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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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Finding the phase difference in Rf-SQUID [closed]

In my solution I have assumed that $\phi_{12}$ and $\phi_{ab}$ are gauge invariant. This gives me a final expression where I need to insert the flux, which I set equal to $LI$. I'm unsure which ...
2 votes
1 answer
462 views

BCS Theory: Bogoliubov Transformation for Fermions

I would like to follow up on this question. The Bogoliubov transformation is written as follows (I assume that $u_{\mathbf{k}} = u_k$ and $v_{\mathbf{k}} = v_k$ as well as $u_k, v_k\in\mathbb{R}$): \...
5 votes
1 answer
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How is the BCS ground state a coherent state?

A coherent state is defined as the eigenstate of the annihilation operator $\hat{a}$. It can be obtained from the vacuum of the number operator by acting with displacement operator: $$|z\rangle=\hat{D}...
1 vote
1 answer
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Kinetic Inductance and Magnetic Flux

Superconductors (SCs) are known to have kinetic inductance which is the manifestation of the inertial mass of superfluid. In this link, the concept is explained as follows: When a current flows the ...
1 vote
2 answers
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How can I build a superconductor at home?

How can I make a superconductor at home? I have been interested in making one from scratch, but I have no idea where to begin. I have heard about YBCO superconductors and I feel as though that is the ...
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Is it possible to have a system that show superconducting behavior in magnetization and insulating behavior in resistivity? [closed]

Is it possible to have a system that show superconducting behavior in magnetization measurements and insulating behavior in resistivity measurements? if yes then please provide some references? In ...
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Josephson relations when $V$ approaches the superconducting gap

The standard Josephson relations are $I = I_0 \sin(\phi)$ and $V = \phi_0 \dot{\phi} / 2\pi$. However these equations break down when $I$ exceeds $I_0$, or when $V$ exceeds $V_\text{gap} = 2\Delta / e$...
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1 answer
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Is Number Operator a Generalized Momentum?

In superconducting circuit, the number operator, $\hat{n}$, and phase operator, $\hat{\varphi}$ are conjugate pairs. Is $\hat{n}$ the canonical momentum, conjugate momentum, and also generalized ...
-1 votes
1 answer
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Significance of the phase of the condensate as compared to that of the regular Fermi sea in the Anderson-Higgs mechanism

I do not fully understand how the phase of the charged Cooper pair condensate is different from the phase of e.g. the Fermi liquid in a regular metal. The state of the metal (any quantum state really) ...
1 vote
1 answer
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Superconducting ground-state and Higgs mechanism

I found this article on spontaneous symmetry breaking in superconductors. Using the same arguments as Weinberg, the author demonstrates that the properties of a superconductor are the consequences of ...
8 votes
1 answer
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Superconductivity in graphene with spin orbital coupling, is it proper to let the order parameter on two sub-lattice equal?

I am reading this article: Edge superconducting correlation in the attractive-U Kane-Mele-Hubbard model. Considering just the first part of the article, where a negative-U Hubbard model with the ...
1 vote
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Interpretation of spectral function for Anomalous Green Function

This question assumes we have quasi-particles which can be diagonalized by a BV transformation (here I am using imaginary time and I am in position space): $$ \hat{c}_{i\sigma}(\tau) = ...
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How to derive the ODE from the EOM of vortex?

In the Lagrangian mode we have the equation of motion \begin{align} \partial_\mu F^{\mu\nu}&=j^\nu. \\ D_{\mu }D^{\mu}\phi +\mu^{2}\phi-\lambda(\phi^{*}\phi)\phi &=0. \end{align} Since we ...
1 vote
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Do superconductors have an inner magnetisation?

When applying a magnetic field to a (type I) superconductor, the $B$-field vanishes in its interior. Often I read that the inner $H$-field does not vanish due to the magnetisation of the ...
1 vote
2 answers
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Why does the magnetic field penetrate inside the superconductor?

why does the magnetic field penetrate (that is exponentially decaying over the thin region) inside the superconductor? Does it actually contradicts Meissner effect?
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Why there is a difference in the volume fraction of a superconductor when you do measurement in Field Cooled (FC) and Zero Field Cooled (ZFC) mode?

