Nernst and Seebeck Coefficients of the Cuprate SuperconductorYBa2_2Cu3_3O6.67_{6.67}: A Study of Fermi Surface Reconstruction

The Seebeck and Nernst coefficients $S$ and $\nu$ of the cuprate superconductor YBa$_2$Cu$_3$O$_y$ (YBCO) were measured in a single crystal with doping $p = 0.12$ in magnetic fields up to H = 28 T. Down to T=9 K, $\nu$ becomes independent of field by $H \simeq 30$ T, showing that superconducting fluctuations have become negligible. In this field-induced normal state, $S/T$ and $\nu/T$ are both large and negative in the $T \to 0$ limit, with the magnitude and sign of $S/T$ consistent with the small electron-like Fermi surface pocket detected previously by quantum oscillations and the Hall effect. The change of sign in $S(T)$ at $T \simeq 50$ K is remarkably similar to that observed in La$_{2-x}$Ba$_x$CuO$_4$, La$_{2-x-y}$Nd$_y$Sr$_x$CuO$_4$ and La$_{2-x-y}$Eu$_y$Sr$_x$CuO$_4$, where it is clearly associated with the onset of stripe order. We propose that a similar density-wave mechanism causes the Fermi surface reconstruction in YBCO.Comment: Final version accepted for publication in Phys. Rev. Lett. New title, shorter abstract, minor revision of text and added reference

Scale-invariant magnetoresistance in a cuprate superconductor

The anomalous metallic state in high-temperature superconducting cuprates is masked by the onset of superconductivity near a quantum critical point. Use of high magnetic fields to suppress superconductivity has enabled a detailed study of the ground state in these systems. Yet, the direct effect of strong magnetic fields on the metallic behavior at low temperatures is poorly understood, especially near critical doping, $x=0.19$. Here we report a high-field magnetoresistance study of thin films of \LSCO cuprates in close vicinity to critical doping, $0.161\leq x\leq0.190$. We find that the metallic state exposed by suppressing superconductivity is characterized by a magnetoresistance that is linear in magnetic field up to the highest measured fields of $80$T. The slope of the linear-in-field resistivity is temperature-independent at very high fields. It mirrors the magnitude and doping evolution of the linear-in-temperature resistivity that has been ascribed to Planckian dissipation near a quantum critical point. This establishes true scale-invariant conductivity as the signature of the strange metal state in the high-temperature superconducting cuprates.Comment: 10 pages, 3 figure

Fermi Surface of the Electron-doped Cuprate Superconductor Nd_{2-x}Ce_xCuO_{4} Probed by High-Field Magnetotransport

We report on the study of the Fermi surface of the electron-doped cuprate superconductor Nd$_{2-x}$Ce$_x$CuO$_{4}$ by measuring the interlayer magnetoresistance as a function of the strength and orientation of the applied magnetic field. We performed experiments in both steady and pulsed magnetic fields on high-quality single crystals with Ce concentrations of $x=0.13$ to 0.17. In the overdoped regime of $x > 0.15$ we found both semiclassical angle-dependent magnetoresistance oscillations (AMRO) and Shubnikov-de Haas (SdH) oscillations. The combined AMRO and SdH data clearly show that the appearance of fast SdH oscillations in strongly overdoped samples is caused by magnetic breakdown. This observation provides clear evidence for a reconstructed multiply-connected Fermi surface up to the very end of the overdoped regime at $x\simeq 0.17$. The strength of the superlattice potential responsible for the reconstructed Fermi surface is found to decrease with increasing doping level and likely vanishes at the same carrier concentration as superconductivity, suggesting a close relation between translational symmetry breaking and superconducting pairing. A detailed analysis of the high-resolution SdH data allowed us to determine the effective cyclotron mass and Dingle temperature, as well as to estimate the magnetic breakdown field in the overdoped regime.Comment: 23 pages, 8 figure

On the Geometry and Entropy of Non-Hamiltonian Phase Space

We analyze the equilibrium statistical mechanics of canonical, non-canonical and non-Hamiltonian equations of motion by throwing light into the peculiar geometric structure of phase space. Some fundamental issues regarding time translation and phase space measure are clarified. In particular, we emphasize that a phase space measure should be defined by means of the Jacobian of the transformation between different types of coordinates since such a determinant is different from zero in the non-canonical case even if the phase space compressibility is null. Instead, the Jacobian determinant associated with phase space flows is unity whenever non-canonical coordinates lead to a vanishing compressibility, so that its use in order to define a measure may not be always correct. To better illustrate this point, we derive a mathematical condition for defining non-Hamiltonian phase space flows with zero compressibility. The Jacobian determinant associated with time evolution in phase space is altogether useful for analyzing time translation invariance. The proper definition of a phase space measure is particularly important when defining the entropy functional in the canonical, non-canonical, and non-Hamiltonian cases. We show how the use of relative entropies can circumvent some subtle problems that are encountered when dealing with continuous probability distributions and phase space measures. Finally, a maximum (relative) entropy principle is formulated for non-canonical and non-Hamiltonian phase space flows.Comment: revised introductio

Path Integral for Quantum Operations

In this paper we consider a phase space path integral for general time-dependent quantum operations, not necessarily unitary. We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum Markovian master equation). We consider the path integral for quantum operation with a simple infinitesimal generator.Comment: 24 pages, LaTe

Microscopic Foundation of Nonextensive Statistics

Combination of the Liouville equation with the q-averaged energy $U_q = _q$ leads to a microscopic framework for nonextensive q-thermodynamics. The resulting von Neumann equation is nonlinear: $i\dot\rho=[H,\rho^q]$. In spite of its nonlinearity the dynamics is consistent with linear quantum mechanics of pure states. The free energy $F_q=U_q-TS_q$ is a stability function for the dynamics. This implies that q-equilibrium states are dynamically stable. The (microscopic) evolution of $\rho$ is reversible for any q, but for $q\neq 1$ the corresponding macroscopic dynamics is irreversible.Comment: revte

Thermodynamic Description of the Relaxation of Two-Dimensional Euler Turbulence Using Tsallis Statistics

Euler turbulence has been experimentally observed to relax to a metaequilibrium state that does not maximize the Boltzmann entropy, but rather seems to minimize enstrophy. We show that a recent generalization of thermodynamics and statistics due to Tsallis is capable of explaining this phenomenon in a natural way. The maximization of the generalized entropy $S_{1/2}$ for this system leads to precisely the same profiles predicted by the Restricted Minimum Enstrophy theory of Huang and Driscoll. This makes possible the construction of a comprehensive thermodynamic description of Euler turbulence.Comment: 15 pages, RevTe