Where is the quantum critical point in the cuprate superconductors?

Abstract

Transport measurements in the hole-doped cuprates show a "strange metal" normal state with an electrical resistance which varies linearly with temperature. This strange metal phase is often identified with the quantum critical region of a zero temperature quantum critical point (QCP) at hole density x=x_m, near optimal doping. A long-standing problem with this picture is that low temperature experiments within the superconducting phase have not shown convincing signatures of such a optimal doping QCP (except in some cuprates with small superconducting critical temperatures). I review theoretical work which proposes a simple resolution of this enigma. The crossovers in the normal state are argued to be controlled by a QCP at x_m linked to the onset of spin density wave (SDW) order in a "large" Fermi surface metal, leading to small Fermi pockets for x<x_m. A key effect is that the onset of superconductivity at low temperatures disrupts the simplest canonical quantum critical crossover phase diagram. In particular, the competition between superconductivity and SDW order_shifts_ the actual QCP to a lower doping x_s < x_m in the underdoped regime, so that SDW order is only present for x<x_s. I review the phase transitions and crossovers associated with the QCPs at x_m and x_s: the resulting phase diagram as a function of x, temperature, and applied magnetic field consistently explains a number of recent experiments.

6 pages, 5 figures, Talk at the Conference on Quantum Criticality and Novel Phases, Dresden; (v2)+(v3) added clarifications and refs; (v4) added discussion on electron-doped superconductors and three-dimensional figure; (v5) Included addendum based on discussions at conference, and 2 new figures; (v7) discussion of early experimental work of Panagopoulos et al

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• Fermi-liquid instabilities at magnetic quantum phase transitions
• Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor
• Magnetic order in the pseudogap phase of high-$T_C$ superconductors
• Electron pockets in the Fermi surface of hole-doped high-Tc superconductors
• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• Polar Kerr Effect Measurements of YBa2Cu3O6+x: Evidence for Broken Symmetry Near the Pseudogap Temperature
• Quantum Oscillations in the Underdoped Cuprate YBa2Cu4O8
• A multi-component Fermi surface in the vortex state of an underdoped high-Tc superconductor
• Shubnikov-de Haas oscillations in YBa_2Cu_4O_8
• Spin correlations in the electron-doped high-transition-temperature superconductor Nd{2-x}Ce{x}CuO{4+/-delta}
• Antiphase Stripe Order as the Origin of Electron Pockets Observed in 1/8-Hole-Doped Cuprates
• Phenomenology of the normal state in-plane transport properties of high-$T_c$ cuprates
• de Haas-van Alphen oscillations in the underdoped cuprate YBa${}_2$Cu${}_3$O${}_{6.5}$
• Fermi Surface Evolution in an Electron-Doped High-Tc Superconductor Revealed by Magnetic Quantum Oscillations
• Tuning competing orders in La2-xSrxCuO4 cuprate superconductors by the application of an external magnetic field
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• Algebraic charge liquids
• Magnetic-field-enhanced incommensurate magnetic order in the underdoped high-temperature superconductor YBa(2)Cu(3)O(6.45)
• Competition between spin density wave order and superconductivity in the underdoped cuprates
• Electrical resistivity near Pomeranchuk instability in two dimensions
• Field-induced soft-mode quantum phase transition in La${}_{1.855}$Sr${}_{0.145}$CuO${}_4$
• Destruction of Neel order in the cuprates by electron-doping
• Paired electron pockets in the hole-doped cuprates

