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Questions tagged [condensed-matter]

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

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How can I plot numerically density of states against energy for semi-Dirac materials? [on hold]

maybe its not good question for this forum but i need to ask it .so please don't mind my question is that how can i plot density of states against energy numerically for the given dispersion ...
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Higgs amplitude mode vs. “spontaneous breaking” of local gauge symmetry

It seems that there are two definitions of the Higgs mode; one primarily used in particle theory, and one used in condensed matter. In the former, we can consider a simple Lagrangian of the form $$ \...
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Nature of density of states for d-wave, s-wave and extended s-wave pairing symmetries

For d-wave, $\Delta(k)=\Delta_{d} (\cos{(k_{x})}-\cos{(k_{y})})$ For s-wave, $\Delta(k)=\Delta_{0}$ For extended s-wave ,$\Delta(k)=\Delta_{s} (\cos{(k_{x})}+\cos{(k_{y})})$ How will be the nature ...
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+100

What is the meaning of the diamagnetic current in linear response theory?

When we consider the response of a quantum lattice model with Hamiltonian $H=H_{kin}+H_{int}$ to an applied vector potential $\mathbf{A}(\mathbf{r},t)$ we obtain the current operator $\mathbf{j}(\...
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Marginal interactions for Fermi surfaces

I am struggling to understand Polchinski’s derivation (https://arxiv.org/abs/hep-th/9210046) of the conditions for marginality of the 4-fermi operator. For a scattering process $(\mathbf{p}_1,\mathbf{...
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Is quantum energy uncertainty underestimated in liquid molecules?

Liquids have the molecular property that the collision frequency (collisions per time) among the molecules is extremely high; it is at the order of picoseconds. Consequently, the Quantum uncertainty ...
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1answer
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Creating a spatial variation of phase in a given superconducting sample

Blundell's book on Magnetism, talks about the generalized rigidities as a general consequence of spontaneously broken symmetries. In this context, it mentions that in a superconductor the phase of the ...
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What are the excitations in the near critical 2D-Ising model in a magnetic field?

Apparently it is well known that the 2D Ising model with $T=T_C$ in a small magnetic field has a mass gap and correlation length $\xi \sim h^{- \frac{8}{15}} $. Further, in a paper in 1989 ...
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1answer
27 views

Swap operation with the Heisenberg Hamiltonian

According to REF 1 equation 3, a SWAP operation can be achieved via the Heisenberg Hamiltonian for spins $H=J(t)\mathbf{S}_1\mathbf{S_2}$ $U^{1/2}_{SWAP}=e^{-i\frac{\pi}{8}}\exp\left(i\frac{\pi}{2}\...
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What is prerequisite for learning electrical transportation in material science? [closed]

I am doing my master's thesis, i already know Quantum mechanics, solid state physics, still studying Thermoelectric properties of nano material. I'm curious to know on what topic i can work in and ...
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Localization of $4f$ in rare earth and $3d$ electrons in transition metals

Is there a justification for why are the $4f$ electrons strongly localized about the nucleus in rare-earth atoms but the $3d$ electrons in transition metals extend further out from the nucleus? I have ...
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Does density of states at Fermi level reduce or increase for decreasing the diameter of a nanowire?

As we decrease the diameter of a nano wire /quantum wire, does the density of the states at Fermi level increase or decrease?. If it does then, Why?
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What is the representation of the different classes of nontrivial textures in an ordered field of biaxial nematics in terms of $SU(2)$-like rotations?

I was reading Mermin's classic review on Topological Defects in Ordered Media, in which he describes ordered media with non-Abelian Fundamental Groups by taking the example of biaxial nematics with ...
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How to decouple the equations in tilted Dirac systems?

I am trying to solve for wavefunctions of 2D tilted Dirac systems, the Hamiltonian for which is given as: $$\hat H = v_{x}\sigma_{x}\hat p_{x}+v_{y}\sigma_{y}\hat p_{y}+I_{2}(v_{t}^{x}\hat p_{x}+v_{t}...
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How is it possible a quadratic Hermitian Hamiltonian $H = b^\dagger b^\dagger + b b$, with $b$ boson, cannot be diagonalized?

How can a Hermitian Hamiltonian $H = b^\dagger b^\dagger + b b$, with $b$ boson, cannot be diagonlized? Given a Hamiltonian $$\hat H = b^\dagger b^\dagger + b b \tag{1}$$ with $b, b^\dagger$ boson ...
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1answer
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How do knife blades become dull?

