Questions tagged [condensed-matter]

The study of physical properties of condensed phases of matter, including solids and liquids.

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Kitaev Chain - Obtaining a real-orthogonal matrix that block-diagonlises the Kitaev Chain

I encounter a subtle problem regarding the Kitaev Chain. In Kitaev framework, he tried to express the Hamiltonian into real-orthogonal basis. Suppose the Majorana system is described by $$ H = \frac{i}...
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Why the mean field value of Lagrangian multiplier is real in slave boson method for Kondo problem and other

When dealing Kondo problem (or any other similar problems) with slave boson method, we write $$S_i=\frac{1}{2}\sum_{\alpha\beta}f_\alpha^\dagger\sigma^{i}_{\alpha\beta}f_\beta$$ with constraint $n_f=1$...
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electronic conductivity in superconductors

In studying simple drift based conductivity in metals and semiconductors, we follow the simplistic drift based model wherein, $$J = e(n\mu_n + p\mu_p)E = e(nV_{d,n} + pV_{d,p})$$ This is a completely ...
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Quantum rigidity and zero-point energy

I am currently going through the Nature review on cuprate superconductors by Keimer at all and I am having a bit of difficulty understanding this sentence, which is located near the top of page 181: ...
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Inverse temporal power-law increase of DC voltage under the application of constant DC current

Is there any material in which the DC voltage follows an inverse temporal power-law increase, under the action of a constant DC current? This implies a situation in which a constant current, I, is the ...
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Is a black hole just plasma in crystalline form so dense that light cannot enter? [closed]

Is the ring we see around the object the same phenomenon known as triboluminescence? What's the maximum density known matter can exist in limited volume? Wouldn't everything else technically be the ...
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How to calculate two-particle spectrum/density of states

In quantum many body theory, there is a convenient process for calculating the single particle density of states using the imaginary-time Green's function $$\mathcal{G}(k,i\omega)= \langle \psi(k,i\...
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Can Kohn anomaly be driven by parameters other than temperature?

The Kohn anomaly is the singular behavior of phonon softening in materials, for which a mean-field theory is the BCS type and is usually described to be driven by lowering the temperature till some ...
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Non-linear corrections to the Oseen-Frank free energy density

A nematic liquid crystal is essentially a fluid of long, rod-like molecules whose average orientation is dictated by a vector field $\mathbf {\hat {n}} $. The so-called Frank-Oseen (free) energy (...
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What is the historical context to specify resistivity of metals in $\mu\Omega$cm instead of $\mu\Omega$m?

The resistivity of metals usually lies in the range 1-10 $\mu \Omega$cm at room temperature as given in Chapter 1 of Ashcroft's and Mermin's Solid State Physics. Why is it not given in $\mu \Omega$m. ...
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Operator inequality between the Heisenberg Hamiltonian and the total spin

Consider a collection of $N$ spin-1/2 particles (qubits) with total spin $$\vec{S} = \frac{1}{2}\sum_{n=1}^N \vec{\sigma}_n$$ and a Heisenberg Hamiltonian $$H = -J \sum_{\langle n,m\rangle} \vec{\...
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How to properly get low energy effective field theory of superfluid?

I am following chapter 3 of X. G. Wen's book "Quantum Field Theory of Many-Body Systems". The following action for a weakly interacting Bose gas is derived: $$S[\varphi,\varphi^*] = \int dt \...
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Besides of photon, what else can excite electron from valence band to conduction band, then to form exciton?

The title is my question. Besides of photon, what else can excite electron from valence band to conduction band, then to form exciton? thank you.
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How to prove that a two-photon transition amplitude is absent in a crystal that obeys inversion symmetry?

In crystals that obey inversion symmetry retain their polarization form in $x\to -x$, we can prove that even order susceptibilities get canceled. But I want to know if there exists any way that I can ...
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How much information can be stored in a system with synthetic dimensions?

Okay this is a completely serious question and keep in mind I have a PhD in theoretical condensed matter physics, in which I have somewhat of a specialization in Floquet physics. So as the title says, ...
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Can a point $\vec R$ in direct lattice be uniquely mapped to a point in the reciprocal space?

Given a point in the direct lattice $\vec R=\vec a_1+\vec a_2+\vec a_3$ (say), what is the reciprocal lattice vector $\vec G$ corresponding to $\vec R=\vec a_1+\vec a_2+\vec a_3$? The reciprocal ...
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What is the connection between reciprocal lattice vectors $\vec G$ and the Miller indices?

