Low Field Anomaly in the Specific Heat of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">s</mml:mi></mml:math>-Wave Superconductors due to the Expansion of the Vortex Cores

Abstract

The magnetic field dependence of the electronic specific heat $C(H)$ in the $s$-wave superconductor ${\mathrm{NbSe}}_{2}$ shows curvature at low fields, resembling the near $\sqrt{H}$ term in $C(H)$ which has been reported in high- ${T}_{c}$ superconductors and attributed to a ${d}_{{x}^{2}{\ensuremath{-}y}^{2}}$-wave pairing state. In ${\mathrm{NbSe}}_{2}$ we find that the low field behavior in $C(H)$ is described quantitatively by the expansion of vortex cores and the field dependence of the magnetic induction $B$ above ${H}_{c1}$. The associated change in the density of quasiparticle states localized in the vortex cores provides a simple explanation for the ``low field anomaly'' in $C(H)$ observed in $s$-wave superconductors.