Superconductivity, Charge-Density-Waves, and Bipolarons in the Holstein model

Abstract

The electron-phonon (e-ph) interaction remains of great interest in condensed matter physics and plays a vital role in realizing superconductors, charge-density-waves (CDW), and polarons. We study the two-dimensional Holstein model for e-ph coupling using determinant quantum Monte Carlo across a wide range of its phase diagram as a function of temperature, electron density, dimensionless e-ph coupling strength, and the adiabatic ratio of the phonon frequency to the Fermi energy. We describe the behavior of the CDW correlations, the competition between superconducting and CDW orders and polaron formation, the optimal conditions for superconductivity, and the transition from the weak-coupling regime to the strong-coupling regime. Superconductivity is optimized at intermediate e-ph coupling strength and intermediate electron density, and the superconducting correlations increase monotonically with phonon frequency. The global maximum for superconductivity in the Holstein model occurs at large phonon frequency, the limit where an attractive Hubbard model effectively describes the physics.

arXiv comment9 pages, 6 figures

References in corpus (38)

• Electron-phonon interactions from first principles
• Evidence for ubiquitous strong electron-phonon coupling in high-temperature superconductors
• Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3Oy
• Superconductivity in Fullerides
• Interfacial mode coupling as the origin of the enhancement of Tc in FeSe films on SrTiO3
• Interplay of electron-lattice interactions and superconductivity in Bi2Sr2CaCu2O8+d
• Coupling Of The B1g Phonon To The Anti-Nodal Electronic States of Bi2Sr2Ca0.92Y0.08Cu2O(8+delta)
• A Systematic Study of Electron-Phonon Coupling to Oxygen Modes Across the Cuprates
• Enhanced Superconductivity and Suppression of Charge-density Wave Order in 2H-TaS${}_2$ in the Two-dimensional Limit
• Breakdown of Migdal-Eliashberg theory; a determinant quantum Monte Carlo study
• Superconductivity in the A15 Structure
• Polaron Crossover and Bipolaronic Metal-Insulator Transition in the half- filled Holstein model
• Gap formation and soft phonon mode in the Holstein model
• Phonon mechanism in the most dilute superconductor: n-type SrTiO3
• Pressure dependence of the charge-density-wave and superconducting states in GdTe${}_3$, TbTe${}_3$ and DyTe${}_3$
• Eliashberg theory of phonon-mediated superconductivity -- when it is valid and how it breaks down
• Determinant quantum Monte Carlo study of the two-dimensional single-band Hubbard-Holstein model
• Holstein model in infinite dimensions at half-filling
• Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime
• Quantitative reliability of Migdal-Eliashberg theory for strong electron-phonon coupling
• Two-dimensional Holstein-Hubbard model: Critical temperature, Ising universality, and bipolaron liquid
• Superconductivity and charge density wave order in the 2D Holstein model
• Superconductivity, charge-density waves, antiferromagnetism, and phase separation in the Hubbard-Holstein model
• Strong Coupling Limit of the Holstein-Hubbard Model
• A bound on superconducting $T_c$'s
• Competition between antiferromagnetic and charge order in the Hubbard-Holstein model
• Pseudogap crossover in the electron-phonon system
• Low-energy (< 10 meV) feature in the nodal electron self-energy and strong temperature dependence of the Fermi velocity in Bi(2)Sr(2)CaCu(2)O(8+delta)
• Quantum Monte Carlo study of lattice polarons in the two-dimensional multi-orbital Su-Schrieffer-Heeger model
• Polaron Crossover and Bipolaronic Metal-Insulator Transition in the Holstein model at half-filling
• Temperature-filling phase diagram of the two-dimensional Holstein model in the thermodynamic limit by self-consistent Migdal approximation
• Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model
• Electron-phonon coupling in cuprate and iron-based superconductors revealed by Raman scattering
• The effects of non-linear electron-phonon interactions on superconductivity and charge-density-wave correlations
• Anomalous relaxation kinetics and charge density wave correlations in underdoped BaPb1-xBixO3
• Doping dependence of ordered phases and emergent quasiparticles in the doped Hubbard-Holstein model
• Electron-phonon coupling in undoped cuprate $YB{a}_{2}C{u}_3{O}_6$ estimated from Raman and optical conductivity spectra
• Spectral properties and enhanced superconductivity in renormalized Migdal-Eliashberg theory

Cited by in corpus (24)

• Bipolaronic high-temperature superconductivity
• Phase Diagram of the Su-Schrieffer-Heeger-Hubbard model on a square lattice
• Fast and scalable quantum Monte Carlo simulations of electron-phonon models
• A perspective on machine learning and data science for strongly correlated electron problems
• Stripe correlations in the two-dimensional Hubbard-Holstein model
• A hybrid Monte Carlo study of bond-stretching electron-phonon interactions and charge order in BaBiO${}_3$
• Charge order in the kagome lattice Holstein model: A hybrid Monte Carlo study
• Bipolaronic superconductivity out of a Coulomb gas
• Dynamical tuning of the chemical potential to achieve a target particle number in grand canonical Monte Carlo simulations
• Ground state and spectral properties of the doped one-dimensional optical Hubbard-Su-Schrieffer-Heeger model
• Attractive Su-Schrieffer-Heeger-Hubbard Model on a Square Lattice Away from Half-Filling
• Machine learning the relationship between Debye temperature and superconducting transition temperature
• Instability of metals with respect to strong electron-phonon interaction
• Learning by Confusion: The Phase Diagram of the Holstein Model
• Magnetic, charge, and bond order in the two-dimensional Su-Schrieffer-Heeger-Holstein model
• High-temperature superconductivity induced by the Su-Schrieffer-Heeger electron-phonon coupling
• Enhancement of Charge Density Wave Correlations in a Holstein Model with an Anharmonic Phonon Potential
• Supersolid Phase in the Diluted Holstein Model
• The competition between antiferromagnetism and superconductivity in a doped Hubbard model with anisotropic interaction
• Charge correlations suppress unconventional pairing in the Holstein model
• Electron addition spectral functions of low-density polaron liquids
• Spectral signatures of residual electron pairing in the extended-Hubbard-Su-Schrieffer-Heeger model
• Doping dependence and multichannel mediators of superconductivity: Calculations for a cuprate model
• Tuning superconductivity and charge density wave order by next-nearest-neighbor hopping integral in honeycomb Holstein model