Questions tagged [symmetry]

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

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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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19 votes
1 answer
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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 ...
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17 votes
2 answers
754 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 ...
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17 votes
1 answer
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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 ...
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16 votes
2 answers
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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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14 votes
1 answer
189 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 ...
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12 votes
3 answers
242 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 ...
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12 votes
1 answer
121 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 ...
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12 votes
1 answer
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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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11 votes
3 answers
845 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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11 votes
2 answers
608 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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11 votes
1 answer
413 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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11 votes
1 answer
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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 ...
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10 votes
1 answer
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How to extract the crystal symmetry from VASPs POSCAR/CONTCAR file?

VASPs POSCAR/CONTCAR file does not contain any direct information about the cell symmetry. If I run for example a calculation on simple TiN in space group 225, this symmetry is (should be) preserved. ...
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10 votes
1 answer
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Get fractional coordinates from special Wyckoff positions

I'm trying to get the fractional coordinates for $\ce{Mo}$ and $\ce{MoS_2-2H}$ in $\ce{MoS_2-2H}$, where 2H is the phase. $\ce{MoS_2-2H}$ is a bilayer, in which each layer is separated from each other ...
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10 votes
1 answer
206 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 ...
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10 votes
1 answer
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Should one consider the spatial degeneracies of the electronic state while calculating the Gibbs free energy?

The Gibbs free energy of a molecule is generally expressed as a sum of translational, rotational, vibrational, electronic and nuclear contributions. The electronic contribution $G_{elec}$ is formally ...
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10 votes
1 answer
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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 ...
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10 votes
1 answer
92 views

Correlation tables between irreps for f orbitals

I want to define occupied orbitals in terms of IRREPs for tungsten which has f orbitals. The highest possible point group for $\ce{WF2}$ in MOLPRO is $D_{2\mathrm h}...
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10 votes
1 answer
178 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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10 votes
0 answers
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How to generate a complete set of doped (substituted) structures? [duplicate]

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 ...
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9 votes
1 answer
149 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 ...
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9 votes
1 answer
865 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 ...
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9 votes
1 answer
363 views

Proposing a 2D quasicrystal; what are the necessary and sufficient conditions? (If it looks like a duck and quacks like a duck, or...?)

Quasicrystals show repeating motifs or patterns but are not periodic. And yet their Fourier transforms invariably demonstrate a pattern of sharp peaks revealing that there is still an underlying... ...
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9 votes
1 answer
285 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 ...
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9 votes
1 answer
169 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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9 votes
1 answer
114 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 ...
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8 votes
2 answers
415 views

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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8 votes
1 answer
538 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 ...
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8 votes
0 answers
76 views

Crystallography: How to sample *unique* structures from configuration space? (binary alloy supercell) [closed]

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, ...
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8 votes
0 answers
102 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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8 votes
0 answers
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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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7 votes
2 answers
235 views

Why do we need to use fake k-points when doing HSE band structure in VASP?

I want to know why we need fake k-points in HSE band structure calculation? I mean why we can't take a simple high symmetric path like we do in PBE calculation?
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7 votes
1 answer
83 views

Symmetry group of p-benzoquinone

I am trying to calculate the UV-visible spectrum of p-benzoquinone. In the literature, the point group of p-benzoquinone is $D_{2h}$, but when I optimize this molecule in the ground state with ...
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7 votes
1 answer
135 views

Case study : Symmetry operation between VASP and Quantum espresso

I am doing simple scf calculation to find similarities in the output of VASP and QE. Recently, I encounter an interesting case. ...
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7 votes
0 answers
64 views

Is the formula of a Dyson orbital independent of whether there is degeneracy or not in the HOMO of the neutral?

A Dyson orbital is defined as: $$ \textrm{Dy}(x) = \int dx_1 \ldots dx_{N-1} \, (\Psi^+(x_1,\ldots,x_{N-1}))^* \, \Psi^0(x_1,\ldots,x_{N-1}, x),\tag{1} $$ where $\Psi^0$ and $\Psi^+$ are the total ...
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  • 595
7 votes
0 answers
88 views

Construct a parity operator at a TRIM point? [closed]

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 ...
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6 votes
1 answer
128 views

About LaCrO3 space group stability

I found two space groups of $\ce{LaCrO3}$ material Pnma and Pm-3m. If someone is familiar with this material, please help to understand which phase is more stable. what are the factors that determine ...
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6 votes
0 answers
53 views

Constructing the symmetry operator from k.p Hamiltonian [closed]

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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5 votes
1 answer
341 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 ...
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  • 375
5 votes
1 answer
278 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 ...
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  • 4,268
5 votes
1 answer
68 views

How can I distinguish between n, pi, pi* orbitals when looking for excited states?

I recently asked about how to distinguish between transition types. I got an answer there about determining the character or type of the orbitals. My problem now is that I'm not sure how to determine ...
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5 votes
0 answers
28 views

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

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....
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5 votes
0 answers
77 views

Spacetime translation of Noether's current density [closed]

I've heard so many times that spacetime translation invariance is assumed when we speak about Noether's current density. Could someone explain to me, why is that so? What if we don't assume it? To be ...
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5 votes
0 answers
232 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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4 votes
1 answer
95 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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  • 191
4 votes
1 answer
71 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 ...
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4 votes
0 answers
31 views

Do the VBM and CBM have to be on the high symmetry point? [duplicate]

I am trying to generate the band structure of a slab, a lot of tutorials tell me that I need to generate the high symmetry K point path, but I am wondering that if the VBM and CBM have to be on the ...
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  • 1,661
3 votes
2 answers
84 views

How to quantify the lattice distortion from XRD?

In real crystals, the atoms may not always sit at their ideal lattice sites. How to quantify this lattice distortion? Based on my understanding from X-ray diffraction books, the Radial Distribution ...
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  • 613
3 votes
0 answers
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Examples of anti-symmetric rank-3/4 tensors?

The anti-symmetric rank-3 and rank-4 tensors hold the following properties: \begin{align} \sigma_{mnk} &=-\sigma_{nmk} \\ \sigma_{mnkp} &=-\sigma_{nmkp} \end{align} Note I'm using ...
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