Breakdown of One-Paramater Scaling in Quantum Critical Scenarios for the High-Temperature Copper-oxide Superconductors

Abstract

We show that if the excitations which become gapless at a quantum critical point also carry the electrical current, then a resistivity linear in temperature, as is observed in the copper-oxide high-temperature superconductors, obtains only if the dynamical exponent, $z$, satisfies the unphysical constraint, $z<0$. At fault here is the universal scaling hypothesis that, at a continuous phase transition, the only relevant length scale is the correlation length. Consequently, either the electrical current in the normal state of the cuprates is carried by degrees of freedom which do not undergo a quantum phase transition, or quantum critical scenarios must forgo this basic scaling hypothesis and demand that more than a single correlation length scale is necessary to model transport in the cuprates.

arXiv comment4 pages, 1 .eps figure. Physical Review Letters, in press

References in corpus (10)

• "Deconfined" quantum critical points
• Locally critical quantum phase transitions in strongly correlated metals
• Electronic Phase Diagram of High-T_c Cuprate Superconductors from a Mapping of the In-Plane Resistivity Curvature
• Powerlaw optical conductivity with a constant phase angle in high Tc superconductors
• Non-zero temperature transport near quantum critical points
• Universal scaling relation in high-temperature superconductors
• Interplay of disorder and spin fluctuations in the resistivity near a quantum critical point
• What angle-resolved photemission experiments tell about the microscopic theory for high-temperature superconductors
• Quantum Phase Transitions in a Cuprate Superconductor Bi_{2}Sr_{2-x}La_{x}CuO_{6+δ}
• Exposing the spin glass ground state of the non-superconducting La${}_{2-x}$Sr${}_x$Cu${}_{1-y}$Zn${}_y$O${}_4$ high-$T_c$ oxide

Cited by in corpus (42)

• Electrodynamics of Correlated Electron Materials
• Towards strange metallic holography
• Scale-invariant magnetoresistance in a cuprate superconductor
• Mottness: Identifying the Propagating Charge Modes in doped Mott Insulators
• Magnetoresistance near a quantum critical point
• Quantum Critical Transport and the Hall Angle
• Criticality in correlated quantum matter
• Scaling theory of the cuprate strange metals
• "Bad Metal" Conductivity of Hard Core Bosons
• Incoherent non-Fermi liquid scattering in a Kondo lattice
• High Frequency Behavior of the Infrared Conductivity of Cuprates
• Colloquium: Hydrodynamics and holography of charge density wave phases
• Mottness in High-Temperature Copper-Oxide Superconductors
• Stripe-like nanoscale structural phase separation and optimal inhomogeneity in superconducting BaPb${}_{1-x}$Bi${}_x$O${}_3$
• Stability of Quantum Critical Points in the Presence of Competing Orders
• Slow relaxation and diffusion in holographic quantum critical phases
• Doped Mott insulators are insulators: hole localization in the cuprates
• Constructing the AdS dual of a Fermi liquid: AdS Black holes with Dirac hair
• Impact of irrelevant deformations on thermodynamics and transport in holographic quantum critical states
• Holographic superconductor with momentum relaxation and Weyl correction
• Scaling properties of the optical conductivity of Bi-based cuprates
• Fractional Electromagnetism in Quantum Matter and High-Energy Physics
• Unparticles and Anomalous Dimensions in the Cuprates
• Critical Behavior in Doping-Driven Metal$-$Insulator Transition on Single-Crystalline Organic Mott-FET
• Hyperscaling violating black hole solutions and Magneto-thermoelectric DC conductivities in holography
• Two types of superconducting domes in unconventional superconductors
• Mottness Collapse and T-linear Resistivity in Cuprate Superconductors
• The n_s - T_c correlations in granular superconductors
• Optical conductivity near finite-wavelength quantum criticality
• Hidden Charge 2e Boson: Experimental Consequences for Doped Mott Insulators
• Dichotomy in the $T$-linear resistivity in hole-doped cuprates
• High-Temperature Criticality in Strongly Constrained Quantum Systems
• Critical charge instability on verge of the Mott transition and the origin of quantum protection in high-$T_c$ cuprates
• Quantum fluctuations of charge order induce phonon softening in a superconducting cuprate
• ω/T scaling of the optical conductivity in strongly correlated layered cobalt oxide
• S-Wave Superconductivity in Anisotropic Holographic Insulators
• Magnetic Field Effects on the Transport Properties of High-Tc Cuprates
• The Future of the Correlated Electron Problem
• Transport in a One-Dimensional Hyperconductor
• Fractionalize This
• Critical current density of hole doped high-Tc cuprates and heavy fermion superconductors: relevance to the possible quantum critical behavior
• Stranger than Metals