Thermodynamic signature of a magnetic-field-driven phase transition   within the superconducting state of an underdoped high-temperature   superconductor
  More than a quarter century after the discovery of the high temperature superconductor (HTS) YBa$_2$Cu$_3$O$_{6+\delta}$ (YBCO) studies continue to uncover complexity in its phase diagram. In addition to HTS and the pseudogap there is growing evidence for multiple phases with boundaries which are functions of temperature ($T$), doping (p) and magnetic field. Here we report the low temperature electronic specific heat (C$_{elec}$) of YBCO6.47 (p=0.08) up to a magnetic field (H) of 34.5 teslas (T), a poorly understood region of the underdoped H-$T$-p phase space. We observe two regimes: below a characteristic magnetic field H'$\approx$10 T, C$_{elec}/T$ obeys an expected H$^{1/2}$ behavior, however, near H' there is a sharp inflection followed by a linear-in-H behavior. H' rests deep within the superconducting phase and the linear-in-H behavior is observed in the zero resistance regime. In the limit of zero temperature, C$_{elec}/T$ is proportional to the zero-energy electronic density of states. Thus this inflection is evidence of a magnetic-field-driven quantum phase transition. 
J. B. Kemper, O. Vafek, J. B. Betts, F. F. Balakirev, W. N. Hardy,   Ruixing Liang, D. A. Bonn and G. S. Boebinger
cond-mat.supr-con