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Questions tagged [condensed-matter]

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

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Integrability of generalized Richardson-Hubbard model

Recently I got a bit interested in the possibility of finding spectrum of few interesting class of lattice quantum mechanical hamiltonians like Richardson's pairing hamiltonian, 1D Hubbard hamiltonian,...
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Physical examples of log CFTs

There are examples of CFTs having correlators with logarithms. What are the examples of physical systems exhibiting such logarithmic behaviour (particularly in $d>2$ dimensions)?
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1answer
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Diffraction peaks and Miller indices

How do we find out if a diffraction peak is observable using miller-indices?
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24 views

Second Chern class in 2D Haldane model from Atiyah-Singer Index Theorem?

I was reading through a physics-centered exposition of the Atiyah-Singer index theorem and I wondered what it would mean to talk about Haldane's model for the case of a manifold with a boundary. It is ...
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1answer
28 views

What is the difference between Born–Oppenheimer approximation and Condon approximation

Both Born-Oppenheimer approximation and Condon approximation kind of refer to the separation of electronic and nuclear wave function. I'm confused what exactly is their difference. Do we need to use ...
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Rashba spin orbit coupling in tight-binding model

The standard Hamiltonian for a two dimensional fermionic system in a lattice with a Rashba SOI is: \begin{equation} \hat{H} = \frac{p^2}{2m} + U(r) + \alpha_R \hat{z} (\boldsymbol{\sigma} \times \...
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2answers
29 views

Topological materials and fractionalized excitations

I've been told several times that topological materials (such topological insulators) must have "fractionalized" excitations. Equivalently, if a material does not have fractionalized excitations, it ...
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1answer
35 views

How is Meissner effect consistent with the frozen field lines inside the superconductor?

From Meissner effect we know that the magnetic field $\vec{B}$ is zero inside the superconductor. Since $\vec{B}=0$ inside the superconductor (ignoring the tiny penetration effect for the moment), ...
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How self consistency condition works for a superconductors which is finite and does not have periodic boundary condutions?

So if a superconducting system has periodic boundary conditions the s wave superconducting order parameter calculation by self consistency condition is pretty straightforward. However what if I have ...
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25 views

Procedure for Effective Hamiltonian using Perturbation Theory? (Bilayer Graphene model)

Sorry if this is a dumb question as I'm just starting out, but in this paper https://arxiv.org/pdf/1803.08057.pdf on Twisted Bilayer Graphene, the authors claim to use "standard perturbation theory" ...
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1answer
57 views

Bose-Einstein condensation summation to integral

I have a question about Bose-Einstein condensation. Namely, people say that if we go from the summation over the number of particles to an integral using the density of states, we make a flaw in the ...
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1answer
34 views

If I apply a position dependent temperature gradient to a s wave superconductor, would I get a position dependent superconducting order parameter?

What would happen if a s wave superconductor placed in a position dependent temperature gradient, where $T(x)<T_c$ is always satisfied. Would I get a position dependent superconducting order ...
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1answer
42 views

Laughlin state energy gap

I've been reading Girvin's lecture notes on quantum hall effect and in a section on Haldane pseudo-potentials (paragraphs beneath equation 1.108) he says: Because the relative angular momentum of a ...
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Superconductivity energy gap - BCS Theory

What is the origin of superconductor energy gap and physical description on BCS theory and how BCS theory explains the Meissner effect. Can anybody provide me the link to video lectures on all these ...
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38 views

Issues with Miller indices

I have read that to find the intercepts of a plane represented by Miller indices is to take the reciprocal of each index. However, I noticed that does not give the original plane if we had to reduce ...
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0answers
31 views

How does on-site energy M influence Berry curvature and topological transitions in Haldane's model?

SOLUTION: The following papers almost fully-answer my question: https://arxiv.org/pdf/0904.2117.pdf https://arxiv.org/pdf/1111.5020.pdf Essentially, the Dirac points move and merge as M changes. I ...
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22 views

Heat capacity of LJ fluid vs Ideal gas

I am making my first MD simulation about a Lennard-Jones fluid: an Argon system made up of $500$ particles. I need to write e report and answer to some questions. I computed the heat capacity of the ...
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What does the sign of Berry curvature physically mean?

