Thermodynamics and quantum criticality in cuprate superconductors

Abstract

We will present elementary scaling arguments focussed on the thermodynamics in the proximity of the quantum critical point in the cuprate superconductors. Extending the analysis centered on the Grüneisen parameter by Rosch, Si and coworkers to the cuprates, we demonstrate that a combination of specific heat- and chemical potential measurements can reveal the nature of the zero temperature singularity. From the known specific heat data it follows that the effective number of time dimensions has to equal the number of space dimensions, while we find a total of six scaling laws governing the temperature and density dependence of the chemical potential, revealing directly the coupling constant scaling dimension.

arXiv comment4 pages no figures

References in corpus (20)

• "Deconfined" quantum critical points
• Hidden Order in the Cuprates
• Quantum phase transitions
• The break up of heavy electrons at a quantum critical point
• The doping dependence of T* - what is the real high-Tc phase diagram?
• Singular quasiparticle scattering in the proximity of charge instabilities
• Quantum Criticality: competing ground states in low dimensions
• Universally diverging Grueneisen parameter and the magnetocaloric effect close to quantum critical points
• Powerlaw optical conductivity with a constant phase angle in high Tc superconductors
• Singular Fermi Liquids
• Divergence of the Grueneisen Ratio at Quantum Critical Points in Heavy Fermion Metals
• The ground state of heavily-overdoped non-superconducting La${}_{2-x}$Sr${}_x$CuO${}_4$
• Universal Magnetic Properties of $L{a}_{2-\delta }S{r}_{\delta }Cu{O}_4$ at Intermediate Temperatures
• Unexpected Behavior of the Local Compressibility Near the B=0 Metal-Insulator Transition
• Temperature dependence of electrical resistivity of high-Tc cuprates - from pseudogap to overdoped regions
• Thermodynamic Signature of a Two-Dimensional Metal-Insulator Transition
• Crossover from coherent to incoherent electronic excitations in the normal state of Bi2Sr2CaCu2O8
• Chemical potential shift in lightly-doped to overdoped Bi${}_2$Sr${}_2$Ca${}_{1-x}${\it R}${}_x$Cu${}_2$O${}_{8+y}$ ({\it R} = Pr, Er)
• Magnetic Field Dependence of the Transverse Plasmon in SmLa_0.8Sr_0.2CuO_4
• Thermodynamical Cross-Relations for Superconductors at the Critical Point

Cited by in corpus (8)

• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• Scaling theory of the cuprate strange metals
• Hartree-Fock Computation of the High-Tc Cuprate Phase Diagram
• Temperature dependence of the bulk energy gap in underdoped Bi-2212: Evidence for the mean-field superconducting transition
• The specific heat jump at the superconducting transition and the quantum critical nature of the normal state of Pnictide superconductors
• Fermionic quantum criticality and the fractal nodal surface
• Thermodynamic properties of Bi2Sr2CaCu2O8 calculated from the electronic dispersion
• BCS Superconductivity in Quantum Critical Metals