Questions tagged [superconductivity]

Superconductivity is the transmission of current with no resistive losses, and is one of the most active areas of condensed matter physics research.

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Correct way of computing the conductivity from Kubo's formula in superconductivity

Consider a full Hamiltonian $H=H_0 +H_1$ on a lattice with hopping terms $H_0$ of the form $t c^* c$ and attractive interaction $H_1= -V c^* c^* c c$ so that superconductivity can occur. We can then ...
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Why is a band insulator showing no meissner effect?

In order to see if a system could show meissner effect, one has to calculate the linear response of EM field, and to see whether the diamagnetic term($\mathbf{j}\sim\rho\mathbf{A}$) is canceled by the ...
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Forming Majorana creation/annihilation operators from Dirac creation/annihilation operators

In the content of 1D p-wave topological superconductor, we usually say that we can decompose a complex electron creation operator at site $j$ into \begin{equation} c_{j} = \gamma_{2j-1} + i \gamma_{2j}...
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Has the equivalent of the Higgs boson in condensed matter been detected?

I know that the Higgs mechanism has some analogous models to theories that describe the behaviour of quasiparticles in condensed matter, like in superconductivity and other spontaneous symmetry ...
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What is the construction of Charge Qubit - Cooper pair box?

I have to dive deeper into the construction and architecture of quantum computers but I am stuck with how a charge qubit is manufactured. I know the basic circuit but I am unable to understand the ...
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How do I go from the eigenvalues (band structure) and eigenvectors of a 2D superconductor to its optical conductivity?

In the supplementary information of this Ni et al. paper "Plasmons in graphene moiré superlattices", we have a "Kubo formula" that's used to obtain the optical conductivity of a ...
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Decomposing complex fermions into Majorana fermions (in 1D p-wave superconductor) and its relation to Majorana rep in (3+1)D QFT

I am following Topological Insulators and Topological Superconductors by B. A. Bernevig and T. L. Hughes. In ch. 16, the lattice model of 1D p-wave superconductor is solved by decomposing the complex ...
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Particle Hole Symmetry of BdG Hamiltonians

It is straight-forward to verify that any Hermitian BdG Hamiltonian of the form $$ \mathcal{H} = (c_1^\dagger, c_1, c_2^\dagger, c_2,...) \begin{pmatrix} H_{11} & H_{12} & \cdots \\ H_{21} &...
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Electron phonon coupling within field integral formalism

Reading Altland and Simons' "Condensed matter field theory" I am stuck in the exercise called "electron phonon coupling" in section 4.5. The exercises is about integrating out the ...
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Analogue of scalar potential in London equation

The London Equations to describe superconductivity phenomenologically are: $$ E = \frac{\partial}{\partial t}(\Lambda J)$$ $$B = -c \nabla \times (\Lambda J)$$ with $\Lambda = m/ne^2$. It is ...
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Which is the best simulation program to simulate type-II superconductors?

I'm currently doing a research project and I want to do a simulation on type-II superconductors being suspended due to flux pinning and seeing how changing temperature and applied magnetic field can ...
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Do the accelerated (-2 charged) Cooper pairs in a closed superconducting circuit emit photons?

According to my current knowledge, the Cooper-pairs in a closed superconducting circuit should "feel" a centrifugal force. The (-2) charged pairs are therefore accelerated. Do the Cooper ...
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Superconductivity in ceramics

I understand that superconductivity mainly occurs due to the formation of the Cooper pairs in which electrons, instead of repelling each other, actually attract because one electron actually attracts ...
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How to calculate a single Abrikosov vortex's structure in superconductor through Ginzberg-Landau theory when $\kappa$ near $1/\sqrt{2}$?

As the title. We can find the approximate solution for large $\kappa$ in any textbook about superconductor.
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Majorana modes at the edge of a QSHI

I am currently looking at Fu and Kane paper: Phys. Rev. B 79, 161408(R). They write the QSHI edge states as $H_{\text{edge}}=\psi^{\dagger}(-iv\sigma_{z}\partial_{x})\psi$ where $\psi=(\psi_{\uparrow},...
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What's the relation between irreducible representation and $d$-vector?

