Fragmented superconductivity in the Hubbard model as solitons in Ginzburg-Landau theory

Abstract

The phenomena of superconductivity and charge density waves are observed in close vicinity in many strongly correlated materials. Increasing evidence from experiments and numerical simulations suggests both phenomena can also occur in an intertwined manner, where the superconducting order parameter is coupled to the electronic density. Employing density matrix renormalization group simulations, we investigate the nature of such an intertwined state of matter stabilized in the phase diagram of the elementary $t$-$t^{\prime }$-$U$ Hubbard model in the strong coupling regime. Remarkably, the condensate of Cooper pairs is shown to be fragmented in the presence of a charge density wave where more than one pairing wave function is macroscopically occupied. Moreover, we provide conclusive evidence that the macroscopic wave functions of the superconducting fragments are well-described by soliton solutions of a Ginzburg-Landau equation in a periodic potential constituted by the charge density wave. In the presence of an orbital magnetic field, the order parameters are gauge invariant, and superconducting vortices are pinned between the stripes. This intertwined Ginzburg-Landau theory is proposed as an effective low-energy description of the stripe fragmented superconductor.

14 pages, 9 figures

References in corpus (28)

• Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3Oy
• Theory of Intertwined Orders in High Temperature Superconductors
• The ITensor Software Library for Tensor Network Calculations
• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• Dislocations and vortices in pair density wave superconductors
• Coexistence of superconductivity with partially filled stripes in the Hubbard model
• Discovery of a Cooper-Pair Density Wave State in a Transition-Metal Dichalcogenide
• Ground State Phase Diagram of the $t$-$t^{\prime }$-$J$ model
• Detection of a Pair Density Wave State in UTe${}_2$
• High Temperature Superconductivity in a Lightly Doped Quantum Spin Liquid
• Robust d-wave superconductivity in the square-lattice $t$-$J$ model
• Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions
• Stripes and spin-density waves in the doped two-dimensional Hubbard model: ground state phase diagram
• Intertwined order and holography: the case of the parity breaking pair density wave
• Error estimates for extrapolations with matrix-product states
• Intertwined spin, charge and pair correlations in the two-dimensional Hubbard model in the thermodynamic limit
• Emergent Superconductivity and Competing Charge Orders in Hole-Doped Square-Lattice $t$-$J$ Model
• Pair-Density-Wave in the Strong Coupling Limit of the Holstein-Hubbard model
• Pair density wave in doped three-band Hubbard model on two-leg square cylinders
• Superconducting stripes in the hole-doped three-band Hubbard model
• Tunable Stripe Order and Weak Superconductivity in the Moiré Hubbard Model
• Fano interference of the Higgs mode in cuprate high-Tc superconductors
• Microscopic mechanism for fluctuating pair density wave
• Fragmented Cooper pair condensation in striped superconductors
• Fluctuating intertwined stripes in the strange metal regime of the Hubbard model
• Robust charge-density wave correlations in the electron-doped single-band Hubbard model
• Topological phases in the Fermi-Hofstadter-Hubbard model on hybrid-space ladders
• Ferromagnetism and Skyrmions in the Hofstadter-Fermi-Hubbard Model

Cited by in corpus (2)

• Observation of emergent scaling of spin-charge correlations at the onset of the pseudogap
• Superfluid dome in the spatially modulated two-dimensional XY model