Charge-density-wave order with momentum $(2Q,0)$ and $(0,2Q)$ within the spin-fermion model: continuous and discrete symmetry breaking, preemptive composite order, and relation to pseudogap in hole-doped cuprates

Abstract

We analyze charge order within the the spin-fermion model. We show that magnetically-mediated interaction gives rise to charge order ${\Delta }_k^Q=⟨c_{\mathbf{k}+\mathbf{Q}}^{†}{c}_{\mathbf{k}-\mathbf{Q}}⟩$ with momenta $\mathbf{Q}=Q_x=(2Q,0)$ and $\mathbf{Q}=Q_y=(0,2Q)$, if the magnetic correlation length $\xi$ exceeds some critical value. We argue that ${\Delta }_k^Q$ and ${\Delta }_{-k}^Q$ are not equivalent, and their symmetric and antisymmetric combinations describe density modulations and bond current. We derive GL functional for four-component $U(1)$ order parameters ${\Delta }_{\pm k}^Q$ with $\mathbf{Q}=Q_x$ or $Q_y$. Within mean-field we find two types of CDW states, I and II, depending on system parameters. In state I density and current modulations emerge with the same $\mathbf{Q}=Q_x$ or $Q_y$, breaking $Z_2$ lattice rotational symmetry, and differ in phase by $\pm \pi /2$. The selection of $\pi /2$ or $-\pi /2$ additionally breaks $Z_2$ time-reversal symmetry, such that the total order parameter manifold is $U(1)\times Z_2\times Z_2$. In state II density and current modulations emerge with different $\mathbf{Q}$ and the order parameter manifold is $U(1)\times U(1)\times Z_2$. We go beyond mean-field and show that discrete symmetries get broken before long-range charge order sets in. For state I, the system first breaks $Z_2$ lattice rotational symmetry ($C_4\to C_2$) at $T=T_n$ and develops a nematic order, then breaks $Z_2$ time-reversal symmetry at $T_t<T_n$, and finally breaks $U(1)$ symmetry of a common phase of even and odd components of ${\Delta }_k^Q$ at $T=T_{\mathrm{cdw}}<T_t<T_n$ and develops a true charge order. We argue that the preemptive orders lift $T_{\mathrm{cdw}}$ and reduces $T_{\mathrm{sc}}$ such that at large $\xi$ charge order may develop prior to superconductivity. We obtain the phase diagram and present quantitative comparison with ARPES data for hole-doped cuprates.

references added. 124 pages, 26 figures

References in corpus (35)

• Electrodynamics of Correlated Electron Materials
• Ubiquitous Interplay between Charge Ordering and High-Temperature Superconductivity in Cuprates
• Charge order driven by Fermi-arc instability in Bi2201
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• From a single-band metal to a high-temperature superconductor via two thermal phase transitions
• From a single-band metal to a high-temperature superconductor via two thermal phase transitions (Supporting Material)
• Striped superconductors: How the cuprates intertwine spin, charge and superconducting orders
• Distinct Charge Orders in the Planes and Chains of Ortho-III-Ordered YBa${}_2$Cu${}_3$O${}_{6+\delta }$ Superconductors Identified by Resonant Elastic X-ray Scattering
• Quenched disorder and vestigial nematicity in the pseudo-gap regime of the cuprates
• Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates
• Spin dynamics in the pseudogap state of a high-temperature superconductor
• Self-Consistent Vertex Correction Analysis for Iron-Based Superconductors: Mechanism of Coulomb-Interaction-Driven Orbital Fluctuations
• Evidence for unusual superconducting correlations coexisting with stripe order in La(1.875)Ba(0.125)CuO(4)
• Superconductivity and spin-density-waves in multi-band metals
• On the Reconstructed Fermi Surface in the Underdoped Cuprates
• Cascade of phase transitions in the vicinity of a quantum critical point
• Electronic phase diagram of high temperature copper oxide superconductors
• Kerr effect as evidence of gyrotropic order in the cuprates
• Gap anisotropy and universal pairing scale in a spin fluctuation model for cuprates
• Berry phase mechanism for optical gyrotropy in stripe-ordered cuprates
