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Register a new userSqueezed-field path-integral description of BCS superconductors
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We develop a squeezed-field path-integral representation for BCS superconductors utilizing a generalized completeness relation of squeezed-fermionic coherent states. We derive a Grassmann path integral of fermionic quasiparticles that explicitly includes the collective degrees of freedom of the order-parameter dynamics governed by the classical Anderson pseudospin model. Based on this method, we analyze the spectral function of the single-particle excitations, and show that the squeezed-field path integral for the BCS Hamiltonian describes the dispersion relation and the mass gap of the Higgs amplitude mode of BCS superconductors, as well as the quasiparticle and quasihole excitation branches described by the BCS mean-field approximation.
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We propose a generalization of the Feynman path integral using squeezed coherent states. We apply this approach to the dynamics of Bose-Einstein condensates, which gives an effective low energy description that contains both a coherent field and a squeezing field. We derive the classical trajectory of this action, which constitutes a generalization of the Gross Pitaevskii equation, at linear order. We derive the low energy excitations, which provides a description of second sound in weakly interacting condensates as a squeezing oscillation of the order parameter. This interpretation is also supported by a comparison to a numerical c-field method.
The free energy, non-gradient terms of the Ginzburg-Landau expansion, and the jump of the specific heat of a multiband anisotropic-gap clean BCS superconductor are derived in the framework of a separable-kernel approximation. Results for a two-band superconductor, d-wave superconductor, and some recent models for MgB_2 are derived as special cases.
We present a systematic study of the response properties of two-band (multi-gap) superconductors with spin-singlet (s-wave) pairing correlations, which are assumed to be caused by both intraband (lambda_{ii}, i=1,2) and interband (lambda_{12}) pairing interactions. In this first of three planned publications we concentrate on the properties of such superconducting systems in global and local thermodynamic equilibrium, the latter including weak perturbations in the stationary long-wavelength limit. The discussion of global thermodynamic equilibrium must include the solution (analytical in the Ginzburg-Landau and the low temperature limit) of the coupled self-consistency equations for the two energy gaps Delta_i(T), i=1,2. These solutions allow to study non-universal behavior of the two relevant BCS-Muhlschlegel parameters, namely the specific heat discontinuity Delta C/C_N and the zero temperature gaps Delta_i(0)/pi k_B T_c, i=1,2. The discussion of a local equilibrium situation includes the calculation of the supercurrent density as a property of the condensate, and the calculation of both the specific heat capacity and the spin susceptibility as properties of the gas of thermal excitations in the spirit of a microscopic two-fluid description. Non-monotonic behavior in the temperature dependences of the gaps and all these local response functions is predicted to occur particularly for very small values of the interband pair-coupling constant lambda_{12}.
A major impediment to solving the problem of high-$T_c$ superconductivity is the ongoing confusion about the magnitude, structure and doping dependence of the superconducting gap, $Delta_0$, and of the mysterious pseudogap found in underdoped samplescite{TallonLoram}. The pseudogap opens around the ($pi$,0) antinodes below a temperature $T^*$ leaving Fermi arcs across the remnant Fermi surfacecite{Kanigel} on which the superconducting gap forms at $T_c$. One thing that seems agreed is that the ratio $2Delta_0/k_BT_c$ well exceeds the BCS value and grows with underdopingcite{Miyakawa1,Miyakawa2}, suggesting unconventional, non-BCS superconductivity. Here we re-examine data from many spectroscopies, especially Raman $B_{1g}$ and $B_{2g}$ scatteringcite{Sacuto,Guyard}, and reconcile them all within a two-gap scenario showing that the points of disagreement are an artefact of spectral-weight loss arising from the pseudogap. Crucially, we find that $Delta_0(p)$, or more generally the order parameter, now scales with the mean-field $T_c$ value, adopting the weak-coupling BCS ratio across the entire phase diagram.
We investigate the non-equilibrium behavior of BCS superconductors subjected to slow ramps of their internal interaction strength. We identify three dynamical regimes as a function of ramp duration. For short ramp times, these systems become non-superconducting; however, fermions with opposite momenta remain paired albeit with reduced amplitudes, and the associated pair amplitude distribution is non-thermal. In this first regime, the disappearance of superconductivity is due to the loss of phase coherence between pairs. By contrast, for intermediate ramp times, superconductivity survives but the magnitude of the order parameter is reduced and presents long-lived oscillations. Finally, for long ramp times, phase coherence is almost fully retained during the slow interaction quench, and the steady-state is characterized by a thermal-like pair amplitude distribution. Using this approach, one can therefore dynamically tune the coherence between pairs in order to control the magnitude of the superconducting order parameter and even engineer a non-equilibrium state made of pre-formed pairs.
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