Interplay Between $d$-wave Superconductivity and a Bond Density Wave in the one-band Hubbard model

Abstract

It is now well established that superconducting cuprates support a charge density wave state in the so-called underdoped region of their phase diagram. We investigate the possibility of charge order in the square-lattice Hubbard model, both alone and in coexistence with $d$-wave superconductivity. The charge order has a period four in one direction, is centered on bonds and has a $d$ form factor. We use the variational cluster approximation, an approach based on a rigorous variational principle that treats short-range correlations exactly, with two clusters of size $2\times 6$ that together tile the infinite lattice and provide a non-biased unit for a period-four bond density wave (BDW). We find that the BDW exists in a finite range of hole doping and increases in strength from $U=5$ to $U=8$. Its location and intensity depends strongly on the band dispersion. When probed simultaneously with $d$-wave superconductivity, the energy is sometimes lowered by the presence of both phases, depending on the interaction strength. Whenever they coexist, a pair-density wave (a modulation of superconducting pairing with the same period and form factor as the BDW) also exists.

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• Superconductivity in the twisted bilayer transition metal dichalcogenide WSe${}_2$ : a quantum cluster study
• Incorporation of charge- and pair-density-wave states into the one-band model of d-wave superconductivity
• Single-particle spectral function formulated and calculated by variational Monte Carlo method with application to $d$-wave superconducting state
• Influence of spin and charge fluctuations on spectra of the two-dimensional Hubbard model
• The phase diagram of the underdoped cuprates at high magnetic field
• Intrinsic Cluster-Shaped Density Waves in Cellular Dynamical Mean-Field Theory
• Charge- and pair-density-wave orders in the one-band Hubbard model with dynamical mean field theory
• Effective pairing theory for strongly correlated d-wave superconductors
• The $t$-$t^{\prime }$-$t^{\prime \prime }$-$U$ Hubbard model and Fermi-level peak
• Magnetic properties and temperature variation of spectra in the Hubbard model
• Structure of the Charge-Density Wave in Cuprate Superconductors: Lessons from NMR
• Doping dependence of chiral superconductivity in near $45^{\circ }$ twisted bilayer cuprates
• Stability of the coexistent superconducting-nematic phase under the presence of intersite interactions
• Spiral magnetism and chiral superconductivity in Kondo-Hubbard triangular lattice model