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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Question about superconductivity

A long cylinder of radius $R$ is made from two different material. Its radius $r<r_0$ $(r_0<R)$ part is a material with superconducting transition temperature $T_1$, and its $r_0<r<R$ ...
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What is the physical meaning of phase in a superconductor?

I am trying to understand the physical meaning of phase in the order parameter of a superconductor. In particular,I was looking at this article that states the phase $e^{i\theta}$ in the BCS ground ...
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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 ...
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Why is the AdS/CFT approach to superconductors rarely cited in condensed matter publications?

Let me put things into perspective by comparing with other applications of string theory. Nowadays review papers written by cosmologists about inflation models often discuss string theory scenarios ...
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What theory describes high temperature superconductivity more sucessfully?

We know that there are so many theories on the high temperature superconductivity in cuprate. E.g. the U(1)/SU(2) gauge theory description of doped Mott insulator[Lee, Nagaosa, Wen], the phase-string ...
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Could energy be stored into (not extracted from) the quantum zero point field (like a battery)?

In order to explain the question clearly, I will make a short introduction. In 1962, Josephson predicted that for a sufficiently thin insulating layer, it should be possible for Cooper pairs to ...
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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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Derivation of the BCS Hamiltonian

$$ \hat{H}_{\mathrm{BCS}}=\sum_{k \sigma} \varepsilon_{k} c_{k \sigma}^{\dagger} c_{k \sigma}-\sum_{k k^{\prime}} G_{k k^{\prime}} c_{k \uparrow}^{\dagger} c_{-k \downarrow}^{\dagger} c_{-k^{\prime} \...
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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 ...
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Formulating BCS theory in the functional integral with a real order parameter

Often in BCS theory, people take the order parameter $\Delta$ to be real. I tried to construct a BCS theory with a real order parameter from the start and ran into some trouble. I'd be interested to ...
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Does the path integral of Cooper pairs have a Berry-phase term?

In a BCS superconductor, by Hubbard-Stratonovich transformation, we can integrate out the electrons and get an effective theory for Cooper pairs like $$ S = \int \mathrm{d} \tau \mathrm{d}^3 x \left( (...
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Spherical symmetry of Cooper pair wave function

Can someone please explain to me how the wave function of a Cooper pair is spherically symmetric?
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Mermin Wagner theorem in superconductors, massive Goldstone mode

For a continuous symmetry breaking one receives a massless Goldstone mode which leads to divergent phase fluctuations in 2 and 1 dimension, thus we end up with a disordered state. However in ...
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If BdG Hamiltonian has particle-hole redundancy, how can it be trusted in discussing the topological properties of superconductors?

In BdG Hamiltonians, the particle-hole symmetry is not a true symmetry but rather a redundancy of description. In my oppinion, saying with the presence of particle-hole symmetry is just saying: hey, ...
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Why does Pressure Increase the Tc (Critical Temperature) of a Superconductor?

Just a heads up - please make this answer understandable to around 1st year degree level physics - not PhD research. So I can understand it - thanks. I was wondering why they Critical Temperature (Tc)...
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What is the relation between pseudogap and time reversal symmetry breaking?

Some papers concerning high-$T_c$ superconductor discuss the pseudogap and time reversal symmetry breaking. My questions are: What is the characteristic of order-parameter in pseudogap? How to ...
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Excitation spectrum in BCS theory and mean field theory

I've recently been learning about the BCS theory of superconductivity. An extremely rough idea is as follows: given the interacting BCS Hamiltonian $$ H = \sum_{\vec{k}\sigma} \xi_{\vec{k}} c^{\dagger}...
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Why is the energy of a vortex in a superconductor finite?

I just had a glimpse of the Ginzburg-Landau theory of superconductivity. I am surprised that that the energy of a vortex is finite. This is surprising because as far as I know, in superfluids, the ...
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Current State of Research on high $T_c$ Superconductors

After looking at these two RevModPhys articles, I have found myself perplexed by the current state of high $T_c$ superconductivity research. Seeing as I cannot find any SE articles more recent than 5 ...
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4 votes
2 answers
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Relation between critical temperature and density of states

The BCS theory predicts that the critical temperature of the superconducting transition is given by $$ T_c \approx \theta \exp \left (- \frac{1}{U D(\epsilon_F)} \right ) $$ where $\theta$ is the ...
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Does the theory of holographic superconductors have any application?

I recently became aware of the relatively novel concept of holographic superconductors, and I was wondering whether anyone here has read something about experimental application of these theories. ...
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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}...
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Why is the surface integral ignored when deriving the current equation from Ginzburg-Landau theory?

The Ginzburg-Landau free energy is defined as $$F = \int dV \left \{\alpha |\psi|^2 + \frac{\beta}{2}|\psi|^4 + \frac{1}{2m^*} \left| \left(\frac{\hbar}{i}\nabla - \frac{e^*}{c}\vec{A}\right)\psi \...
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Is there a violation in the Onsager-Kelvin relation in Normal metal - superconductor junctions?

I'm currently reading the paper https://journals.aps.org/prb/pdf/10.1103/PhysRevB.48.15198 It is about charge $I$ and heat $I_H$ currents in NS junctions due to temperature $(\Delta T)$ and voltage $(...
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Why does type-I superconductor behave differently than type-II as $H$ is increased?

As one increases the external magnetic field $H$ above a critical value $H_c$, a type-I superconductor abruptly changes to a normal conductor. But for type-II, the transition is not sharp but gradual ...
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Indefinite Number of Particles in BCS Superconductor and the Higgs-Anderson Mechanism

In general, the BCS ground state wave function can be written as $$|\psi_G\rangle=\prod_k (|u_k|+e^{i\theta}|v_k|c_{k\uparrow}^\dagger c_{-k\downarrow}^\dagger)|\phi_0\rangle $$ According to ...
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how can I understand spin fluctuation in iron based superconductors?

