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One problem is that band theory isn't everything! Crucially, band theory completely neglects the interactions between electrons. The fact that often one can do this and obtain near correct results is actually amazing, and worth several lecture courses to flesh out the reasons. However, it cannot always be correct. In many materials the electron-electron ...

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Ohm's law is generally NOT correct, it's called a law for historical reasons only!! It's a law in the same sense in which Hooke's law is a law... it holds only for certain systems under certain conditions, but it's widely known because it's simple and linear! It's not just superconductors, diodes are a neat everyday example of Ohm's law failing to hold. But ...

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The problem with trying to pass huge amounts of current through a superconductor is that any flowing current creates a magnetic field circling around it (Ampere's law). A superconductor also expels all magnetic fields from inside itself (Meissner effect), so what you get is a lot of magnetic field lines all bunched up just outside the surface of the ...

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Symmetry of the superconducting gap First of all, a bit of theory. Superconductivity appears due to the Cooper paring of two electrons, making non-trivial correlations between them in space. The correlation is widely known as the gap parameter $\Delta_{\alpha\beta}\left(\mathbf{k}\right)\propto\left\langle ... 17 Physics theory and experimental reality have something like a mathematical epsilon delta relationship, imo. Here is a review of the matter. From the introduction in the PDF of the paper Resistance in Superconductors: The ability of a wire to carry an electrical current with no apparent dissipation is doubtless the most dramatic property of the ... 15 A fermion is any particle, elementary or composite, that obeys Fermi-Dirac (as opposed to Bose-Einstein) statistics relating to how identical particles behave when you swap two of them. Due to an important but complicated result, this is taken to amount to having half-integer spin. A lepton is one type of elementary particle with spin 1/2. The only leptons ... 13 It's difficult to say how close we are to "resolving high temperature superconductivity", as the answer depends very much on your definition of "resolved". For example, have we mapped the phase diagrams? Yes. Do we understand the relevant experimental facts? Yes and no. Is there a complete theory of HTSC that predicts how to create a high temperature ... 13 Ohm's law works for ordinary conductors for a reason: the particles carrying the current (usually, but not always electrons) scatter incoherently and inelastically from features of the conductor. In the case of an electron current, at low temperature this scattering is caused by impurities in the conductor; at high temperatures, the dominant source of ... 12 There is a critical current density for every superconductor where the superconductor acts as an ordinary conductor and a voltage difference can be measured between its ends. 11 Usually "quantum liquid" refers to the ground state of a Hamiltonian that do not break translation symmetry of the Hamiltonian. (In a sense, "quantum gas" = "quantum liquid".) "Quantum spin liquid" refers to the ground state of a spin Hamiltonian that do not break spin-rotation and translation symmetries of the Hamiltonian. 11 Helium is relatively rare on Earth, 0.00052% of the atoms or molecules in the atmosphere (or the same fraction of the volume; much lower fraction of the mass). The concentration of helium in the atmosphere is low. Moreover, it's dropping because of atmospheric escape. About 4 tons of helium escape from the atmosphere every day because there's a significant ... 10 It is an incorrect picture to envision the Cooper pairs as existing as an isolated occurrence in a lattice, since the very existence of Cooper pairs depends on a supporting cast of other electrons. In his work, Cooper showed that the ground state of a metal is unstable against an arbitrarily small net attraction between two electrons of opposite momentum, ... 9 A quick answer: "screening" currents in the superconductor are proportional to the vector potential. With an appropriate choice of gauge, the screening current appears as a mass term in the wave equation for the vector potential. From "An Informal Introduction to Gauge Field Theories": (This excerpt from Google books) 9 Actually, induction works, although it is often used a bit differently than you described. You can place a warm superconductor loop into a normal coil. As you switch the coil on, there will be some current inside the superconductor, but since it is not cold yet, this current quickly dies down. Then you cool the superconductor below its critical temperature. ... 9 A fermion is any particle characterized by Fermi–Dirac statistics and obeying the Pauli exclusion principle. So for example quarks are fermions, as are Helium-3 atoms. A fermion does not have to be an elementary particle. I'm not even sure that it has to be spin$\tfrac{1}{2}$, though I can't think of any fermions that aren't. A lepton is a spin ... 