In many papers, especially these related to the triplet superconductor, the superconductor order parameter, the d-vector, always appears together with the irreducible representation of the space group....
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What determines the height at which a superconductor hovers? [duplicate]

What determines the height at which a superconductor levitates? Can you just place it randomly in the magnetic field? What are the limits of superconductors?
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Deriving Continuum BdG equation from Tight-Binding model for Graphene-Superconductor interface

Background My question concerns Beenakker's paper on "Specular Andreev Reflection in Graphene": cond-mat/0604594 (arxiv)/Phys.Rev.Lett. 97, 067007 (The same topic is also discussed in Rev. ...
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$I-V$ curve of rf-driven Josephson junctions (Shapiro steps)

I look for a rigorous mathematical explanation of so-called Shapiro steps in Josephson junctions, the AC phenomenon of current jumps at specific values of voltage as presented in the picture below. A ...
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How is the supercurrent created?

Why and how is the supercurrent generated in a superconductor in response to an applied magnetic field? Does it flow only along the surface? If yes, why?
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Geometric formulation of Ginzburg-Landau Theory

I'm now trying to integrate the Maxwell equation and the Ginzburg-Landau Theory in the geometric form because it can be suitable for FEM based simulation. Wikipedia tells me the form of the equation ...
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Symmetry of the energy gap and specific heat in BCS theory

I know that in BCS theory an energy gap $\Delta(\mathbf{k})$ with s-wave symmetry would lead, in the limit for very low temperature, to a term in the free energy proportional to: $$ F \simeq e^{-\beta ...
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Is there a superconductor that is insulator above the transition temperature?

Is there a superconductor that is insulator above the transition temperature? What is the transition temperature of that compound? Thanks for your answer!
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Does the superconducting Energy Gap Depend on the Density of Carriers?

Does the superconducting energy gap depend of the charge carrier concentration? If so, what is the dependency and is there a way to prove it theoretically?
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The ratio of cooper pairs and normal electrons in superconducting state

Is there a certain ratio between cooper pairs and normal electrons above which the sample can be said to be in a superconducting state? According to the Ginzburg-Landau theory the sample is in a ...
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When two objects with a potential difference existing between them are connected by a superconductor, will the potential difference cease to exist?

We know that voltage/potential difference is the amount of work done or energy released by the battery/cell for transferring a unit charge for higher potential to lower potential. Now, when we connect ...
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How to obtain the optical constants (dielectric function or complex conductivity) of a material from its band structure?

I know that the complex conductivity ($\sigma = \sigma_1+i\sigma_2$) is related to the dielectric function ($\epsilon = \epsilon_1+i\epsilon_2$) by: $$ \epsilon_1 = 1 - \frac{4\pi\sigma_2}{\omega} \\\...
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Reference request for vertex correction of electron-phonon interaction beyond Migdal's theorem

I am considering the calculation of the vertex correction due to electron-phonon interactions. Specifically, I am looking for solutions to the integral (Eqn. 1) $$\int dq G(q)D(q-p)G(p+k)$$ where $dq=...
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What are possible experimental (optical/microscopic/spectroscopic) observables for identifying and differentiating superconductivity?

In a system one is analysing for superconductivity signatures, what are possible experimental (optical/microscopic/spectroscopic) observables for identifying and differentiating superconductivity?
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How to prove that equivalent spinless $p$ wave superconductor can be emerged from $s$ wave superconductor + topological insulator heterojunction?

In L. Fu and Kane's paper they that spinless px+ipy wave superconductor can emerge from s wave superconductor + topological insulator heterojunction,But my result is not the same as their paper.Could ...
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Meissner Effect and Lorentz Force Paradox?

The Meissner effect expels magnetic field lines in a super conductor, see the picture below. Left is normal conducting, right is the superconducting state. If I have a superconducting wire of radius $...
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Gibbs free energy density in superconductivity $g=f-\frac{1}{4\pi}B\cdot H$

By definition, $G=F+PV$, where $G, F, P, V$ are Gibbs free energy, Helmholtz free energy, pressure and volume, respectively. How to derive the formula shown in the title ($g$ and $f$ are the density ...
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Supercurrent phase and gauge change: why a specific choice for the quantum phase?