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• Spin-glass behavior in Ni-doped La1:85Sr0:15CuO4
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• Charge density waves in cuprate superconductors beyond the critical doping
• Novel magnetic order in pseudogap state of high Tc copper oxides superconductors
• Scaling theory of the cuprate strange metals
• Instabilities near the onset of spin density wave order in metals
• Proximity of Iron Pnictide Superconductors to a Quantum Tricritical Point
• Electronic phase diagram of high temperature copper oxide superconductors
• Hartree-Fock Computation of the High-Tc Cuprate Phase Diagram
• Spectroscopic Evidence for Charge Order Melting via Quantum Fluctuations in a Cuprate
• Fermi surface reconstruction and drop of Hall number due to spiral antiferromagnetism in high-$T_c$ cuprates
• Reconstructing the quantum critical fan of strongly correlated systems via quantum correlations
• Lifshitz Transition in Underdoped Cuprates
• Proximity of the Superconducting Dome and the Quantum Critical Point in the Two-Dimensional Hubbard Model
• Quantum critical scaling at the edge of Fermi liquid stability in a cuprate superconductor
• Antiferromagnetism and Superconductivity in Cerium based Heavy Fermion Compounds
• Crossover of Charge Fluctuations across the Strange Metal Phase Diagram
• Dual parquet scheme for the two-dimensional Hubbard model: modelling low-energy physics of high-$T_c$ cuprates with high momentum resolution
• Correlation between Fermi surface transformations and superconductivity in the electron-doped high-$T_c$ superconductor Nd${}_{2-x}$Ce${}_x$CuO${}_4$
• Normal state specific heat in the cuprates La${}_{2-x}$Sr${}_x$CuO${}_4$ and Bi${}_{2+y}$Sr${}_{2-x-y}$La${}_x$CuO${}_{6+\delta }$ near the critical point of the pseudogap phase
• Signature of quantum criticality in cuprates by charge density fluctuations
• Fermi Surface of the Electron-doped Cuprate Superconductor Nd_{2-x}Ce_xCuO_{4} Probed by High-Field Magnetotransport
• Visualizing Strange Metallic Correlations in the 2D Fermi-Hubbard Model with AI
• Zero-field Quantum Critical Point in CeCoIn${}_5$
• Quantum critical point shifts under superconductivity: the pnictides and the cuprates
• Strong magnetic fluctuations in superconducting state of CeCoIn${}_5$
• Antiferromagnetism and Superconductivity in CeRhIn${}_5$
• Breakdown of Fermi liquid behavior at the (π,π)=2k_F spin-density wave quantum-critical point: the case of electron-doped cuprates
• Quantum phase transition inside the superconducting dome of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ probed by optical magneto-sensing using NV-centers in diamond
• Signature of frustrated moments in quantum critical CePd${}_{1-x}$Ni${}_x$Al
• Emergence of quantum critical behavior in metallic quantum-well states of strongly correlated oxides
• Identification of a Critical Doping for Charge Order Phenomena in Bi-2212 Cuprates via RIXS
• Quantum phase transitions of antiferromagnets and the cuprate superconductors
• Pristine quantum criticality in a Kondo semimetal
• Quantum Criticality and Incipient Phase Separation in the Thermodynamic Properties of the Hubbard Model
• Nature and symmetry of the order parameter of the noncentrosymmetric superconductor Li2Pt3B
• Experimental evidence for Zeeman spin-orbit coupling in layered antiferromagnetic conductors
• Anomalous change in the de Haas-van Alphen oscillations of CeCoIn${}_5$ at ultra-low temperatures
• Emergent dome of nematic order around a quantum anomalous Hall critical point
• Quantum Criticality and Novel Phases: Summary and Outlook
• Spin Zeros and the Origin of Fermi Surface Reconstruction in the Cuprates
• Quantum fluctuations of charge order induce phonon softening in a superconducting cuprate
• Competing orders suppressed by disorder around a hidden quantum critical point in cuprate high Tc superconductors
• Revised phase diagram of the high-$T_c$ cuprate superconductor Pb-doped Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ revealed by anisotropic transport measurements
• Gutzwiller-projected wave functions for the pseudogap state of underdoped high-temperature superconductors
• Influence of Thermal Fluctuations of Spin Density Wave Order Parameter on the Quasiparticle Spectral Function
• Observation of pseudogap in MgB2
• Extension of dynamical mean-field theory by inclusion of nonlocal two-site correlations with variable distance
• The Iso-electronic Series $C{a}_{2-x}S{r}_{x}Ru{O}_4$: Structural Distortion, Effective Dimensionality, Spin Fluctuations and Quantum Criticality
• Anomalous superconductivity and superfluidity in repulsive fermion systems
• Pressure tuned superconductivity and normal state behavior in Ba(Fe${}_{0.943}$Co${}_{0.057}$)${}_2$As${}_2$ near the antiferromagnetic boundary
• Quantum critical points and phase separation instabilities in Hubbard nanoclusters
• Universality class of quantum criticality in the two-dimensional Hubbard model at intermediate temperatures ($t^2/U\ll T\ll t$)
• Ultralow temperature NMR of CeCoIn${}_5$
• Fractionalized Fermi liquids and the cuprate phase diagram
• de Haas-van Alphen oscillations for non-relativistic fermions coupled to an emergent U(1) gauge field
• Gapped dilatons in scale invariant superfluids
• Rényi entropy of quantum anharmonic chain at non-zero temperature
• Geometric orthogonal metals: Hidden antiferromagnetism and pseudogap from fluctuating stripes
• Pressure-induced enhancement of the superconducting transition temperature in La2O2Bi3AgS6
• Electric--field effect on electron-doped infinite-layer Sr${}_{0.88}$La${}_{0.12}$CuO${}_{2+x}$ thin films
• Anomalous Transport Behavior in Quantum Magnets
• Emergence of Fermi-liquid and BCS physics in overdoped cuprates