For Haldane’s model, I plotted the Berry curvature as follows: [UPDATE II: It appears as if the four peaks on the sides are due to Dirac points being in the process of moving as the on-site energy ...
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Kanamori hamiltonian, rotational invariance and isospin

The Kanamori hamiltonian, if the coefficients satisfy a certain relationship, can be seen to be rotationally invariant. Its symmetry is $U(1)_C\times SU(2)_S\times SO(3)_O$ (I add the subscripts $C,S,...
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What is the closed-loop line integral of Berry curvature in a two-level model?

I am aware that integrating the Berry curvature over the entire Brillouin zone gives us the Chern number. However, I wonder what a closed loop line integral of the Berry curvature means. I think ...
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1answer
42 views

Hall effect in metals

how the Hall resistivity varies with temperature and magnetic field, in case of metals, semiconductors and insulators?. Can anyone suggest me few books or journals to start with. And is the variation ...
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1answer
21 views

Where is the data for work functions of simple metals?

I am looking for actual, published data on the work function of metals (Al, Au, Cu) that I can analyze by myself using Matlab. Google Scholar only offers published articles on the utilization of the ...
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0answers
33 views

Reason for gold being the most malleable and ductile of metals

I understand how fcc structure enables plastic deformation in metals, but why is gold, in particular, the most malleable and ductile of fcc metals? Is there something about the electronic structure ...
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Are Kondo insulators topological insulators? What are their relationship to superconductivity?

Reading about the Kondo effect and Kondo insulators, I found they are strikingly similar to topological insulators. Are Kondo insulators topological insulators? Related question, due to their ...
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1answer
39 views

BCC to FCC lattice conversion

In the book Condensed Matter Physics by Marder I have read that an FCC lattice can be obtained by expanding a bcc lattice along one axis by a factor of $\sqrt{2}$. How can I get that mathematically?
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What is an intuitive explanation of wave ordering vector $Q$? (Pierls Instability)

How does the wave ordering vector $Q$ order a CDW? I saw this vector while studying the following system. We have a system with $N$ sites and $N/2$ spinless fermions and system is in the fully ...
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Variational wave functions in many-body physics

One of the very famous variational wave functions is Gutzwiller wave function (GWF) which explained Mott-insulator transition back in 60s/70s. It is analoguous to the idea of Projector Monte Carlo ...
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25 views

Why hexagonal closed packed structure is not a Bravais lattice?

Why is the hexagonal closed packed structure not a Bravais lattice? How can one readily say that a particular lattice is Bravais lattice or not?
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1answer
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Pauli principle for “Phonons”

I'm reading in Feynman's "Statistical Mechanics" Chap. 6.4 about a system of $M$ interacting particles, they may be bosons or fermions. Let the hamiltonian be $$ H=\sum_i^{3M}p_i^2+\sum_{ij}^{3M}U_{...
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1answer
63 views

How does projector Monte Carlo method work?

Projector Monte Carlo states that if we have a trial wavefunction $|\phi\rangle$ which is not orthogonal to true ground-state $|\psi\rangle$ of the system then application of a projector $$P=\exp{(-\...
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30 views

interpretation of the retarded many-body Green's function as particle propagator

Recently I realized that I might have overlooked, or I misinterpret, something about the retarded Green's Function in the context of many-body theory. Let's consider the simple case with: $$G_R(\vec ...
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0answers
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How to implement running of coupling constants in condensed matter

Good evening. I am currently studying finite range corrections to Bogoliubov theory. Basically I assume that $V(q)=g_0+g_2q^2$, as a low energy expansion. While computing some integrals in this area, ...
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1answer
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Is the Bogoliubov quasiparticle boson or fermion?

The Bogoliubov quasiparticle combines the properties of a negatively charged electron and a positively charged hole, so here we have two fermion and the quasiparticle have an integer spin. By this ...
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Book recommendations - Topological Insulators for dummies

Is there a pedagogical explanation of what is a topological insulator for those that do not even know what the Berry phase is but have a basic understanding of quantum mechanics and solid state ...
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Visualizing k-space tori in 3D

In many introductions to topological insulators (in the exposition of Haldane’s model, for example), we represent the parameter space, a torus, on a plane with axes running from $0$ to $2\pi$. In an ...
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1answer
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What is the physical significance of Gaussian curvature in condensed matter physics?

