All Questions
Tagged with crystals symmetry-breaking
19 questions
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Translational invariance $\neq $ Galilean invariance?
I have the impression that some literature say that Galilean invariance is broken by a uniform lattice. That is, although a uniform lattice like a tight binding model is translationally invariant, it ...
- 2,165
4
votes
1
answer
104
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Why are crystalline structures in solids so common?
Is there any sort of theorem or paper that shows that periodic arrays gives ground states? Or any other theoretical reason why crystals are so common?
- 2,020
2
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1
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124
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Is the formation of crystal due to internal symmetry or spacetime symmetry?
In the contexts of field theory, we have internal symmetries and spacetime symmetries. Referring to crystal, people would say it is due to space translation symmetry. However, I don't think the ...
- 31
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99
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How an applied magnetic field breaks the inversion symmetry in a centrosymmetric system?
I want to understand why magnetic dipole transition breaks the inversion symmetry in a centrosymmetric system and gives rise to second-order nonlinearity.
- 1
4
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3
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Why is the translational symmetry broken?
In the book Condensed Matter Field Theory by Altland, on page 5, it is given that
$$H[\pi, \phi]=\int d x\left(\frac{\pi^{2}}{2 m}+\frac{k_{\mathrm{s}} a^{2}}{2}\left(\partial_{x} \phi\right)^{2}\...
- 2,313
6
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Why phonons are Goldstone modes?
I read this in the lecture notes by David Tong:
"Gapless excitations often dominate the low-temperature behaviour of a system, where they are the only excitations that are not Boltzmann ...
- 83
1
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0
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79
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2D semiconductor's time reversal symmetry
We know that 2d semiconductors have time-reversal symmetry breaking' properties.
How can I check the spatial inversion symmetry properties and time-reversal symmetry of materials?
Please explain it ...
- 11
4
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2
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423
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Does a crystalline ferromagnetic solid break the rotational symmetry twice?
Both Heisenberg ferromagnets and crystalline solids break the rotational symmetry in space. Now consider a crystalline ferromagnetic solid. By virtue of being in a crystalline phase, it already broke ...
- 12.3k
1
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2
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63
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Separating Hamiltonians in spontaneous symmetry breaking investigation
I read a book about spontaneous symmetry breaking. In the book, the author says:
Using a Fourier transformation, it's always possible to divide the Hamiltonian into two parts, one is collective part ...
- 786
1
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0
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139
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Breaking of spherical symmetry in crystals
I have been reading the book Transition Metal Compounds, and when the author begins to discuss transition metals in crystals, they state
When we put a transition metal ion in a crystal, the ...
- 1,022
2
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0
answers
89
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Does pseudospin break the crystal symmetry?
Pseudospin is a concept to describe a superposition of two quantum states.
Sometimes, I see a pseudospin texture in the momentum space which breaks a crystal symmetry.
A simple example is the ...
- 21
6
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2
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661
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Symmetry Breaking of Crystals
How do crystals break translational and rotational invariance? If I arbitrary displace a crystal, it is still the same and its energy is still the same. So how then is translational symmetry broken? ...
1
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1
answer
380
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Is nematic ordering time-reversal invariant?
I am confused about the definition of nematic order in crystals. In this paper https://www.nature.com/articles/nmat4138, they say that nematic order is "a lowering of the rotational symmetry while ...
user165990
0
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1
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1k
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Order parameter for liquid to crystalline solid transition under the broken continuous group of translation
The order parameter for liquid to crystalline solid transition is given by the Fourier transform of the density $$\tilde{\rho}(\textbf{k})=\int\rho(\textbf{r})e^{i\textbf{k}\cdot\textbf{r}}d^3\textbf{...
- 27.2k
0
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0
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50
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The reference which mentioned that the rotational symmetry guarantees the off-diagonal term of the conductivity matrix is antisymmetric?
The two-dimensional conductivity matrix can be written as $\sigma=\left[\begin{array}{cc}\sigma_{xx} & \sigma_{xy}\\\sigma_{yx} & \sigma_{yy}\end{array}\right]$ which represents the current ...
- 477
9
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1
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Why do 3D Wigner crystals form a bcc rather than an fcc lattice?
When an electron gas has low enough density, the electons' Coulomb repulsion can be strong enough relative to their kinetic energy that they spontaneously form a Wigner crystal. Since the electrons ...
- 49.4k
33
votes
1
answer
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Understanding time crystals
In very recent publications, two groups in Maryland (paper: "Observation of a Discrete Time Crystal") and Harvard (paper: "Observation of discrete time-crystalline order in a disordered dipolar many-...
- 4,800
1
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1
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How does the surface of a material always break inversion symmetry?
I am trying to visualize this for an HCP structure. Take the profile view as such:
just working in 2d.
So my understanding is if we can take a point (x,y) -> (-x,-y) and get the same crystal than ...
- 817
3
votes
0
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428
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Why is there a 'loophole' in Mermin Wagner for rotations?
I'm just starting out in my mathematics career by looking at some simple stuff on broken symmetries in statistical mechanics. Since 3D is 'hard' it would be very nice to look at 2D toy models of ...
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