Anisotropic thermodynamics and $T/\sqrt H$ scaling of d-wave superconductors in the vortex state

TL;DR

This paper investigates the anisotropic thermodynamic properties of 2D d-wave superconductors in the vortex state, revealing directional oscillations in density of states and distinct scaling laws for different field orientations.

Contribution

It introduces a detailed analysis of angular-dependent density of states and scaling behaviors in d-wave superconductors under magnetic fields, highlighting anisotropic effects.

Findings

Fourfold oscillations in density of states with magnetic field angle

Different power laws for frequency and temperature dependencies in nodal vs anti-nodal directions

Implications for specific heat measurements in anisotropic superconductors

Abstract

The density of states of a 2D d-wave superconductor in the vortex state with applied magnetic field $\bf H$ in the plane is shown to exhibit fourfold oscillations as a function of the angle of the field with respect to the crystal axes. We find further that the frequency dependence of the density of states and the temperature dependence of transport coefficients obey different power laws, thus leading to different magnetic scaling functions, for field in the nodal and anti-nodal direction. We discuss the consequences of this anisotropy for measurements of the specific heat.