. Lett. 2017, 8, 13, 2999–3007 The above figure shows symmetry analysis for the band structure. The author writes: The band symmetry and parity ...
5
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1answer
137 views

Is there a difference in performance when the symmetry is specified via ibrav in Quantum ESPRESSO?

I have been using cif2cell for converting CIF files into quantum ESPRESSO input files. But cif2cell always keeps the ibrav value to be zero and indicates the CELL_PARAMETERS. As per the quantum ...
12
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1answer
113 views

What does it mean to assign group operations to distinct sets for space groups?

I am trying to understand space groups in crystallography. In International tables for crystallography, for a nonsymmorphic space group, they list some symmetry operations. 8 of them are listed under ...
9
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1answer
94 views

Partial density of states in random solid solutions

This question comes as a follow-up to https://mattermodeling.stackexchange.com/a/2214/116; nonetheless, it is relevant on its own as well. To designate a particular crystal structure to a random ...
9
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1answer
114 views

Why does mcsqs change the space group of generated SQS?

I made a binary special quasi-random structure (SQS) using mcsqs (distributed as part of the ...
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84 views

How to classify ionic and covalent excited-states?

In spectroscopy it is common to describe excited-states as ionic or covalent. I understand the concept on a toy model e.g. $\ce{H2}$ with a minimal basis set \begin{align} \Phi_0 &= [\chi_A(1) + \...
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2answers
372 views

Effect of ISYM tag on Partial Density of States (VASP version < 6)

This is from the entry for LORBIT in the VASP Wiki. For LORBIT >= 11 and ...
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1answer
304 views

Inversion symmetry in 2D materials

Transition metal dichalcogenides (TMDs) are composed of three atomic planes and often two atomic species: a metal and two chalcogens. The honeycomb, hexagonal lattice has three fold symmetry and can ...
9
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1answer
250 views

Get fractional coordinates from special Wyckoff positions

I'm trying to get the fractional coordinates for Mo and S, for MoS$_2$-2H, where 2H means the phase. MoS$_2$-2H is a bilayer, in which each layer is separated from each other by Van der Waals forces. ...
8
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Symmetry of glide planes [closed]

I am trying to understand the symmetry elements of space group number 194 (P$6_3$/mmc), which is hexagonal and has 24 symmetry operations. In the table of symmetry operations it says that it has three ...
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4answers
374 views

How is group theory used to deduce which of these integrals are equal to 0?

The number of all two-electron integrals: $$ \tag{1} \langle \phi_1 \phi_2|\phi_3\phi_4 \rangle = \int d^3\mathbf r' \int d^3\mathbf r'' \, \phi_1(\mathbf r'') \, \phi_2(\mathbf r') \frac{1}{|\mathbf ...
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2answers
596 views

How to deduce phase transitions from a phonon calculation?

I came across the concept of using phonons to establish a material's dynamical stability, based on whether or not imaginary frequencies are present in its phonon band structure. What I am struggling ...
16
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1answer
2k views

How to understand the time-reversal symmetry in graphene?

A lot of references say that the Dirac cone in graphene is protected by inversion and time-reversal symmetries. How can one understand this statement? How can one show explicitly that the gapless ...
11
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1answer
183 views

Dealing with symmetry of ordered primitive cell during DFT structure relaxation

I have a large disordered cubic structure that I would like to do AIMD on to look at cation diffusion. I found the primitive cell and then ordered it to create several configurations. I will then ...
18
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1answer
1k views

Is the number of possible Bravais lattices a mathematical fact?

Almost anyone that has taken a Solid State Physics course will know, that any 3D crystal must be in one of the 14 Bravais lattices due to symmetry operations and space filling. In 2015, a paper was ...
14
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1answer
153 views

conceptual problem about the energy band along the High symmetry point in the Brillouin zone

When we calculate the band structure of certain material, we only have to calculate the value along the high symmetry point which enclose the Irreducible Brillouin Zone. Why the information lie in the ...
9
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1answer
355 views

What is the difference between U(1) and O(2) symmetry?

To my understanding, they both refer to circular symmetry. I know U(1) is the complex plane, and I think O(2) is real numbers. I have seen them used more or less interchangably, but is there actually ...