• Effect of the pseudogap on T${}_c$ in the cuprates and implications for its origin
• Mean field theory of competing orders in metals with antiferromagnetic exchange interactions
• Gapless superconductivity and the Fermi arc in the cuprates
• A controlled expansion for certain non-Fermi liquid metals
• Time-reversal symmetry breaking by a $(d+id)$ density-wave state in underdoped cuprate superconductors
• Magneto-optical signatures of a cascade of transitions in La${}_2-x$Ba${}_x$CuO${}_4$
• Pseudogap in underdoped cuprates and spin-density-wave fluctuations
• An ARPES view on the high-Tc problem: phonons vs spin-fluctuations
• Quantum critical point shifts under superconductivity: the pnictides and the cuprates
• Quantum critical point for stripe order: An organizing principle of cuprate superconductivity
• Composite charge order in the pseudogap region of the cuprates
• Optical conductivity of a two-dimensional metal at the onset of spin-density-wave order
• Broken translational symmetry in an emergent paramagnetic phase of graphene
• Stripes in cuprate superconductors: Excitations and dynamic dichotomy
• PuPt2In7: a computational and experimental investigation

Cited by in corpus (174)

• Theory of Intertwined Orders in High Temperature Superconductors
• Resonant x-ray scattering studies of charge order in cuprates
• Resonant X-ray Scattering Study of Charge Density Wave Correlations in YBa${}_2$Cu${}_3$O${}_{6+x}$
• Connection between charge-density-wave order and charge transport in the cuprate superconductors
• Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy
• Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates
• Thermodynamic evidence for nematic phase transition at the onset of pseudogap in YBa${}_2$Cu${}_3$O${}_y$
• The symmetry of charge order in cuprates
• Intertwined vestigial order in quantum materials: nematicity and beyond
• Weak-Pairing Higher Order Topological Superconductors
• Mott physics and spin fluctuations: a unified framework
• Pseudogap from ARPES experiment: three gaps in cuprates and topological superconductivity
• Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates
• Re-entrant charge order in overdoped (Bi,Pb)${}_{2.12}$Sr${}_{1.88}$CuO${}_{6+\delta }$ outside the pseudogap regime
• Ising nematic quantum critical point in a metal: a Monte Carlo study
• High-temperature charge density wave correlations in La${}_{1.875}$Ba${}_{0.125}$CuO${}_4$ without spin-charge locking
• Charge Order in the Pseudogap Phase of Cuprate Superconductors
• Mott physics and spin fluctuations: a functional viewpoint
• Synchrotron x-ray scattering study of charge-density-wave order in HgBa${}_2$CuO${}_{4+\delta }$
• Superconductivity vs bound state formation in a two-band superconductor with small Fermi energy -- applications to Fe-pnictides/chalcogenides and doped SrTiO3
• Doping dependent charge order correlations in electron-doped cuprates
• Bond order instabilities in a correlated two-dimensional metal
• Competing Orders in a Nearly Antiferromagnetic Metal
• Commensurate antiferromagnetic excitations as a signature of the pseudogap in the tetragonal high-Tc cuprate HgBa${}_2$CuO${}_{4+\delta }$
• Connecting high-field quantum oscillations to zero-field electron spectral functions in the underdoped cuprates
• Interplay between pair-density-wave and charge-density-wave orders in underdoped cuprates
• Charge ordering in superconducting copper oxides
• Spin-Fluctuation-Driven Nematic Charge-Density-Wave in Cuprate Superconductors: Impact of Aslamazov-Larkin-Type Vertex Correction
• Intertwined Order in a Frustrated 4-leg $t-J$ Cylinder
• Intra-Unit-Cell magnetic correlations near optimal doping in $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6.85}$
• Density-wave instabilities of fractionalized Fermi liquids
• Pseudogap, charge order, and pairing density wave at the hot spots in cuprate superconductors