Knives are normally used to cut softer objects. So the edge of the knifes blade is harder than the substance it cuts through. A blades geometry is more complex, but let's simplify it to the blade ...
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Absence of fermion sign problem at half filling

It is said that in the hubbard model, at $\mu = 0$ , there is no sign problem. I do not see why $\mu = 0$ is necessary in the above argument? For the hubbard hamiltonian, \begin{aligned} H=-t & \...
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1answer
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Conventional unit cells and Bravais lattices

Conventional unit cell is defined in the following: A definition of a conventional unit cell of a lattice is one that contains the same point group symmetries as the overall lattice and is the ...
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1answer
23 views

Localized and extended states in Landau levels due to disorder in Integer Quantum Hall Effect

In the presence of a random potential due to the presence of disorder, the degenerate Landau levels split into a band. It is given that the states in the middle of this band are extended and the ones ...
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Wave Function of the Tight Binding Model

The Gutzwiller wavefunction, i talked in brief in this other question, is introduced to compute the expectation value of the Hubbard Hamiltonian. It is composed by a uncorrelated Slater determinant (...
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Pseudospin in Graphene

According to my understanding, since the honeycomb lattice is not a Bravais lattice, we consider it a superposition of two lattices (say A and B). The spinor wavefunction $\begin{bmatrix}\psi_1\\ \...
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Are there Goldstone bosons in 1D or 2D?

The Mermin-Wagner theorem states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with short-range interactions in dimensions d ≤ 2. And Goldstone bosons ...
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1answer
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Show that the Fermi surface is perpendicular to the Brillouin zone boundary in the nearly free electron approximation

How can one show that the Fermi surface is perpendicular to the Brillouin zone boundary in the nearly free electron approximation? Similar question without an answer: Why does the Fermi Surface cross ...
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What is the reason why at low temperatures the electromagnetic interaction becomes short ranged?

We know that at very low temperatures, the electrons start forming Cooper pairs and generate some sort of eddy current, so that a magnetic flux that is trying to penetrate the low-temperature object ...
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Is it possible to determine configurational entropy of a material experimentally?

Configurational entropy is the entropy due to arrangement of atoms in a material. Is it possible to estimate it thorugh any experiment ?
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3answers
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How to show that the electrons responsible for a current have an energy within $k_BT$ of the Fermi energy?

It is commonly written in textbooks that in metals the electrons responsible for an electric current are the ones that have an energy about $E_F$ and a few $k_BT$ around that energy. See for example ...
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Multifractal behavior of Anderson localized wave function

In Localization theory, I have found wave function at the critical follows multifractal behavior in Anderson 3d model. Also, in Anderson 1d, 2d disorder model the wave function shows multifractal ...
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1answer
60 views

Charge-Vortex Duality for Bosons

Consider a (2+1)d continuum field theory with the Minkowski action $$\mathcal{L}=|\partial\phi|^2-r|\phi|^2-u|\phi|^4,$$ where $\phi$ is a complex field. The theory undergoes a quantum phase ...
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1answer
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Turning into superconductivity---continuous or discontinuous?

The figure below is Onnes' original data. The transition region is very narrow. It suggests a first order phase transition, but still not so conclusive. What is the latest understanding of the ...
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Does the absolute number of Dirac monopoles (ignoring chirality) in a level of a two-level system matter?

In condensed matter systems, integrating Berry curvature within an adiabatic loop in parameter space over a Dirac point of some model usually gives one its chirality ($\pm 1$, for instance). In the ...
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Reference for topology for topological insulators

In the field of topological insulators What topological space do they talk of? Looking for some resources that sheds light on the topology part of topological insulator
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Pulling apart the atoms of a topological insulator

Consider a topological insulator. In order to destroy a topological phase, the band gap of the bulk system should close at some point (passing thru a conducting state), but if the atoms that make up ...
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What happens to topological insulators at finite temperature?

There is a similar question here, but I had a few things I wanted to ask. So basically pretty much all analysis/ theory of topological insulators is for pure wave-functions and conservative ...
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What is the tight binding Hamiltonian for Graphene in terms of the Pauli Matrices?

