Questions tagged [condensed-matter]
The study of physical properties of condensed phases of matter, including solids and liquids.
4,711
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Where can I read about Valleytronics?
Where can I read about Valleytronics? Are there any good books or review papers on this topic? And which are the most influential papers?
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44
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Brillouin Zone Summation
If one has the following summation:
$$\frac{1}{A}\sum_{\vec{k}} F(\vec{k})$$
which is taken over all k-space and $A$ is the area of the unit cell from the system itself. I want to them limit this to ...
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spin operator in fermion creation and annihilation operators
There's a site (quantum well, atomic orbit, etc) that can host a pair of electrons, with corresponding creation and annihilation operators:
$c^\dagger_\uparrow,c_\uparrow,c^\dagger_\downarrow,c_\...
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50
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Quantum pressure of a Bose gas in a harmonic trap: Why is the result divergent?
The quantum pressure of a Bose gas in the Thomas Fermi limit with contact interactions in a symmetric harmonic trap is determined by (Pitaevskij & Stringari, 2016):
$E_{K}=\int d\mathbf{r}\frac{\...
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Question about the duality between 2+1 d transverse-field Ising model (TFIM) and $\mathbb{Z}_2$ gauge theory
I was reading McGreevy's Lecture notes Where do QFTs come from?
, and on chapter 5 he talks about a duality between the $2+1d$ transverse-field Ising model (TFIM) and the $\mathbb{Z}_2$ gauge theory, ...
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Tight binding hamiltonian graphene [duplicate]
I'm stuck on solving a question regarding the tight-binding hamiltonian for graphene.
I have been given a hamiltonian that looks like this (where the spin has been omitted since hopping is independent ...
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1
answer
33
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Identity of bosonic coherent states
I have a short question about the meaning of the identity of the bosonic coherent states.
Before I ask the question I will explain some background.
The eigenstate of the bosonic annihilation operator $...
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27
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Expansion of interaction potential in terms of spherical harmonics in unconventional superconductivity
I am currently reading the book Introduction to Unconventional Superconductivity by V. P. Mineev and K. V. Samokhin. In Equation (1.6), the interaction potential $V$ is expanded in terms of spherical ...
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1
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Non-Saturation in Interacting Bose Gas Integral
I am independently working through some problems on Bose-Einstein condensation. In particular, I am trying to show that—in the Hartree-Fock mean-field approximation—for a Bose gas with contact ...
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Berry curvature and eigenvalues [closed]
I have a simple question. I have 4 Berry curvatures corresponding to the band structure described by the eigenvalues. How can I verify from which eigenvalue is the specific berry curvature?
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Electron in magnetic field and slowly varying potential $V(x)$
What are the approximation methods for the spectrum and wavefunctions of a 2D electron in a perpendicular magnetic field $B$ and a scalar potential $V(x)$ which is slowly varying on the scale of the ...
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Leading thermal corrections to Lindhard susceptibility
I am interested in deriving the leading temperature-dependent correction to the zero-temperature static Lindhard susceptibility of a homogeneous free electron gas. My starting point is the following ...
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Tight-Binding Hamiltonian Graphene
I'm stuck on solving a question regarding the tight-binding hamiltonian for graphene.
I have been given a hamiltonian that looks like this (where the spin has been omitted since hopping is independent ...
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0
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18
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Symmetries near the K/K' points in graphene
I am trying to understand one paper and I have a problem with symmetries.
The authors introduce the 2x2 Bloch Hamiltonian as
$$
\mathcal{H}(\textbf{k}) = \textbf{h}(\textbf{k}) \cdot \sigma,
$$
where $...
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1
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How does one produce a condensate?
In physics textbooks, one learns about Bose-Einstein condensate and it is all about taking thermodynamic limits. Of course, in real life, infinite systems do not exist. So, picture the following ...
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Retarded green function of tight-binding Hamiltonian [closed]
I want to compute the retarded Green function of a one-dimensional tight-binding model on $N$ sites with periodic-boundary conditions.
The Hamiltonian is:
$$
H_0=\sum_k \epsilon_k c_k^\dagger c_k
$$
...
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Continuum formulation of the Kitaev chain
In Kitaev's seminal paper (https://arxiv.org/abs/cond-mat/0010440), the Kitaev chain is described in a lattice formulation. On the other hand, many of the original papers on the the related ...
