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Superconductors are solid lattices composed out of atoms and molecules. The conduction band when temperatures are very low allow the phenomenon of non resistance, but this can occur only while a lattice exists. If at that low temperature the lattice would disintegrate there would be no superconductivity. A solid expressed by the lattice has a surface, that ...

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[some] people believe...it would power a phone indefinitely without an additional power source. Is it safe to say anything it powers is a resistor and this cannot be our interest? Correct. A superconductor can transmit power from point A to point B without any Ohmic loss, but it is not an infinite source of power. A superconducting magnet can act as a ...

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The Coulomb gauge condition $\nabla\cdot A$ does not uniquely specify a gauge. For any given field configuration, there are still infinitely many choices of $A$ which have that property. One says that there is still *residual gauge freedom * after imposing the Coulomb gauge condition. Normally this freedom goes away if you demand that the fields vanish at ...

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As per WikiPedia, as of 2020, A room-temperature superconductor is a material that is capable of exhibiting superconductivity at operating temperatures above 0 °C (273 K; 32 °F), that is, temperatures that can be reached and easily maintained in an everyday environment. As of 2020 the material with the highest accepted superconducting temperature is an ...

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Because at $T=0$ all the particles are in the ground state and hence participate in $|\Psi_{\text{BCS}}\rangle$, so you just need one type of creation operator $c^\dagger$ for the Cooper pair: $$|\Psi_{\text{BCS}}\rangle = \prod_\mathbf{k}(u_\mathbf{k}^\ast+v_\mathbf{k}^\ast c^\dagger_{\mathbf{k},\uparrow} c^\dagger_{-\mathbf{k},\downarrow}),$$ and the BCS ...

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I used the pdf that you get when you search on google for the following: "Second-quantization representation of the Hamiltonian of an interacting electron gas in an external potential"

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It seems to be almost right, except some missing terms. In the kinetic energy part, you should have the additional $\zeta_{-k'}+\zeta_{k''}.$ This is because when evaluating $\left< \Psi_{ex}|\epsilon_k\hat{c}_{-k'\downarrow}^\dagger\hat{c}_{-k'\downarrow}|\Psi_{ex} \right>$, you will get a $1$ instead of $v_{-k'}$ when you move $\hat{c}_{-k'\downarrow}... 5 One of the best definitions for BEC is from the (diagonalised in the basis$\{\chi_i\}$) single-particle density matrix$\rho_1$: $$\rho_1(\mathbf{r}, \mathbf{r}') = \sum_i n_i \chi^\ast _i (\mathbf{r})\chi_i (\mathbf{r}').$$ If$n_i$is of order 1 for all$i\$;, then you are in the "normal" (not Bose-condensed) state; If one (exactly one) ...

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see also arXiv:2012.10771, "Anomalous behavior in high-pressure carbonaceous sulfur hydride" by Dogan and Cohen

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