Why there is a difference in the volume fraction of a superconductor when you do Field Cooled and Zero field cooled? What does that difference indicate?
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1 answer
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Why the resistance in superconductors is zero? [duplicate]

Why the resistance in superconductors is zero? I know the BCS cooper pair formation but why in principle it behaves like that?
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Will every material with strong electron-phonon coupling ($\lambda > 1$) have polarons?

Does polaron formation need only strong electron-phonon coupling? Or does it need something else?
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Derivation of the number operator in the energy basis of a qubit

I am trying to model the capacitive coupling of two transmon qubits. I would like to write the number operator in the energy basis, currently, I am working on using $$ \hat H = \hat H_1 + \hat H_2 + \...
1 vote
1 answer
255 views

Do surface currents in superconductors only arise due to an externally applied magnetic field?

On the topic of surface currents or (screening currents) which are responsible for non decaying eddy currents that expel an externally applied magnetic field, does this phenomenon only occur when ...
0 votes
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940 views

Numerical solution of the BCS gap equation, with Coulomb potential

I'm interested in the excitons condensation, which is described by an equation which is very similar to the standard BCS gap equation. I will be referring to this article: http://arxiv.org/abs/cond-...
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1 answer
248 views

Energy Stored In Superconductor

I have two questions regarding this topic: What is the equation to calculate the energy stored in a superconductor when you apply a current. I’ve been looking it up and have been getting ...
2 votes
1 answer
300 views

Microscopic derivation of the Josephson effect

In section 18.7 of Bruus & Flensberg the authors provide a microscopic derivation of the Josephson effect. The hamiltonian on both sides of the tunnelling junction is just the typical BCS ...
1 vote
1 answer
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Density of states of BCS superconductor and the transverse NMR relaxation time $1/T_1$

I am trying to calculate the spin susceptibility of BCS superconductors at finite temperatures. It's well known that for conventional superconductors, the transverse NMR relaxation $1/T_1$ exhibits a ...
3 votes
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Why are zero-modes preserved on turning on coupling in twisted bilayer graphene model?

In the paper https://arxiv.org/abs/1808.05250 on page 3, they talk about how when the parameter $\alpha$ in the Hamiltonian in Eq. (5) equals $0$, we get zero modes at the Dirac points K and K’. This ...
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Tenfold way symmetry classification for systems with pseudomomentum

For classifying Hamiltonians $H(\vec{k})$ of topological insulators/superconductors in the tenfold way, one has to see whether the Hamiltonians obeys (disobeys) symmetries of the following type (let's ...
4 votes
2 answers
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How do we justify the chemical potential term in a Hamiltonian of interacting fermions?

Consider a noninteracting fermi gas of electrons. If we know the chemical potential it makes sense that the Hamiltonian is $$\sum_{|k| > k_f} E_kc_k^{\dagger}c_k +\sum_{|k| < k_f}E_k c_kc_k^{\...
2 votes
1 answer
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Deriving equations of motion using Landau functional

I am having a difficult time understanding the derivation of the equation of motion using Ginsburg-Landau theory. Suppose $\mathcal{F}[\psi]$ is the free energy functional. Why is it that: $$ \...
6 votes
1 answer
310 views

Temperature-pressure plot for superconducting records?

Eremets et al. (arXiv:1812.01561, Nature 569, 528–531 (2019)) and Hemley et al. (arXiv1808.07695, PRL 122, 027001 (2019)) have reported new high-temperature record for superconductivity, as covered by ...
4 votes
2 answers
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Would a superconductor act similarly to copper when braking a strong magnet on a pendulum

I recently watched this gif (higher quality available here) from this video, showing a magnet swinging towards a large disk of copper, where it stops gently before hitting the magnet. I understand ...
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Connection between superconductivity and breaking of $U(1)$ symmetry in superconductors

$\newcommand{\Ket}[1]{\left|#1\right>}$Suppose I have a total Hamiltonian $H = H_0 + V$ given by the usual kinetic term $$H_0 = \frac{\hbar^2}{2m} \sum_{\mathbf{k}, \sigma = \uparrow, \downarrow} \;...
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1 answer
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A "Classical" Explanation of The Meissner Effect?

I know that the Meissner Effect is fundamentally quantum, but can a similar logic to the one used for normal conductors be applied to superconductors? I am referring to the idea that in normal ...
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1 answer
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Do magnets also attract super conductors?

