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The reason for the coeff is in the definition of $\mathbf{B}$ vs. $\mathbf{H}$: $$\mathbf{B} = \mathbf{H}+4\pi \mathbf{M},$$ and that $4\pi$ is there because it is not in the definition of the Coulomb force between magnetic poles when Gaussian units are employed. No matter what you do you will have a $4\pi$ thing somewhere in the Maxwell-Ampere-Lorentz-...

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Particle-hole symmetry is only antilinear in the one-particle space. It is linear and unitary when acting on the many-particle Fock space. See footnote after eq 4 in S.Ryu, A.Schnyder, A.Furusaki, A.Ludwig, Topological insulators and superconductors: ten-fold way and dimensional hierarchy New J. Phys. 12, 065010 (2010). ArXiv:0912.2157. Supose that the one ...

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A more fundamental answer to why the particle-hole operator is taken that way is to look towards QFT. There we have particles and antiparticles and we can assign a charge of $+q$ to a particle and $-q$ to the antiparticle. Thus a operator that interchanges particles and antiparticles $\mathcal{C}$ must satisfy $\mathcal{C}|p\rangle=|\bar{p}\rangle$ so if we ...

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You certainly can have Cooper pairs of positively charged holes instead of negatively charged electrons. (Note that these are holes in the solid-state sense). Like the comments mention, you can also have positron cooper pairs in antimatter, at least in principle, but there are no known physical cases of that. As an explicit example, in so-called "hole-...

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Consider first a time-independent gauge transformation. Then the vanishing of the gradient implies only that $$\theta'-\theta+\frac{q}{\hbar}\chi= {\rm constant}.$$ But we also know that $\theta-\theta'=0$ if $\chi=0$. Therefore the constant is zero. For a time dependent gauge transformation, one needs to include the gauge covariance of the Josephson ...

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It should first be noted that Off-Diagonal Long-Range Order (ODLRO) and superfluidity do no necessarily go hand in hand. ODLRO is associated with a Bose-Einstein condensed phase (BEC), which usually also behaves as a superfluid and the latter thus inherits the ODLRO property. However, you can have systems that are superfluid but where BEC is not possible (...

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In a conductor the electric field applies a force to the conduction electrons so those electrons accelerate. The electrons then scatter off lattice vibrations (phonons) and decelerate. The current settles to an equilibrium state when the acceleration and deceleration have equal magnitudes, and when we do circuit analysis we assume that the circuit has ...

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Technically speaking, yes, but practically speaking, no. The levitation system of maglev trains generally only relies on static fields, which hypothetically could be reproduced with permanent magnets. You can even make models using permanent magnets. However, for actual practical systems (at least for human transport), permanent magnets are too weak - this ...

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The study of condensed matter systems using holography (AdS/CFT) is often referred to as AdS/CMT, holographic superconductors being one topic in this subfield. There is now a textbook called "Holographic Quantum Matter" by Hartnoll, Lucas, and Sachdev. The free arXiv preprint version is here. If you wanted to find very recent papers on this ...

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The particle-hole energy spectrum is symmetric around zero energy. When $g\to 0$, we have two zero energy levels, corresponding to the Majorana zero modes which are localized far away from each other and separated by a gaped medium. It is not possible to move these levels from zero energy individually (as one needs to respect particle-hole symmetry). The ...

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I found particularly useful chapter 10 of the Zaanen et al. book where several applications of the holographic superconductivity are discussed. However, this is a 2015 Ref. I am really interested in this topic and following the developments of your question.

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