Inversion of specific heat oscillations with in-plane magnetic field angle in two-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-wave superconductors

Experiments on several novel superconducting compounds have observed oscillations of the specific heat when an applied magnetic field is rotated with respect to the crystal axes. The results are commonly interpreted as arising from the nodes of an unconventional order parameter, but the identifications of nodal directions are sometimes controversial. Here we show with a semiclassical model calculation that when the magnetic field points in the direction of the nodes, either minima or maxima can occur in the specific heat depending on the temperature $T$ and the magnetic field $H$. An inversion of the angular oscillations takes place with respect to those predicted earlier at low temperature by the nodal approximation. This result, together with the argument that the inversion takes place based on an approximation valid at moderate fields, indicates that the inversion of specific heat oscillations is an intrinsic feature of nodal superconductors.