I am following the following lecture notes: http://web.mit.edu/6.763/www/FT03/Lectures/Lecture9.pdf In the last slide, we see how a gauge change for the EM field impact the phase of the wavefunction. ...
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Will superconductor levitate on Earth magnetic field?

We know earth has both gravity and magnetism (which is very weak). geomagnetism starts at south pole and ends at north pole. If I take a large sheet of superconductor (very thin and several kilometers ...
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How the electric field inside an ideal current carrying wire can be zero?

I know that there are several posts on the same idea, and I have read most of them, but still, my questions persist. I have listed the other posts on the topic at the end of this post. All the other ...
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Magnetic levitation using permanent magnets

Is it possible to achieve magnetic levitation (rail) using permanent magnets? So no electromagnets or superconductivity. If yes, how? If not, why not?
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How to observe off-diagonal long range order in superfluid?

off-diagonal long range order in superfluid is an effect that the matrix element of the single particle's density matrix remains finite in the long distance limit. My question is: how to prove this ...
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What is the “BCS” ground state of a p-wave superconductor?

$\newcommand{\Ket}[1]{\left|#1\right>}$ In BCS theory (I always understood this as referring only to s-wave pairing), the ground state wavefunction takes the form $\Ket{BCS} = \prod_k(u_k + v_k c_{...
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Protected Majorana Zero modes in Kitaev Chain

Kitaev's one-dimensional p-wave superconductor Hamiltonian${}^\dagger$ is \begin{equation} {\cal H}_{JW}=-J\sum\limits_i(c_{i}^\dagger c_{i+1} + c_{i+1}^\dagger c_{i} + c_{i}^\dagger c_{i+1}^\...
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Why is the supercurrent the functional derivative of the Ginzberg Landau free energy with respect to the vector potential?

In the book "Superconductivity, Superfluids and Condensates", they write down the macroscopic free energy to be $$ F_s(T) = F_n(T) + \int\left(\frac{1}{2m^*}\left|\left(\frac{\hbar}{i}\...
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Contemporary resources for holographic superconductivity

I am looking for more recently-written works (either major papers or review articles) on holographic superconductivity, preferably from 2019 or 2020. The main reviews I know are the following: Sean A. ...
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Hoe does the entropy in BCS superconductor behave?

In low-temperature superconductor the formation of Cooper pairs results with zero resistinvity. The transition to the normal state is second-order phase transition. In Ehrenfest classification it ...
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Can stable magnetic field induce current?

I read about a experiment conducted in 1933 by W.Meissner that follows: Metal was put in constant magnetic field then been cooled down in order to enter superconductivity state. Then researchers ...
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Analogy between Meissner effect and dielectric breakdown

For a conventional superconductor, there is a critical external magnetic field beyond which a superconductor will transition to its normal state. To me this phenomenon seems analogous to its electric ...
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Specific heat of a vortex lattice in a d-wave superconductor

I am looking for a reference that discusses the thermodynamic properties of Abrikosov lattices in d-wave superconductors, especially the discussion to calculate the specific heat of vortex lattice in ...
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Superconductivity Properties, energy gap

What are the properties of a material to become superconducting? Is the existence of an energy gap already sufficient for superconductivity? Greetings
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Converting a perturbing Hamiltonian to the following form

I'm reading through Tinkham's Super Conductivity and I am having some issues with getting to equation (3.97). Beginning with the perturbing Hamiltonian the relevant equation is: $$ \hat{H}=\frac{ie\...
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Schrodinger equation of spin-singlet wave function

I'm reading the book Introduction to superconductivity by Michael Tinkham and encountered a small math problem. In page 44, we need to substitute the spin-singlet two electrons wave function $\sum\...
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What are gapless superconductors?

How are superconducting materials classified as gapped or gapless, also is this same as saying that a superconductor is conventional or unconventional? Could you explain how this is linked to topology ...
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Open non-periodic boundary condition

In the paper "Marra, Nitta, PRB 100, 220502(R)", they have used 'open non-periodic boundary condition' during direct diagonalisation of the lattice Hamiltonian. What exactly is 'open non-...

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