Nodes of the Gap Function and Anomalies in Thermodynamic Properties of Superfluid 3^3He

Departures of thermodynamic properties of three-dimensional superfluid $^3$He from the predictions of BCS theory are analyzed. Attention is focused on deviations of the ratios $\Delta(T=0)/T_c$ and $[C_s(T_c)-C_n(T_c)]/C_n(T_c)$ from their BCS values, where $\Delta(T=0)$ is the pairing gap at zero temperature, $T_c$ is the critical temperature, and $C_s$ and $C_n$ are the superfluid and normal specific heats. We attribute these deviations to the momentum dependence of the gap function $\Delta(p)$, which becomes well pronounced when this function has a pair of nodes lying on either side of the Fermi surface. We demonstrate that such a situation arises if the P-wave pairing interaction $V(p_1,p_2)$, evaluated at the Fermi surface, has a sign opposite to that anticipated in BCS theory. Taking account of the momentum structure of the gap function, we derive a closed relation between the two ratios that contains no adjustable parameters and agrees with the experimental data. Some important features of the effective pairing interaction are inferred from the analysis.Comment: 17 pages, 4 figure

BCS Model in Tsallis' Statistical Framework

We show that there is an effect of nonextensivity acting upon the BCS model for superconductors in the ground state that motivates its study in the Tsallis' statistical framework. We show that the weak-coupling limit superconductors are well described by $q \sim 1$, where q is a real parameter which characterizes the degree of nonextensivity of the Tsallis' entropy. Nevertheless, small deviations with respect to q = 1 provide better agreement when compared with experimental results. To illustrate this point, making use of an approximated Fermi function, we show that measurements of the specific heat, ultrasonic attenuation and tunneling experiments for tin (Sn) are better described with q = 0.99.Comment: 13 pages, amssym

Excitonic pairing between nodal fermions

We study excitonic pairing in nodal fermion systems characterized by a vanishing quasiparticle density of states at the pointlike Fermi surface and a concomitant lack of screening for long-range interactions. By solving the gap equation for the excitonic order parameter, we obtain a critical value of the interaction strength for a variety of power-law interactions and densities of states. We compute the free energy and analyze possible phase transitions, thus shedding further light on the unusual pairing properties of this peculiar class of strongly correlated systems.Comment: 9 pages, 7 figures, minor revisions made, final versio

2D Weyl Fermi gas model of Superconductivity in the Surface state of a Topological Insulator at High Magnetic fields

The Nambu-Gorkov Green's function approach is applied to strongly type-II superconductivity in a 2D spin-momentum locked (Weyl) Fermi gas model at high perpendicular magnetic fields. When the chemical potential is sufficiently close to the branching (Dirac) point, such that the cyclotron effective mass, $m^{\ast }$, is a very small fraction of the free electron mass, $m_{e}$, relatively large portion of the $H-T$ phase diagram is exposed to magneto-quantum oscillation effects. This model system is realized in the 2D superconducting state, observed recently on the surface of the topological insulator Sb$_{2}$Te$_{3}$, for which high field measurements were reported at low carrier densities with $m^{\ast}=0.065m_{e}$. Calculations of the pairing condensation energy in such a system, as a function of $H$ and $T$, using both the Weyl model and a reference standard model, that exploits a simple quadratic dispersion law, are found to yield indistinguishable results in comparison with the experimental data. Significant deviations from the predictions of the standard model are found only for very small carrier densities, when the cyclotron energy becomes very large, the Landau level filling factors are smaller than unity, and the Fermi energy shrinks below the cutoff energy.Comment: 10 page