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Hall Conductivity of Maxwell Action [closed]
I am currently reading David Tong's notes on Chern-Simon's theory and below equation (5.5), he makes the statement:
"The action (5.5) has no Hall conductivity because this is ruled out in d = 3+...
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What's physical meaning of 2-point correlation function in holographic condensed matter?
Background: In AdS/CFT, we can do calculations in AdS spacetime, and get the result in CFT. When we consider RN-AdS black hole/brane, 2-point correlation functions in CFT can be obtained, which are ...
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Examples of operators like multi body fermions in finite potential well with total energy being sum of energies, and not entirely homogeneous
I'm looking for examples of systems with operators like the 2 fermion system in finite potential well where the total energy
$\lambda(k) = \lambda_1(k) + \lambda_2(k)$
where $k$ is the depth of the ...
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1
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Fourier transform of the Heisenberg antiferromagnetic model
I have a short question about the Fourier transform of the antiferromagnetic Heisenberg model.
The Hamiltonian, written in terms of bosonic operators, is:
$$ \widehat{H} = -NJ\hbar^2s^2 + J\hbar^2s \...
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4
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Meaning of the momentum vectors $\mathbf{k}$ in electronic band structure
In solid-state physics, I struggle to understand momentum vectors $\mathbf{k}$ in reciprocal space. We usually draw a picture of a Brillouin zone as follows (hexagonal in this case):
And we can then ...
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1
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Fractional filling of Laughlin wavefunction
I am not clear about the following argument why Laughlin wavefunctions have $1/m$ filling.
The single-electron wavefunction in the zeroth Landau level is
\begin{equation}
\psi_{m}(z)\sim z^m e^{-|z|...
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Quantum phase transition in condensed matter
I want to know that, for any spin-chains in condensed matter Physics like X-Y spin model, Kitaev model 1-D only in which degenerate point is critical point. Is it necessary that the critical points ...
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Why does flowing current break time reversal symmetry?
I am reading about the Quantum Hall Effect. In a course, they wrote that
How does one get a Hall effect? The key is to break time-reversal symmetry. A flowing current breaks time-reversal symmetry, ...
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Why does mirror/inversion symmetry exclude nearest-neighbor spin-orbit coupling in the Kane-Mele model?
I've been reading about the Kane-Mele model and noticed that it does not include nearest-neighbor spin-orbit coupling, with explanations often pointing to mirror symmetry as the reason. Could someone ...
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1
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Quasiparticle Density of States
In this paper we have the following:
The corresponding quasiparticle density is given by the equation
$$n_{qp} = 4N_0 \int_\Delta ^\infty dE \frac{E}{\sqrt{E^2 - \Delta^2}} f(E),$$
where $N_0$ is the ...
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1
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Tricky Integral: Evaluating Renormalized Ultraviolet "Divergent" Integral
I am trying to rederive the results presented in the paper, in particular equation (30). That is, I am trying to compute the correction to the ground-state energy of a dipolar condensate due to beyond-...
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Quantum master equation for light in medium with dissipation
The effective theory of photons in medium is usually obtained by inserting the electric susceptibility $\chi$ (linear or nonlinear) into $\int \mathrm{d}{\mathbf{D}} \cdot \mathbf{E}$ and complete the ...
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Cuprate Superconductors parameters
What are the parameters for cuprate superconductors, is it the same with normal superconductors? Because I was wondering if the high temp and low temp makes the difference.
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What is Robert B. Laughlin saying about quantum field theory?
Robert B. Laughlin, A Different Universe states the following concerning the relationship between superconductivity and quantum field theory. I do not understand why he says "the microscopic ...
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Discretising Hexgonal Brillouin Zone
I am looking at a system at which I have a 2D Hexagonal Brillouin Zone (BZ). The aim is to take the following type of procedure:
$$
\frac{A}{(2\pi)^2}\int_{BZ} F(\vec{k}) d\vec{k} \hspace{5pt} \...
5
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2
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Ground state energy of infinite Heisenberg XXX model with open or periodic boundary conditions equal?
I was wondering if there is anywhere a formal proof that shows that the ground state energy of a Heisenberg XXX model with periodic boundary conditions becomes equal to the ground state energy with ...
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How to know the relationship among the superconducitng phase , the gap, and the gapless edge states?
I feel puzzled about how to decide whether a material is in the superconducting phase, whether the gap can decide the superconducting phase, and whether there exists the gapless edge states.