If a superconductor can be repelled by a magnet (or, well, locked in a certain position by the magnet) can a magnet be attracted to a superconductor. What would happen if you take a peace of metal, ...
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1 answer
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How to fit Werthamer-Helfand-Hohenberg (WHH) equation in a $H_{c2}$ vs $T$ equation?

The Werthamer-Helfand-Hohenberg (WHH) formula $$μ_0H_{c2}(0)=0.693μ_0T_c\frac{dH_{c2}}{dT}|T→Tc$$ was used to estimate μ$_0$H$_c$2(0) at 0 K where only orbital breaking effects are considered in the ...
4 votes
1 answer
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Which part of a real Type II Superconductor magnetization loop represents the Meissner state?

So if we consider an ideal type II superconductor the magnetization should look like this The Meissner state is to be found between $0$ and $H_{c1}$ and the superconductor works as an ideal diamagnet ...
3 votes
2 answers
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Interpolation formula for BCS superconducting gap

In BCS theory, the superconducting gap is given by solving at different temperatures the integral $$\frac{1}{N(0)V}=\int_0^{\hbar\omega_c}\frac{\tanh\frac{1}{2}\beta(\xi^2+\Delta^2)^{1/2}}{(\xi^2+\...
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1 answer
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How does the entropy in BCS superconductor behave?

In low-temperature superconductor the formation of Cooper pairs results with zero resistivity. The transition to the normal state is second-order phase transition. In Ehrenfest classification it means ...
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How is the coupling between order parameter and strain determined from symmetry?

In the article Ehrenfest Relations for Ultrasound Absorption in Sr2RuO4, Sigrist M., Progress of Theoretical Physics, Vol. 107, No. 5, May 2002 A superconductor with proposed p-wave pairing and ...
2 votes
1 answer
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Eddy current brake with superconductor

There are eddy current brakes used with metal plates to stop trains. It converts kinetic energy of the metal plate to heat via eddy current on it. So what if we have a superconducting metal plate and ...
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Induced current in a superconductor

I was recently solving a problem from Jaan Kalda's handouts; Parallel to and at a distance $h$ above the surface of an infinite planar superconductor is an infinitely long straight wire with current $...
1 vote
1 answer
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How to understand the concept of a fluxon, the dual of the Cooper pair?

I've been reading the paper Bifluxon: Fluxon-Parity-Protected Superconducting Qubit by Kalashnikov et al. which deals with a novel type of superconducting qubit. Without going into too much of the ...
0 votes
1 answer
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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 ...
1 vote
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Why is a bosonic condensate not easy to be scattered in a superconductor? [duplicate]

Why does an individual fermionic electron scatter off lattice defects easily while the Cooper pairs are insusceptible? I know they condensate to a same macroscopic quantum state, but still, why can ...
1 vote
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Can one experimentally confirm whether the effective attractive interaction is retarded and its relation with superconductivity?

It's widely believed that in convential BCS superconductors, only after taking the retardation effect into consideration the weak attractive interaction mediated by phonons can overwhelm the strong ...
8 votes
6 answers
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Are photons inside the media massive? If yes, why there is no Meissner effect?

We all know in vacuum travels with speed $c$, hence its rest mass has to be 0. In the media the light speed $v<c$. Then the photon renormalized by the medium (call it "quasi-photon" if ...
2 votes
1 answer
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Normal metal-superconductor action (revealing Andreev reflection)

Short Example A conventional Josephson junction, which consists of a superconductor-insulator-superconductor (SIS) sandwich and is biased by a constant current $I$, has the following action: $$S_{SIS}\...
2 votes
1 answer
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Is there a way to quickly change the current in a superconducting loop?

In rocket designs such as VASIMR, superconducting nozzles are frequently used to focus the resulting plasma jet. This leaves out the question of TVC control mandatory in chemical rocket engines, and ...
0 votes
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Superconductor Cube levitating in Vertical magnetic field

Suppose there's a Magnetic field in vertical direction and we hold and release a superconductor cube so experimentally it is seen that the cube floats/hovers in the same orientation as it was released ...
0 votes
2 answers
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Meissner effect and flux quantization

The Meissner effect states that when we cool the superconductor below the critical temperature and we apply a magnetic field at its direction, then there is field expulsion inside the superconductor. ...
3 votes
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Why does flux pinning prevent a superconductor from moving?

I've seen this answer, which clarifies that superconductors float on top of permanent magnets not because of the Meissner effect, but because of flux pinning. The superconductor is cooled, and in that ...

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