In basic models concerning two-level systems, we deal with manifolds such as the Bloch sphere and torus. I believe that the Chern number is what dominates the theory in terms of ties to differential ...
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What is the difference between the Kubo and Kubo-Greenwood formulas?

The general formula for linear response functions (and particularly for a conductivity) is referred to as the Kubo formula or the Kubo-Greendoow formula. What is the difference between them? In the ...
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27 views

Tunneling junction in electromagnetic field [closed]

Why in presence of electromagnetic field hamiltonian,describing 2 systems with tunneling(for example josephson junction ) $$H=H_L+H_R+T(I+I^{\dagger})$$ where $I=c_Lc^{\dagger}_R$ is tunneling ...
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1answer
45 views

$4\times4$ Dirac Hamiltonian in Graphene

When linearizing the Hamiltonian of Graphene in reciprocal space around $\vec{q} = \vec{k}-\vec{K}_\pm = \vec{0}$, where $\vec{K}_\pm$ are two independent Dirac points, one can get two Hamiltonians, ...
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How do we know that the system is metallic from linear Density of states?

In principle, if we have a finite weight of LDOS at the fermi energy, we have a metallic state. What bin size should we choose around the Fermi energy to know whether the system is metallic? For eg, ...
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Which are the current open problems in solid state physics? [closed]

I am chemist trying to get an idea of which are the trends now in solid state physics and what problems researchers in this area try to solve. I kindly ask you to name the problems that are found more ...
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21 views

Dresselhaus linear and cubic terms

I've been trying to understand Dresselhaus effect, described here. I've been looking up references to find when the cubic term becomes more dominant than the linear term and vice versa. For example, ...
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0answers
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How does Laughlin argument for hierarchical fractional quantum Hall effect work?

For 1 level and 1 layer $1/q$ FQHE let's say $q=5$ we have the following argument for Laughlin gauge principle. It says that if we adiabatically increase the flux from $0$ to $q\phi_0$ of a corbino ...
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0answers
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Topological soliton objects in Minkowski v.s. Euclidean spacetime?

What makes the distinctions between the soliton objects in Minkowski or in Euclidean spacetime? It looks that usually, the Euclidean path integral is easier to be performed in many cases. In fact, ...
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0answers
30 views

Are broken time reversal symmetry and inversion symmetry forbidden in a Weyl semimetal?

In much of the literature floating around, it is commonly implied that an important part of obtaining a Weyl semimetal phase is to break either time reversal symmetry or inversion symmetry. However, ...
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1answer
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What is the meaning of a Fourier Transform in an electric field $E(\omega,t)$?

There is this electric field in one dimension: $$ E(\omega,t) = E_0 \cos(\omega t) $$ It is reaching the surface of a semiconductor. The number of photons reaching the surface per unit of area is ...
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33 views

Why $n=1$ in Bragg' s condition?

While studying XRD pattern , most of the time we use n= 1 in the Bragg equation. Why we prefer n=1? Why don't we use n = 2 or 3 ?
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1answer
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What is nesting/ what is a nesting vector in energy contour plots?

I am making different plots for a 2-d non-interacting tight binding Hamiltonian $$ H = - t \sum_{<ij>, \sigma} c_{i \sigma}^{\dagger} c_{j \sigma} + h.c$$ I get the dispersion relation $$\...
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48 views

Understanding the fractional quantum Hall effect in Chern-Simons formalism described in Wen's book

So I study fractional quantum hall effect with Chern-Simons formalism by using Wen's book, this is an excellent book, but it assumes that you know field theory very well thus it has gaps between steps....
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Practical/experimental difference between (quantum) Heisenberg and (classical) Ising model

I have read a few discussions about the difference between the Heisenberg model (using quantum spin operators) and Ising model (with spins $\pm 1$), notably this one or this Quora post. All the ...