• Pair Density Waves in Superconducting Vortex Halos
• Topological superconducting phases from inversion symmetry breaking order in spin-orbit-coupled systems
• Nonequilibrium enhancement of high-temperature superconductivity in a 3D model of cuprates
• Emergent loop current order from pair density wave superconductivity
• The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters
• Feedback of superconducting fluctuations on charge order in the underdoped cuprates
• Topological phase transitions in multi-component superconductors
• Orbital symmetry of charge density wave order in La1.875Ba0.125CuO4 and YBa2Cu3O6.67
• Incommensurate phonon anomaly and the nature of charge density waves in cuprates
• Fractionalized pair density wave in the pseudo-gap phase of cuprate superconductors
• Light induced enhancement of superconductivity via melting of competing bond-density wave order in underdoped cuprates
• Coupling between dynamic magnetic and charge-order correlations in the cuprate superconductor Nd${}_{2-x}$Ce${}_x$CuO${}_4$
• Renormalization group analysis of the pair-density-wave and charge order within the fermionic hot-spot model for cuprate superconductors
• Normal state properties of quantum critical metals at finite temperature
• TRILEX and $GW$+EDMFT approach to $d$-wave superconductivity in the Hubbard model
• Enhancement of superconductivity at the onset of charge-density-wave order in a metal
• The nature of effective interaction in cuprate superconductors: a sign-problem-free quantum Monte-Carlo study
• Checkerboard order in vortex cores from pair-density-wave superconductivity
• Superconductivity near a nematic quantum critical point -- the interplay between hot and lukewarm regions
• Evolution of Pairing Orders between Pseudogap and Superconducting Phases of Cuprate Superconductors
• Charge orders, magnetism and pairings in the cuprate superconductors
• Hourglass dispersion and resonance of magnetic excitations in the superconducting state of the single-layer cuprate HgBa2CuO4+δ near optimal doping
• Loop currents in quantum matter
• Spin-Driven Nematic Instability of the Multi-Orbital Hubbard Model: Application to Iron-Based Superconductors
• Evolution of charge order topology across a magnetic phase transition in cuprate superconductors
• Charge-fluctuations in lightly hole-doped cuprates: effect of vertex corrections
• Pseudogap and superconductivity in two-dimensional doped charge-transfer insulators
• Effective SU(2) theory for the pseudogap state
• Crisscrossed stripe order from interlayer tunneling in hole-doped cuprates
• Incommensurate charge ordered states in the $t-t^{\prime }-J$ model
• Unconventional density waves and superconductivities in Fe-based superconductors and other strongly correlated electron systems
• Tilted loop currents in cuprate superconductors
• $p$-orbital density wave with $d$ symmetry in high-$T_c$ cuprate superconductors predicted by the renormalization-group + constrained RPA theory
• Superconductivity without hole-pocket in electron-doped FeSe: Analysis beyond the Migdal-Eliashberg formalism
• Genesis of charge orders in high temperature superconductors
• Competing Unconventional Charge-Density-Wave States in Cuprate Superconductors: Spin-Fluctuation-Driven Mechanism
• Unconventional superconductivity in altermagnets with spin-orbit coupling
• Fluctuating orders and quenched randomness in the cuprates
• The ladder physics in the Spin Fermion model
• The enigma of the pseudogap phase of the cuprate superconductors
• Charge ordering in three-band models of the cuprates
• A strong coupling critique of spin fluctuation driven charge order in underdoped cuprates
• Electronic polymers and soft-matter-like broken symmetries in underdoped cuprates
• Fragile superconductivity in the presence of weakly disordered charge density waves
• Is charge order induced near an antiferromagnetic quantum critical point?
