Low temperature specific heat of the vortex lattice in layered superconductors

The contribution of the vortex fluctuations to the specific heat of the vortex lattice, ${\mathit{C}}_{\mathit{v}}$, in a highly anisotropic layered superconductor is calculated for the field B perpendicular to the layers in the interval ${\mathit{H}}_{\mathrm{c}1\mathrm{}}$≪B≪${\mathit{H}}_{\mathit{c}2}$. The model of the quantum overdamped oscillator for vortex vibrations is used to describe the dynamics of vortices at low temperatures. The specific heat ${\mathit{C}}_{\mathit{v}}$(T,B) is linear in temperature at low T and increases with field, ${\mathit{C}}_{\mathit{v}}$∝lnB in the case of weak pinning and ${\mathit{C}}_{\mathit{v}}$∝B in the case of strong pinning.