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Spectral function of superconductor in the BEC regime: how does Higgs mechanism affect the spectrum?
Consider the standard BCS theory but assume that the interaction energy $U$ that enters the definition of gap parameter (i.e. $\Delta = (U/N)\sum_k \langle c_{-k\downarrow} c_{k\uparrow} \rangle$, ...
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Position-dependent Fermi velocity
In models of strained graphene one seems to obtain a position-dependent Fermi velocity. By this I mean that if the original Dirac operator is
$$ H = v_0(\sigma_1 p_1 + \sigma_2 p_2),$$
with constant ...
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1
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Obtaining the Ising and XY model from the XYZ $O(3)$ model
I have the classical XYZ model Hamiltonian $\mathcal{H}$ with a magnetic field $\vec{H}$ given as
\begin{equation}
\mathcal{H} =
-\sum_{i< j} J^x_{ij}S_i^xS_{j}^x + J^y_{ij}i^yS_{j}^y+ J^z_{ij}S_z^...
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$\vec{k}\cdot\vec{p}$ Hamiltonian approach
I am new to reading into the $\vec{k}\cdot\vec{p}$ approach.
Where for a periodic function $u_{\vec{k}}$, which satisfies the Schrodinger equation:
$$
H_\vec{k}u_{\vec{k}}=E_{\vec{k}}u_{\vec{k}}
$$
...
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1
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CDW correlation function for 1D Dirac fermion in condensed matter
I am following Shankar's lecture notes on bosonization, specifically the theory of left-/right-moving fields for a low-energy 1D fermionic chain. For now, I ignore the Heisenberg time dependence of ...
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1
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Diagonalize a many-body Hamiltonian
Assume we start with a generic many-body Hamiltonian:
$$
H=\sum_{ij} t_{ij} a_i^\dagger a_j+\sum_{mnlk}U_{mnkl}a_{m}^{\dagger}a_{n}^{\dagger}a_la_k.
$$
Now if there is only the one-body part, which ...
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The total energy of an atomic supercell with a local dipole moment in an external electric field
How to define the total energy of an atomic supercell with a local dipole moment in an external electric field?
The figure below illustrates the two cases of the local dipole moment within an atomic ...
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Particle density and current in terms of Green function
Consider a non-relativistic free-fermion system. I am wondering how to calculate observables like average particle density and average current in terms of momentum-space Green functions. I know that ...
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How to calculate the Green function of 1D Kitaev chain?
After performing Jordan-Wigner transformation, a uniform transverse Ising model becomes a 1D Kitaev chain as
$\hat{H}_{p=0,1} = -J\sum_{j=1}^{L}{(\hat{c}_{j}^{\dagger}\hat{c}_{j+1}+\hat{c}_{j}^{\...
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1
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Why does the energy gap of sublattice-symmetric systems never close?
I am studying from this famous site some symmetries useful for topological quantum matter.
At some point, talking about the particle-hole symmetry, it states:
You can however notice that, unlike in ...
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Expectation value of non-interacting groundstate
Assume that I have a tight binding model given in second quantized form as follows;
\begin{equation}
H = \sum_i f_i^{\dagger}f_i + t \sum_{i,j} f_i^{\dagger}f_j
\end{equation}
In real space, ...
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Finite temperature Greens function simplification
I am currently studying topological insulators using Topological insulators and superconductors by Bernevig. In chapter 3, section 3.2.2, he has derived the finite temperature Green's function using ...
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Do the fractional electric charges in FQHE violate the Dirac quantization relation?
Dirac quantization relation says that the electric charge must be quantized if there is a magnetic monopole in our universe. But the fractional quasi-particles and quasi-holes in FQHE have fractional ...
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Real part of Raman response function in linear response theory?
When we calculate the Raman scattering, we usually derive the imaginary part of the Raman response function. The general formula of the imaginary part is given by
\begin{align}
\text{Im}[I(\omega)] \...
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Is the flat band of zigzag ribbon topological or just a state of topological origin?
In my understanding, an edge state has topological origin if its existence is bound to a nontrivial topological invariant. An edge state is topological if it has topological origin.
The flat bands of ...
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Programming a self-consistent hamiltonian in the momentum space
I would like to know what the procedure should be to determine the orbitals of a periodic lattice considering a Hamiltonian in the momentum space. For example, I think the most general expression for ...