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26

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 ...

23

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 ...

17

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 ...

14

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 ...

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

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 ...

9

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

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 ...

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 ...

7

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 ...

7

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. ...

7

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 ...

6

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 ...

6

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)

6

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.

6

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 ...

6

I'll try to give a very short answer to most of the questions. Some parts are already explained in the other answers but a few important aspects are missing. How can the amount of helium be depleting? The Helium ($^4$He) that is used in a number of applications is extracted from natural gas. All other sources are much more difficult and expensive. So ...

5

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

5

OK - taking the questions one at a time. Full disclosure: I'm a member of the phonon tribe, but I'm trying not to let that cloud my response here. "So, as far as I can tell, this is a simple, elegant, experimentally-proven theory explaining cuprate superconductivity. The theory and supporting experiments are at least five years old. But everyone still says ...

5

Looking at your question from the perspective of ideal circuit theory, an ideal resistor has the following I-V relationship: $V_R = I_R R$ The voltage across the resistor is proportional to the current through the resistor with constant of proportionality equal to $R$. In ideal circuit theory, an ideal conductor can be thought of as a "zero ohm resistor". ...

4

I will just answer the first part of question: is phonon attraction stronger than Coulomb? Short answer: No. Longer answer: Nothing (in condensed matter) is ever stronger than the Coulomb force. Longest answer: There are two aspects to consider. First is the self-screening of the electrons, which will add a mass term to the photons, giving a Yukawa-esque ...

4

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 ...

4

Superconductors don't strictly exclude interior magnetic fields. Over a short distance, called a screening length, external magnetic fields can penetrate into a superconductor. This length can be discussed in terms of an effective photon mass, borrowing concepts from particle physics. The heavier a virtual particle, the shorter the distance it can travel ...

4

As the first author of arXiv:1109.4155, my answer to this question is yes. The topological p-wave SC state is insensitive to the sign of the coupling. The argument provided in our paper is quite general, the time-reversal broken SC state is supported by the underlying topological order in the Kitaev spin liquid, as described by the particular spin-gauge ...

3

The owner of superconductors.org has a list of places to find HTSC superconductors, kits, and instructions. You can also review the literature for recipes. HTSC producers usually publish successful and repeatable recipes in refereed journals, and some components are available commercially.

3

The way to minimize drag in any fluid is to minimize disturbing it. Fluids don't have friction the same way solid objects have friction, by a sliding interface. When fluid flows next to a surface, it sticks to the surface. The "sliding" is actually in the form of viscous deformation of the fluid itself in a layer next to the surface (the boundary layer). ...

3

You won't negate any of the friction with the water by preventing it touching the skin, you'll just make the friction worse, because the boat will be slightly bigger. The amount of friction force is entirely determined by the momentum transferred from the boat to the water, and this quantity doesnt really care if the water is touching the boat or not. It is ...

3

The video link is not working for me for some reason so my answer may not be a comment on what the video is showing, but these are my thoughts. My understanding of "locking" is that you lock the phase of one system to another. The term quantum is used if you are talking about the quantum phase of the state. It seems superfluous, but serves as a reminder ...

3

The thermal energy required to break the Cooper pairs determines the value of Tc in BCS superconductors. In the work of McMillan, (Physical Review 167 (2), 1968 p 331-344), he shows that with considerations to phonon excitations in materials, the limitation of phonon vibrational energies is the limiting factor in BCS transition temperatures. In his work, ...

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