9 The short answer is that BCS theory is derived bottom-up from quantum mechanics (you assume that there is some local attractive interaction between electrons, and perform a mean field approximation), while the older Ginzburg-Landau theory is derived top-down from thermodynamics (you assume that superconductivity can be described by some order parameter, and ... 8 The bottom line is the spontaneous symmetry breakdown from global$U(1)$to$\mathbb{Z}_2$and the concomitant rigidity of the omnipresent coherent phase down to which the system breaks, although the microscopic action of a superconductor possesses local$U(1)$gauge symmetry. By rigidity, I mean something reminiscent of a restoring force felt when one tries ... 8 MRI machines use liquid helium to cool down the superconducting magnets that are needed to create the high magnetic field necessary for magnetic resonance imaging. Every high-field magnetic resonance machine, MRI or NMR, has an inner dewar filled with helium and an outer one filled with liquid nitrogen. The insulation is of course not perfect, so a certain ... 8 A magnetic field cannot penetrate a superconductor; since there's no resistance to the flow of electrons, a current is immediately created in the superconductor by the field, and the field produced by that current opposes the original field. This is ordinary magnetic induction, but with zero losses because of the superconductivity. Essentially, whenever a ... 8 It's not the making as opposed to verifying of topological superconductors that is difficult experimentally. One of the most useful techniques in identifying topological properties of a material is Angle-Resolved Photoemission Spectroscopy (ARPES). ARPES can independently image the bulk and surface modes of a 3-D solid with very good energy and momentum ... 8 There are different categories of topological superconductors. I’m guessing that you are referring to the time-reversal invariant (class DIII) ones, in 2D or 3D. Yes, it is possible to distinguish the surface/edge states of 3D/2D topological superconductors from the bulk. I'm not talking about designing some intricate experimental technique to separate out ... 8 Historically, the terms gas, liquid and (crystalline) solid meant, respectively: weak/no interactions between particles, strong interactions but statistical translation/orientation invariance, and finally breaking of translation/orientation invariance. Applied to more spin systems, a liquid would have translational invariance, but some global order --- i.e. ... 8 We have a condensed matter analog of the Higgs mechanism. Colloquially, we say the gauge boson — in this case, the photon — "eats up" the Goldstone boson — in this case, plasmons built up from a condensate of Cooper pairs — giving rise to a new quasiparticle. Unlike photons, this quasiparticle has an energy gap in the dispersion ... 8 I'm afraid the actual situation is much more complicated than you've been told. For one thing, the superconductivity does not occur between neutrons, but between quarks themselves. The topic of high density QCD is a very cool interplay of condensed matter and high energy physics, and a very nice review is available by Frank Wilczek. However, that article ... 8 I tried to add this as a comment, but it is too long so I am making this an answer instead. This is not my text, but the text of one of the commentators on the video: "Superconductors are of two types, which are defined by their Meissner effect. One type repels magnetic fields, which will levitate the superconducting object. A type I superconductor ... 8 When you scatter an electron you change it's energy. So if it wasn't possible to change the energy of an electron you couldn't scatter it. This is basically what happens in superconductors. In a metal at room temperature the electrons have a continuous range of energies. This means if I want to change the energy of an electron by 0.001eV, or even ... 7 The something is the superconducting order parameter, which is loosely$\Delta_{\alpha\beta}(r-r')=\langle\psi_\alpha(r)\psi_\beta(r')\rangle$where$\psi_{\uparrow(\downarrow)}$is the operator that annihilates a spin up (spin down) electron. Now$\Delta$must transform under the symmetry group of the crystal. So the terms$s, p, d$and all their ... 7 The spin of a single electron has been measured since the very first moment when the people understood that every electron possesses a spin. A Stern-Gerlach experiment - a magnetic field - is enough to measure the spin: http://en.wikipedia.org/wiki/Stern-Gerlach_experiment 7 There are many schemes to make topological superconductors. Some of these schemes have restrictions on the chemical potential$\mu\$. You also need to know what type of topological superconductors you are dealing with. You can refer to the periodic table to determine this: In the paper from the link you provided the authors mention two types of ...

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