We know that a family of crystal planes with Miller indices $(hk\ell)$ is orthogonal to the reciprocal lattice vector $\vec G = h \vec b_1 + k \vec b_2 + \ell\vec b_3$. My question is the converse of ...
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Lagrange multipliers in Majorana mean field theories

My question is about a small step in this paper (https://arxiv.org/abs/1710.09381) by Seifert, Meng, and Vojta. Here the authors introduce a Majorana mean-field treatment of a Kitaev-Kondo bilayer ...
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Inner products from lattice models

Let $|x\rangle$ be a coordinate eigenvector, $x=1,\dots N$ denotes the sites. Then what would $\langle x'|e^{-ikx}|x''\rangle$ be? I'm not clear what form $e^{-ikx}|x\rangle$ shall take.
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Transition from nematic phase to smectic phase in calamitic liquid crystals

I am a math student and not very good at physics. I am so confused when I read the paper about the mathematical problems in liquid crystals. My question is about the nematic phase and smectic phases. ...
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Are electrons separated by a large number of unit cells in a solid coherent?

Are electrons separated by large distances in a solid coherent? If I consider the system as being comprised of delocalized Bloch states, then electron states with a given k can interfere with each ...
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Fractional quantum Hall effect: is new physics required to understand it?

Is it true that some of the experimentally observed states in fractional quantum Hall effect are unexplainable by current physics? If so, does this point towards a revision of quantum mechanics, and / ...
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Translating Ashcroft and Mermin's "Second Proof" of Bloch's Theorem to Dirac's Notation

At the end of this post I attach Ashcroft and Mermin's proof of Bloch's theorem which is not essential per se (the proof using lattice symmetries is more general), but is key in being used later as a ...
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If $2p$ is the vorticity or vortex charge in a Fermi sea, what is just $p$?

Sorry in advance to ask such a simple question, but I promise I looked around and could not find a straight answer... I think it might refer to pressure, or a form of pressure, but I am not sure...
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Why does total internal reflection (TIR) drastically reduces the efficiency of LED?

Total internal reflection (TIR) is the primary reason of efficiency loss in LED bulbs. LED chips are made of GaN, which has a much higher refractive index than surrounding materials. Because photons ...
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How to identify optical and acoustic branch, also longitudinal and transvers branch?

I have a picture describing the dispersion relation of silicon in the first brilioun zone. I am right now confused: how to identify the optical branch and the acoustic branch, also longitudinal and ...
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How does the proof for the area law for 1D systems work?

I am currently reading this paper in order to understand the proof of the area law for one dimensional, low energy systems such as 1D spin chains. The main area law theorem is given on page 13 and is ...
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Interference or diffraction? [duplicate]

Suppose I have $N$ slits separated by a distance $a$. We are sending a light source of wavelength comparable to the slit width. Then which of the effect should dominate: Interference or diffraction? ...
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Smoothness in projected Wannier function ( Construction of Smooth gauge)

I do not understand why the projected Wannier function can be localised in real space. Suppose there are $M$ bands of interest and the projector of those bands of interest is $P_{k} = \sum^{M}_{m =1 } ...
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Why does Ginzburg-Landau functional include $h^2/8\pi$ rather than $B^2/8\pi$?

The preceding part of this question is written [here]. It was part of the question but I'd separated due to its length. Why does the Landau Functional in Ginzburg-Landau theory has the term $\left[\...
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Resource recommendation for path integral formalism in condensed matter

I am familiar with Green's function and perturbation theory for many-body systems. I have learned this theory from Henrik Bruus's book Many-Body Quantum Theory in Condensed Matter Physics. This book ...
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Field theory of Superconductivity $-\text{tr}\left([\mathcal{G}_0\right]_{11}\Delta [\mathcal{G}_0]_{22}\bar{\Delta})= ?$

I'm reading Condensed Matter Field Theory by Altland and Benjamin. In chapter 6, Section 6.4, Ginzburg-Landau theory, They have expanded the action around $\Delta =0$, In doing so they wrote- $$-\text{...
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Quantum Hall state at $\nu=0$ in graphene

I don't understand the meaning of the observed quantum Hall (QH) state at filling fraction $\nu=0$ in graphene at a high magnetic field. A high magnetic field lifts the four-fold degeneracy of the ...
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Fermi surface and external fields

From Wikipedia: "In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied from unoccupied electron states at zero temperature". What does ...
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Why does the the dielectric constant of a ferroelectric increases with temperature, below $T_C$?

