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Register a new userThe critical temperature for the BCS equation at weak coupling
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For the BCS equation with local two-body interaction $lambda V(x)$, we give a rigorous analysis of the asymptotic behavior of the critical temperature as $lambda to 0$. We derive necessary and sufficient conditions on $V(x)$ for the existence of a non-trivial solution for all values of $lambda>0$.
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From the viewpoint of operator theory, we deal with the temperature dependence of the solution to the BCS gap equation for superconductivity. When the potential is a positive constant, the BCS gap equation reduces to the simple gap equation. We first show that there is a unique nonnegative solution to the simple gap equation, that it is continuous and strictly decreasing, and that it is of class $C^2$ with respect to the temperature. We next deal with the case where the potential is not a constant but a function. When the potential is not a constant, we give another proof of the existence and uniqueness of the solution to the BCS gap equation, and show how the solution varies with the temperature. We finally show that the solution to the BCS gap equation is indeed continuous with respect to both the temperature and the energy under a certain condition when the potential is not a constant.
We review the study of the superfluid phase transition in a system of fermions whose interaction can be tuned continuously along the crossover from Bardeen-Cooper-Schrieffer (BCS) superconducting phase to a Bose-Einstein condensate (BEC), also in the presence of a spin-orbit coupling. Below a critical temperature the system is characterized by an order parameter. Generally a mean field approximation cannot reproduce the correct behavior of the critical temperature $T_c$ over the whole crossover. We analyze the crucial role of quantum fluctuations beyond the mean-field approach useful to find $T_c$ along the crossover in the presence of a spin-orbit coupling, within a path integral approach. A formal and detailed derivation for the set of equations useful to derive $T_c$ is performed in the presence of Rashba, Dresselhaus and Zeeman couplings. In particular in the case of only Rashba coupling, for which the spin-orbit effects are more relevant, the two-body bound state exists for any value of the interaction, namely in the full crossover. As a result the effective masses of the emerging bosonic excitations are finite also in the BCS regime.
Two principles govern the critical temperature for superconducting transitions: (1)~intrinsic strength of the pair coupling and (2)~effect of the many-body environment on the efficiency of that coupling. Most discussions take into account only the first but we argue that the properties of unconventional superconductors are governed more often by the second, through dynamical symmetry relating normal and superconducting states. Differentiating these effects is essential to charting a path to the highest-temperature superconductors.
The mysterious pseudogap phase of cuprate superconductors ends at a critical hole doping level p* but the nature of the ground state below p* is still debated. Here, we show that the genuine nature of the magnetic ground state in La2-xSrxCuO4 is hidden by competing effects from superconductivity: applying intense magnetic fields to quench superconductivity, we uncover the presence of glassy antiferromagnetic order up to the pseudogap boundary p* ~ 0.19, and not above. There is thus a quantum phase transition at p*, which is likely to underlie highfield observations of a fundamental change in electronic properties across p*. Furthermore, the continuous presence of quasi-static moments from the insulator up to p* suggests that the physics of the doped Mott insulator is relevant through the entire pseudogap regime and might be more fundamentally driving the transition at p* than just spin or charge ordering.
Recently experiments on high critical temperature superconductors has shown that the doping levels and the superconducting gap are usually not uniform properties but strongly dependent on their positions inside a given sample. Local superconducting regions develop at the pseudogap temperature ($T^*$) and upon cooling, grow continuously. As one of the consequences a large diamagnetic signal above the critical temperature ($T_c$) has been measured by different groups. Here we apply a critical-state model for the magnetic response to the local superconducting domains between $T^*$ and $T_c$ and show that the resulting diamagnetic signal is in agreement with the experimental results.
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