• Polar Kerr effect from chiral-nematic charge order
• Incorporation of charge- and pair-density-wave states into the one-band model of d-wave superconductivity
• The (extended) dynamical mean field theory combined with the two-particle irreducible functional renormalization-group approach as a tool to study strongly-correlated systems
• Double stage nematic bond-ordering above double stripe magnetism: application to BaTi${}_2$Sb${}_2$O
• Close inspection of plasmon excitations in cuprate superconductors
• Scattering Interference Signature of a Pair Density Wave State in the Cuprate Pseudogap Phase
• Odd-parity spin-loop-current order mediated by transverse spin fluctuations in cuprates and related electron systems
• Superconductivity above a quantum critical point in a metal -- gap closing vs gap filling, Fermi arcs, and pseudogap behavior
• Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: a Monte Carlo study
• Quantum oscillations in a bilayer with broken mirror symmetry: a minimal model for YBa${}_2$Cu${}_3$O${}_{6+\delta }$
• Emergence of Charge Loop Current in Geometrically Frustrated Hubbard Model: Functional Renormalization Group Study
• SU(2)-symmetry in a realistic spin-fermion model for cuprate superconductors
• Dual structure in the charge excitation spectrum of electron-doped cuprates
• Unconventional high-energy-state contribution to the Cooper pairing in under-doped copper-oxide superconductor HgBa${}_2$Ca${}_2$Cu${}_3$O${}_{8+\delta }$
• Solvable model for a charge-$4e$ superconductor
• Chiral liquid phase of simple quantum magnets
• Electronic spin susceptibilities and superconductivity in HgBa${}_2$CuO${}_{4+\delta }$ from nuclear magnetic resonance
• Higgs Modes in the Pair Density Wave Superconducting State
• Cascade of vestigial orders in two-component superconductors: nematic, ferromagnetic, s-wave charge-4e, and d-wave charge-4e states
• Spin-fermion model with overlapping hot spots and charge modulation in cuprates
• Quantum criticality in two dimensions and Marginal Fermi Liquid
• Theoretical Prediction of the Nematic Orbital-Ordered State in Ti-Oxypnictide Superconductor BaTi2(As,Sb)2O
• Strong competition between ${\Theta }_{II}$-loop-current order and $d$-wave charge order along the diagonal direction in a two-dimensional hot spot model
• Enhanced nematic fluctuations near an antiferromagnetic Mott insulator and possible application to high-$T_c$ cuprates
• Instability towards Staggered Loop Currents in the Three-Orbital Model for Cuprate Superconductors
• Superconducting and charge-density-wave orders in the spin-fermion model: a comparative analysis
• Optical Enhancement of Superconductivity via Targeted Destruction of Charge Density Waves
• $d$-wave bond-order charge excitations in electron-doped cuprates
• $\eta$ collective mode as A${}_{1g}$ Raman resonance in cuprate superconductors
• Angle Resolved Photo-Emission Spectroscopy signature of the Resonant Excitonic State
• Signatures of nematic quantum critical fluctuations in the Raman spectra of lightly doped cuprates
• The Hubbard model on a triangular lattice -- pseudogap due to spin-density-wave fluctuations
• Memory matrix theory of the dc resistivity of a disordered antiferromagnetic metal with an effective composite operator
• Hidden Order as a Source of Interface Superconductivity
• Nematic fluctuations and their wave vector in two-dimensional metals
• Antagonistic in-plane resistivity anisotropies from competing fluctuations in underdoped cuprates
• Fluctuations and Higgs mechanism in Under-Doped Cuprates: a Review
• Adiabatic variation of the charge-density-wave phase diagram in the 123 cuprate (Ca${}_x$La${}_{1-x}$)(Ba${}_{1.75-x}$La${}_{0.25+x}$)Cu${}_3$O${}_y$
• Charge- and pair-density-wave orders in the one-band Hubbard model with dynamical mean field theory
• Thermodynamic electric quadrupole moments of nematic phases from first-principles calculation
• Theoretical insights into electronic nematic order, bond-charge orders, and plasmons in cuprate superconductors
• Anomalous softening of phonon-dispersion in cuprate superconductors
• Electron self-energy from quantum charge fluctuations in the layered t-J model with long-range Coulomb interaction
• Pseudo-spin Skyrmions in the Phase Diagram of Cuprate Superconductors
• Non-degenerate surface pair density wave in the Kagome superconductor CsV${}_3$Sb${}_5$ -- application to vestigial orders
• Interplay between uni-directional and bi-directional charge-density-wave orders in underdoped cuprates
• Topological Defects in Systems with Two Competing Order Parameters: Application to Superconductors with Charge- and Spin-Density Waves