The above figure is taken from C. Kittel. When a ferroelectric substance (say, BaTi${\rm O}_3$) at room temperature is gradually heated, the dielectric constant $\varepsilon_r$ first increases and ...
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What's a Sewing Matrix?

I'm reading a paper on graphene that talks about these sewing matrices, but I don't understand their definition. Upon researching it on the internet, I've found the term in other papers, so I assume ...
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How to derive the expression for the effective potential in Kohn-Sham operator in Kohn-Sham density functional theory?

In density functional theory the Kohn-Sham method provides a systematic way to approaching the correct electron density of a given system. Kohn-Sham method uses a non-interacting reference system ...
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Does particle-hole symmetry always imply half-filling and real correlations $\langle c^\dagger_n c_{n+1} \rangle$?

Suppose we had a lattice Hamiltonian $H$ which was symmetric under the particle-hole transformation $$ c_n \mapsto U^\dagger c_nU=(-1)^nc^\dagger _n$$ such that $[H,U] = 0$, where $c_n$ are Fermionic ...
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The superconductor's electromagnetic response and Meissner current

We know "In the superconducting state, the DC electrical resistivity is zero." But other situations has confused me a bit. There are several situations that superconductors interact with ...
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(Discrepancy in the) Statement of Eigenstate thermalization hypothesis

I am trying to understand ETH and unfortunately came across a seemingly contradicting definition by the same author (Mark Srednicki). I don't know which definition is correct. At this instance in this ...
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What is the difference between Collective excitations and quasiparticle in superconductor? How to consider superconductors' optical response?

In the BCS theory, superconductors can be seen as Cooper pair condensates and quasiparticle excitations (Bogoliubov quasiparticle). But in Ginzburg-Landau's theory of superconductivity phenomenology, ...
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Hourglass fermions + going from glide symmetry eigenvalues to energy eigenvalues

In this paper, the authors describe how you'd get an hourglass fermion. The gist (page 2, second column) is that you have the operator $ \bar M_x$ consisting of a translation along z, $ t( c \hat z /...
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$R$ projection operator in entanglement entropy

I was reading a paper about entanglement entropy. The author introduced a real space cutoff operator $R$ which he claimed to project onto a real space subregion. Then he used $\bar P:=RPR$ as an ...
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Topological properties of twisted TMD homobilayers

I'm reading this article about twisted TMD homobilayers (https://arxiv.org/abs/1807.03311) and there are certain topological properties that I don't understand: On page 3, in the paragraph next to Fig ...
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The reason why the Nielsen-Nimiya Theorem doesn't have to hold true in the Floquet system?

According to the Nielsen-Ninomiya (NN) theorem, under appropriate assumptions, the number of right-handed and left-handed particles must be equal in a lattice system. On the other hand, in recent ...
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How do phonons and electron-electron interactions break phase coherence of electrons? Also, do they break time reversal symmetry?

When considering electron scattering, I appreciate that phonons and electron-electron interactions need to be considered in a different light to scattering from a static, disordered potential. With a ...
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Bogoliubov-Valatin transformation generalisation

Considering the following Heisenberg Hamiltonian (with spin $S$ , and $J<0$ for the case of an antiferromagnet) when we only consider interactions between first neighbors in a square lattice in the ...
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How do you bosonise the spin-$1/2$ operator $S_z$?

Consider a 1D spin-$1/2$ chain. After a Jordan-Wigner transformation, the spin-$1/2$ operator $S^z_i$ takes the form $$ S^z_i = c^\dagger_i c_i - \frac{1}{2} \equiv \rho_i - \frac{1}{2}$$ where $\{ ...
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Alternating Tight Binding Hamiltonian

The alternating Hamiltonian may be written as: $$H = t \sum_{n} (-1)^{n} \left[c^{\dagger}_{n+1}c_{n} + c^{\dagger}_{n}c_{n+1} \right] \; \; .$$ I wanted to know the energy dispersion for this system, ...
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Free acoustic phonon propagator

For fun I am trying to find the propagator of a free acoustic longitudinal phonon, using the vectorial displacement field. The Hamiltonian for our system is $$ H_0 = \sum_{\vec{q}} \omega_{\vec{q}} ( ...
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