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Register a new userCoherence Factors Beyond the BCS Expressions -- A Derivation
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We present a derivation of a previously announced result for matrix elements between exact eigenstates of the pairing Hamiltnonian. Our results, which generalize the well known BCS (Bardeen-Cooper-Schrieffer) expressions for what is known as coherence factors, are derived based on the Slavnov formula for overlaps between Bethe-ansatz states, thus making use of the known connection between the exact diagonalization of the BCS Hamiltonian, due to Richardson, and the algebraic Bethe ansatz. The resulting formula has a compact form after a suitable parameterization of the Energy plane. Although we apply our method here to the pairing Hamiltonian, it may be adjusted to study what is termed the Sutherland limit for exactly solvable models, namely where a macroscopic number of rapidities form a large string.
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Recent advances in time-domain terahertz (THz) spectroscopy have unveiled that resonantly-enhanced strong THz third-harmonic generation (THG) mediated by the collective Higgs amplitude mode occurs in s-wave superconductors, where charge-density fluctuations (CDF) have also been shown to contribute to the nonlinear third-order susceptibility. It has been theoretically proposed that the nonlinear responses of Higgs and CDF exhibit essentially different polarization dependences. Here we experimentally discriminate the two contributions by polarization-resolved intense THz transmission spectroscopy for a single-crystal NbN film. The result shows that the resonant THG in the transmitted light always appears in the polarization parallel to that of the incident light with no appreciable crystal axis dependence. When we compare this with the theoretical calculation here with the BCS approximation and the dynamical mean-field theory for a model of NbN constructed from first principles, the experimental result strongly indicates that the Higgs mode rather than the CDF dominates the THG resonance in NbN. A possible mechanism for this is discussed such as the retardation effect in the phonon-mediated pairing interaction beyond BCS.
We report on the structure and physical properties of bulk Palladium Tellurium superconductor, which is synthesized via quartz vacuum encapsulation technique at 750 C. The as synthesized compound is crystallized in hexagonal crystal structure. Magnetization and Magneto-transport measurements provided the values of lower and upper critical field to be 250 and 1200 Gauss respectively at 2 Kelvin. The Coherence length and GL parameter are estimated from the experimentally determined upper and lower critical fields, which are 45 nm and 1.48 respectively. The jump in Cp(T) at Tc is found to be 1.33 and the Debye temperature and electronic specific heat constant are 203 Kelvin and 6.01mJ/mole-K2 respectively.
Superconducting condensation energy $U_0^{int}$ has been determined by integrating the electronic entropy in various iron pnictide/chalcogenide superconducting systems. It is found that $U_0^{int}propto T_c^n$ with $n$ = 3 to 4, which is in sharp contrast to the simple BCS prediction $U_0^{BCS}=1/2N_FDelta_s^2$ with $N_F$ the quasiparticle density of states at the Fermi energy, $Delta_s$ the superconducting gap. A similar correlation holds if we compute the condensation energy through $U_0^{cal}=3gamma_n^{eff}Delta_s^2/4pi^2k_B^2$ with $gamma_n^{eff}$ the effective normal state electronic specific heat coefficient. This indicates a general relationship $gamma_n^{eff} propto T_c^m$ with $m$ = 1 to 2, which is not predicted by the BCS scheme. A picture based on quantum criticality is proposed to explain this phenomenon.
Since the discovery of superconductivity in the cuprates two decades ago, it has been firmly established that the CuO_2 plane is consequential for high T_C superconductivity and a host of other very unusual properties. A new family of superconductors with the general composition of LaFeAsO_(1-x)F_x has recently been discovered but with the conspicuous lacking of the CuO_2 planes, thus raising the tantalizing questions of the different pairing mechanisms in these oxypnictide superconductors. Intimately related to pairing in a superconductor are the superconducting gap, its value, structure, and temperature dependence. Here we report the observation of a single gap in the superconductor SmFeAsO_0.85F_0.15 with T_C = 42 K as measured by Andreev spectroscopy. The gap value of 2Delta = 13.34+/-0.3 meV gives 2Delta/k_BT_C = 3.68, close to the BCS prediction of 3.53. The gap decreases with temperature and vanishes at T_C in a manner consistent with the Bardeen-Cooper-Schrieffer (BCS) prediction but dramatically different from that of the pseudogap behavior in the cuprate superconductors. Our results clearly indicate a nodeless gap order parameter, which is nearly isotropic in size across different sections of the Fermi surface, and are not compatible with models involving antiferromagnetic fluctuations, strong correlations, t-J model, and the like, originally designed for cuprates.
We study the impact of a time-dependent external driving of the lattice phonons in a minimal model of a BCS superconductor. Upon evaluating the driving-induced vertex corrections of the phonon-mediated electron-electron interaction, we show that parametric phonon driving can be used to elevate the critical temperature $T_c$, while a dipolar phonon drive has no effect. We provide simple analytic expressions for the enhancement factor of $T_c$. Furthermore, a mean-field analysis of a nonlinear phonon-phonon interaction also shows that phonon anharmonicities further amplify $T_c$. Our results hold universally for the large class of normal BCS superconductors.
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