Thermodynamics of d-wave superconductors in a magnetic field

Abstract

We investigate the thermodynamic properties of a two-dimensional d-wave superconductor in the vortex state using a semiclassical approach, and argue that such an approach is valid for the analysis of the experimental data on high-temperature superconductors. We develop a formalism where the spatial average of a physical quantity is written as an integral over the probability density of the Doppler shift, and evaluate this probability density for several model cases. The approach is then used to analyse the behavior of the specific heat and the NMR spin-lattice relaxation rate in a magnetic field. We compare our results with the experimental measurements, and explain the origin of the discrepancy between the results from different groups. We also address the observability of the recently predicted fourfold oscillations of the specific heat for the magnetic field parallel to the copper oxide planes. We consider both the orbital and the Zeeman effects, and conclude that at experimentally relevant temperatures Zeeman splitting does not appreciably reduce the anisotropy, although it does change the field dependence of the anisotropic specific heat. We predict a scaling law for the non-exponentially decaying NMR magnetization, and discuss different approaches to the effective relaxation rate.

24 pages, 15 eps figures

References in corpus (14)

• STM Studies of the Electronic Structure of Vortex Cores in Bi2Sr2CaCu2O8+d
• Impurity-Induced Quasiparticle Transport and Universal Limit Wiedemann-Franz Violation in d-Wave Superconductors
• Low-Energy Quasiparticles in Cuprate Superconductors: A Quantitative Analysis
• Field Induced Reduction of the Low Temperature Superfluid Density in YBa2Cu3O6.95
• Direct Observation and Anisotropy of the Contribution of Gap nodes in the Low Temperature Specific Heat of YBa_2Cu_3O_7
• Quasiparticles of d-wave superconductors in finite magnetic fields
• The Structure of a Vortex in the t-J Model
• Quasiparticle Spectrum of d-wave Superconductors in the Mixed State
• Theory of NMR as a local probe for the electronic structure in the mixed state of the high-$T_c$ cuprates
• Spin-lattice relaxation in the mixed state of YBaCuO: Can we see Doppler-shifted d-wave quasiparticles?
• Interlayer Quasiparticle Transport in the Vortex State of Josephson Coupled Superconductors
• Angle-dependent magnetothermal conductivity in d-wave superconductors
• Magnetic field effects on the density of states of orthorhombic superconductors
• Zeeman and Orbital Effects of an in-Plane Magnetic Field in Cuprate Superconductors

Cited by in corpus (43)

• Nodal Structure of Unconventional Superconductors Probed by the Angle Resolved Thermal Transport Measurements
• Planes, Chains, and Orbits: Quantum Oscillations and High Magnetic Field Heat Capacity in Underdoped YBCO
• Nodal structure of quasi-2D superconductors probed by magnetic field
• Carrier-Concentration Dependence of the Pseudogap Ground State of Superconducting Bi2Sr2-xLaxCuO6+delta Revealed by 63,65Cu-Nuclear Magnetic Resonance in Very High Magnetic Fields
• Anomalous quasiparticle transport in the superconducting state of CeCoIn5
• Weak coupling d-wave BCS superconductivity and unpaired electrons in overdoped La_{2-x}Sr_{x}CuO_{4} single crystals
• Unconventional superconductors under rotating magnetic field I: density of states and specific heat
• Electronic specific heat and low energy quasiparticle excitations in superconducting state of $L{a}_{2-x}S{r}_{x}Cu{O}_4$ single crystals
• Spectrum of low energy excitations in the vortex state: comparison of Doppler shift method to quasiclassical approach
• Superconducting Gap Function in Antiferromagnetic Heavy-Fermion UPd_2Al_3 Probed by Angle Resolved Magnetothermal Transport Measurements
• Hole doping dependences of the magnetic penetration depth and vortex core size in YBa2Cu3Oy: Evidence for stripe correlations near 1/8 hole doping
• Unconventional superconductors under rotating magnetic field II: thermal transport
• Evidence of d-wave Superconductivity in K_(1-x)Na_xFe_2As_2 (x = 0, 0.1) Single Crystals from Low-Temperature Specific Heat Measurements
• Spin susceptibility of charge ordered YBa2Cu3Oy across the upper critical field
• Delocalized Quasiparticles in the Vortex State of an Overdoped High-Tc Superconductor Probed by 63Cu NMR
• Theory of thermal conductivity in extended-$s$ state superconductors: application to ferropnictides
• Quasiclassical theory of superconducting states under magnetic fields: Thermodynamic properties
• Nodal gaps in the nematic superconductor FeSe from heat capacity
• Supercurrent in Nodal Superconductors
• Theory of the critical current in two-band superconductors with application to MgB2
• Nodes vs. minima in the energy gap of iron-pnictides from field-induced anisotropy
• Angular resolved specific heat in iron-based superconductors: the case for nodeless extended $s$-wave gap
• Mixed-State Thermodynamics of Superconductors with Moderately Large Paramagnetic Effects
• Transport properties of 3D extended s-wave states in Fe-based superconductors
• Low Temperature Susceptibility of the Noncentrosymmetric Superconductor CePt_3Si
• Inversion of specific heat oscillations with in-plane magnetic field angle in 2D d-wave superconductors
• Vortex state in d-wave superconductors with strong paramagnetism: transport and specific heat anisotropy
• Searching for zeroes: unconventional superconductors in a magnetic field
• Superfluid density and competing orders in d-wave superconductors
• Determination of the superconducting gap in near optimally doped Bi_2Sr_{2-x}La_xCuO_{6+δ} (x ~ 0.4) from low-temperature specific heat
• Field-angle resolved specific heat and thermal conductivity in the vortex phase of UPd_2Al_3
• Microwave Conductivity of a High Purity d-wave Superconductor
• Two different quasiparticle scattering rates in vortex line liquid phase of layered d-wave superconductors
• Volovik effect on NMR measurements of unconventional superconuctors
• Low temperature superfluid stiffness of d-wave superconductor in a magnetic field
• Heat transport in nonuniform superconductors
• Effect of gap suppression by superfluid current on nonlinear microwave response of d-wave superconductors
• Impurity resonances in the mixed state of high-Tc superconductors
• Phenomenological theory of the superconducting state inside the hidden-order phase of URu${}_2$Si${}_2$
• Paring instability in the mixed state of d-wave superconductor
• Field angle-dependent thermal conductivity in nodal superconuctors
• Thermal Hall conductivity in the strongest cuprate superconductor: Estimate of the mean free path in the trilayer cuprate HgBa${}_2$Ca${}_2$Cu${}_3$O${}_{8+\delta }$
• Crossover of the pairing symmetry from $s$- to $d$-wave in iron pnictide superconductors