• The Crossover from Ordinary to Higher-Order van Hove Singularity in a Honeycomb System: A Parquet Renormalization Group Analysis
• Emergence of strongly correlated electronic states driven by the Andreev bound state in d-wave superconductors
• Structure of the Charge-Density Wave in Cuprate Superconductors: Lessons from NMR
• Quantum Critical Point revisited by the Dynamical Mean Field Theory
• Pairing mechanism for nodal $s$-wave superconductivity in BaFe${}_2$(As,P)${}_2$: Analysis beyond Migdal-Eliashberg formalism
• Doping dependence of d-wave bond-charge excitations in electron-doped cuprates
• Emergence of $d\pm ip$-wave superconducting state at the edge of $d$-wave superconductors mediated by Andreev-bound-state-driven ferromagnetic fluctuations
• Theory of charge dynamics in bilayer electron system with long-range Coulomb interaction
• Emergence of charge order in a staggered loop-current phase of cuprate high-temperature superconductors
• Real space Eliashberg approach to charge order of electrons coupled to dynamic antiferromagnetic fluctuations
• Mean-field thermodynamic quantum time-space crystal: spontaneous breaking of time-translation symmetry in a macroscopic fermion system
• Competition between spin-induced charge instabilities in underdoped cuprates
• $d$- and $p$-wave quantum liquid crystal orders in cuprate superconductors, $\kappa$-(BEDT-TTF)${}_2$X, and coupled chain Hubbard models: functional-renormalization-group analysis
• Smeared nematic quantum phase transitions due to rare-region effects in inhomogeneous systems
• Ring-like shaped charge modulations in the t-J model with long-range Coulomb interaction
• Renormalization Group Analysis of a Fermionic Hot Spot Model
• Quasiparticle interference of heavy fermions in resonant X-ray scattering
• Magnetic fluctuations in pair density wave superconductors
• The Effect of Pointlike Impurities on d_{x^2-y^2} Charge Density Waves in Cuprate Superconductors
• Phase transition into Instanton Crystal
• Polar Kerr effect from a time-reversal symmetry breaking unidirectional charge density wave
• Gutzwiller Charge Phase Diagram of Cuprates, including Electron-Phonon Coupling Effects
• Incipient loop current order in the under-doped cuprate superconductors
• Thermal and thermoelectric transport coefficients for a two-dimensional SDW metal with weak disorder: A memory matrix calculation
• Overlapping hot spots and charge modulation in cuprates
• Prediction of pseudogap formation due to $d$-wave bond-order in organic superconductor $\kappa$-(BEDT-TTF)${}_2$X
• Charge order near the antiferromagnetic quantum critical point in the trilayer high $T_c$ cuprate HgBa${}_2$Ca${}_2$Cu${}_3$O${}_{8+\delta }$
• A calculation for polar Kerr effect in high temperature cuprate superconductors
• Charge and current orders in the spin-fermion model with overlapping hot spots
• Random-strain-induced correlations in materials with intertwined nematic and magnetic orders
• Calculation of the magnetotransport for a spin-density-wave quantum critical theory in the presence of weak disorder
• Spin and bond-charge excitation spectra in correlated electron systems near antiferromagnetic phase
• Glue function of optimally and overdoped cuprates from inversion of the Raman spectra
• Elastoconductivity as a probe of broken mirror symmetries
• Charge-density wave fluctuation driven composite order in the layered Kagome Metals
• $d$-Density Wave (DDW) Scenario Description of the New Hidden Charge Order in Cuprates
• Edge-induced strongly correlated electronic states in two-dimensional Hubbard model: Enhancement of magnetic correlations and self-energy effects
• Fluctuating charge order in the cuprates: spatial anisotropy and feedback from superconductivity
• Simple predictors of $T_c$ in superconducting cuprates and the role of interactions between effective Wannier orbitals in the $d-p$ 3-band model
• Vestigial $d$-wave charge-$4e$ Superconductivity from Bidirectional Pair Density Waves
• A Theoretical Study of Doping Evolution of Phonons in High-Temperature Cuprate Superconductors
• Theory of dual fermion superconductivity in hole-doped cuprates
• High field charge order across the phase diagram of $YB{a}_{2}C{u}_3{O}_y$
• Development of spin fluctuations under the presence of $d$-wave bond order in cuprate superconductors
• Electronic spin-triplet nematic with a twist
• Theoretical perspectives on charge dynamics in high-temperature cuprate superconductors
• Pseudogap in electron-doped cuprates: thermal precursor to magnetism
• Emergent Ising degrees of freedom above double-stripe magnetism
• Strongly correlated model of acousticlike plasmons persisting across the phase diagram of cuprate superconductors
• Symmetry classification of bond order parameters in cuprates