I have been unable to find an expression for the tight binding Hamiltonian of Graphene in terms of the Pauli Matrices. Please share any reference available. Thank You
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Origin of Josephson voltage equation?

i cant find a satisfying explanation, and I cant figure it out myself, a derivation for the josephson equation: $$U(t)=\frac{\hbar}{2e}\frac{d\phi}{dt}$$ where $U(t)$ is the voltage, and $\phi$ is the ...
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Semiconductor and temperature dependence

Does the conductivity of both intrinsic and extrinsic semiconductor increases with temperature or is it that conductivity of extrinsic semiconductor decreases with temperature just like a conductor ?
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Are quasi-particles really particles?

In my understanding, quasi-particles were just some real world particle (like electrons) but in different environment i.e. an electron in a crystal. But Recently, I have started studying Spintronics/...
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1answer
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Meaning of “Exactly solvable in the large $N$ limit” for the SYK model

Every presentation on the SYK Model (check any youtube lecture by Douglas Stanford, Juan Maldacena, Subir Sachdev, Alexei Kitaev, etc.) claims that it is exactly solvable in the large $N$ limit, thus ...
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2answers
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Heisenberg picture of displacement

In a certain model the displacement operator for the normal modes in a lattice is given by $$u_{s}=\sum_{\textbf{k}}\left(\frac{\hbar}{2mn\omega_{k}}\right)^{1/2}(a_{k}e^{iksb}+a_{k}^{+}e^{-iksb}).$$ ...
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Hubbard model in magnetic field

Let's assume I have a Hubbard hamiltonian in a magnetic field. $H=-t\sum_{j,\sigma}c_{j,\sigma}^\dagger c_{j+1,\sigma}+c_{j+1,\sigma}^\dagger c_{j,\sigma}+U\sum_j n_j,_\uparrow n_j,_\downarrow +\...
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1answer
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Symmetric BCS state

The ground state wavefunction for the BCS can be written $$|\Psi_{G}\rangle\equiv\prod_{\textbf{k}}[u_{k}+v_{k}c_{\textbf{k}1}^{+}c_{\textbf{-k}-1}^{+}]|\phi_{0}\rangle,$$ where $|\phi\rangle$ denotes ...
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Superconductivity and phase overlap

Given the following state $$|\Psi^{\phi}\rangle=\prod_{\mathbf{k}}(u_{k}+v_{k}e^{i\phi}c_{k1}^{+}c_{-k-1}^{+})|\phi_{0}\rangle,$$ where $|\phi_{0}>$ is the vacuum, $u_{k}, v_{k}\in\mathbb{R}$, and $...
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2answers
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How to compute thermodynamic magnitudes with the Green's function?

I'm studying the SYK model and there seems two equivalent approaches for solving it. One is the diagrammatic expansion in the large $N$ limit, where we get self-consistent equations (in imaginary time)...
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1answer
46 views

Chemical Potential of an Intrinsic Semiconductor

I was going through an article called "The chemical potential of an ideal intrinsic semiconductor" and I just cannot understand how the author gets that expression for the chemical potential. I know ...
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Matsubara sum regulator and the Dyson equation

Question: How to determine the sign of a time argument of a self energy? The sign of the imaginary time determines the regulartor one has to use when perfoming Matsubara sum. As an example let us ...
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1answer
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Why do we go beyond two-body interaction?

Actually, my question is why do we study many-body interactions. I have just started working in Fractional quantum Hall systems. There we have Coulomb interactions between electrons, which we know is ...
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1answer
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Momentum distribution Fermi liquid and spectral representation

In a Fermi liquid the momentum distribution shows a jump at the Fermi surface, i.e. \begin{equation}\langle n_{k_F-\delta k} - n_{k_F+\delta k}\rangle = Z_{k_F}\end{equation} with $Z_k$ the strength ...
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1answer
58 views

Real and Imaginary time Green's Functions

In real time, one can calculate the two point function of a given theory using \begin{equation} G(\vec{x},t)=\langle \Omega | \phi(\vec{x},t)\phi^\dagger (0,0)|\Omega\rangle =\int_{\phi(0,0)}^{\phi(\...
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Hund's Rule Coupling in an Effective Hamiltonian/Lagrangian

I am reading a book on Skyrmions, and I am at the part where the interaction of skyrmions with electrons is discussed. The chapter speaks of Spin-Transfer Torque (STT) and makes the following ...
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1answer
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How do I find this relation between total energy and fermi energy?

I am currently studying the Sommerfeld model. I understand how to find the fermi energy $\epsilon_F$ by using the density of states function but I am unsure how to answer this question about the total ...