Thermodynamics of the magnetic-field-induced 'normal' state in an underdoped high Tc superconductor

High magnetic fields are used to kill superconductivity and probe what happens to system when it cannot reach the ideal ground state, i.e. what is the normal-state ground state? Early work in High-Tc, where the application of magnetic field destroyed the zero resistance state and recovered a resistivity value that connected continuously with the zero field curve, lead people to believe this magnetic-field-induced-state had fully driven the system normal, revealing the true underlying ground state, without any vestige of superconductivity. Many experiments done in this region of phase space have results interpreted as coming from the low energy ground state excitations. With the emergence of ultra-clean crystals in a unique family of hole doped high-Tc superconductors, YBa2Cu3O 7-delta, YBCO, a new and highly unexpected phenomena of quantum oscillations were discovered, and they followed the standard Liftshitz-Kosevich (LK) theory for a normal metal. The results suddenly made the problem of high-T c appear to be analogous to superconductivity in the organics, which is brought about by a wave-vector nesting and Fermi surface reconstruction. The only problem, it appeared, that needed to be reconciled was with Angle Resolved Photo-Emission Spectroscopy (ARPES) and Scanning Tunneling Microscopy (STM) data that claimed to see no such Fermi surface, instead only "arcs", a set of disconnected segments in the Brillouin zone which quasiparticle peaks are observed at the Fermi energy, which in a mean field description does not allow for a continuous Fermi surface contour. These two discrepancies led to the "arc vs pocket" debate, which is still unresolved. The other kink in the quantum oscillation armor is that, to this date, quantum oscillations in the hole-doped cuprates have only been seen in YBCO, the only cuprate structure to have CuO chains, which conduct and are located in between two CuO2 superconducting planes in the unit cell.;In an attempt to reconcile the "arc vs pocket" debate we measure specific heat on an ultra-clean de-twinned single crystal of underdoped YBCO 6.56 with a Tc = 60 K, up to fields twice irreversibility field, define as the onset of the resistive transition. The zero temperature extrapolation of the electronic contribution to the specific heat, gamma, is the total quasiparticle density of states. For a two-dimensional system with parabolic energy bands, gamma is simply the sum of each pocket multiplied by its effective mass. Therefore, by determining gamma at high fields and using previously determined values for the effective mass from quantum oscillation transport measurements we can simply play a counting game to determine the number of pockets in the Fermi surface. Furthermore, at low fields the response to the specific heat as a function of magnetic field in a d-wave superconductor is known to have a &parl0;H&parr0; dependence, and we can look for deviations from this &parl0;H&parr0; , which are expected to happen when the system is no longer in a superconducting state.;Results from our specific heat experiment shed new light on the true nature of the magnetic field induced "normal" state, and should force reinterpretation of many experimental findings. The specific heat measurements foremost show a smooth evolution of gamma from low to high magnetic fields which follows a Ac &parl0;H&parr0; dependence, with the prefactor, Ac giving the correct magnitude for the anisotropy of the d-wave superconducting gap. This means with the application of magnetic fields strong enough to restore the resistive state, the superconducting gap still exits. Additionally, we see quantum oscillations that follow conventional LK formalism and can determine an effective mass uniquely, where no fitting parameters are required. Interestingly, these oscillations fit on top of the &parl0;H&parr0; finding. How can the &parl0;H&parr0; and quantum oscillation whose phenomena arise from very different physics be reconciled? Looking at our own zero field gamma value of 1.85 mJ mol-1 K-2, which is intrinsic for YBCO, allows the pocket counting game to begin. Coupling bandstructure calculations, angle dependent quantum oscillation measurements, which determine the shape of the pocket, with the zero field gamma value leads to the simplest interpretation; quantum oscillatory phenomena is a manifestation of the CuO chain and BaO insulating layer orbital hybridization band and is likely not relevant to high temperature superconductivity.