In study of iron based superconductors, one of the starting point is that electrons are weakly interacting(or weakly correlated) such that we can still apply many body perturbation theory(so called ...
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Does the Mermin-Wagner theorem forbid superconductivity in the 2D Hubbard-Model?

"In the 2D Hubbard model (two spatial dimensions) the Mermin-Wagner theorem does not allow a phase transition." I am quite illiterate concerning this theorem and hearsay. Does the theorem ...
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What is a Fermi arc?

What is meant with a Fermi arc in the context of Weyl semimetals? Is this the just a one-dimensional Fermi surface? For example, in electron-doped graphene, the Fermi surface consists of 2 disjoint ...
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properties of p-wave superconductors in a self consistent calculation

2D p+ip superconductors have zero energy mid-gap modes localized at the boundaries as well as in the vortex cores as pointed out in several places such as Read, Green and Ivanov. The modes result in ...
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Lorentz force on superconductor vortices

I am reading a paper on superconductivity and in it it says that the vortices are subject to a Lorentz force given by $$\vec{F}_L=\frac{\Phi_0\vec{I} \times \vec{H}}{cH}$$ Here $\vec{F}_L$ is the ...
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The wavefunction of the superconductor A consists of two parts: B and C

In reading this article, I come across this paragraph: The pink marked place is where I can't understand, why can we use direct product of the former but not the later? This is may be a basic ...
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4 votes
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Precisely speaking, does photon become massive or the phonon become massive, due to Higgs mechanism in superconductor?

Consider the low-energy field theories of superfluids and superconductors. In superfluids, the spontaneous breaking of the order parameter's phase creates phonons as the massless Goldstone bosons.(...
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Why does this 'Quantum Pinned' superconductor allow easy repositioning

I'm confused by videos such as this (popular demonstration of 'Quantum Levitation'): https://www.youtube.com/watch?v=Ws6AAhTw7RA So my current understanding of superconductors is that when in the ...
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How can Multiple Andreev Reflections be explained as a succession of individual Andreev reflections?

I have understood the mechanisms at work in single Andreev reflections (N(ormal)-S(uperconducter) interface) and Andreev bound states (N-S-N). For multiple Andreev reflections of order 3, the ...
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How to generalize BdG equation in order to match a graphene with a metal superconductor?

I want to generalize BdG equation in order to compute the conductance of a junction of graphene with a metal superconductor. The previous works done until now on this hetrojunction is devotted to use ...
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Odd-frequency pairing

What is so interesting in odd-frequency pairing in superconductors (Tanaka)? Why is it worth exploring both theoretically and experimentaly?
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Can flux pinning be used for propulsion in Earth's magnetic field?

I was wondering if the following steps would result in a net displacement on a spacecraft operating in Earth's magnetic field: Turn on a superconductor Use a linear actuator to shift some mass Turn ...
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3 votes
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Why in superconducting cylindrical thin tube of radius $R$ the magentic field lines would be exactly parallel to the axis of cylinder?

Consider a superconducting cylindrical coil of length $L$ radius $R$ and having a current I around its mantle, (Assume that current causes magentic field which passes through the superconductor area ...
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How to derive that resistivity is zero from the BCS theory?

The conventional superconductors can be explained using the BCS theory. Usually, the BCS theory is introduced as follows: We would like to consider the Hamiltonian that describes the system of ...
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Is the superconducting gap the same as the many-body gap in superconductor?

In conventional superconductors, it is well known that there is a gap $\Delta_{\text{sc}}$ to electronic or quasiparticle excitations. This is the gap that shows up when one measures the temperature ...
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BCS groundstate as eigenstate of the Cooper pair annihilation operator

In section 3.7 of his book Introduction to Superconductivity (2nd Ed.), Tinkham states that [...] we note that S has the eigenvalue $e^{i\varphi}$ in a BCS state in which the the phase of $\Delta$ [.....
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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^{\...
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3 votes
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BCS and Feynman Diagrams

I am currently studying the strong coupling theory (by Eliashberg) of superconductivity, which is derived by BCS by considering self-energy diagrams and the following interaction potential $$ V(q, i\...
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3 votes
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Is the supercurrent just below critical temperature only carried by quasi particles?

Since the Superconducting gap vanishes at the critical temperature, the thermal energy gets sufficient to break up almost all the cooper pairs. But, as far as I understood, the supercurrent is solely ...
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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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3 votes
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Can $\mathcal{N}=4$ SYM be interpreted as describing a superconductor?

I am quite fond of analogies between QFT and statistical mechanics, although I am not at all an expert in statistical physics. And I was wondering if it would make any sense to view the (Euclidean) ...
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Diagrammatic calcilation of superfluid and normal densities

Superfluid $\rho_\mathrm{s}$ and normal $\rho_\mathrm{n}$ densities in a Bose-condensed system can be calculated microscopically from the current-current response function $\chi_{\alpha\beta}(\mathbf{...
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what is superfluid weight?

In papers about twisted bilayer graphene, there is the conception of "superfluid weight" which is related to superconducting transition temperature. What do the words mean?
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flux threading through superconducting ring

I have been confused over the wording used in this paper describing RSFQ logic circuits: http://www.mukhanov.com/uploads/LikharevSemenov-RSFQReview_IEEETAS91.pdf From page 6: " If such a single flux ...
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