We investigate the competition between superconductivity (SC) and charge density wave (CDW) under a time-dependent periodic field in the attractive Hubbard model. By employing the time-dependent exact diagonalization method, we show that the driving frequency and amplitude of the external field can control the enhancement of either the superconducting pair or the CDW correlation in the system, for which SC and CDW are degenerate in the ground state of the half-filled attractive Hubbard model in the absence of the field. In the strong-coupling limit of the attractive Hubbard interaction, the controllability is characterized by the anisotropic interaction of the effective model. The anisotropy is induced by the external field and lifts the degeneracy of SC and CDW. We find that the enhancement or suppression of the superconducting pair and CDW correlations in the periodically driven attractive Hubbard model can be well interpreted by the quench dynamics of the effective model derived in the strong-coupling limit.
Pump-probe experiments have turned out as a powerful tool in order to study the dynamics of competing orders in a large variety of materials. The corresponding analysis of the data often relies on standard linear-response theory generalized to nonequilibrium situations. Here we examine the validity of such an approach for the charge and pairing response of systems with charge-density wave and (or) superconducting (SC) order. Our investigations are based on the attractive Hubbard model which we study within the time-dependent Hartree-Fock approximation. In particular, we calculate the quench and pump-probe dynamics for SC and charge order parameters in order to analyze the frequency spectra and the coupling of the probe field to the specific excitations. Our calculations reveal that the ``linear-response assumption'' is justified for small to moderate nonequilibrium situations (i.e., pump pulses) in the case of a purely charge-ordered ground state. However, the pump-probe dynamics on top of a superconducting ground state is determined by phase and amplitude modes which get coupled far from the equilibrium state indicating the failure of the linear-response assumption.
We study the competing charge-density-wave and superconducting order in the attractive Hubbard model under a voltage bias, using steady-state nonequilibrium dynamical mean-field theory. We show that the charge-density wave is suppressed in a current-carrying nonequilibrium steady state. This effect is beyond a simple Joule-heating mechanism and a ``supercooled'' metallic state is stabilized at a nonequilibrium temperature lower than the equilibrium superconducting
Tc. On the other hand, a current-carrying superconducting state is dissipationless and thus not subject to the same nonthermal suppression, and can therefore nucleate out of the supercooled metal, e.g., in a resistive switching experiment. The fact that an electric current can change the relative stability of different phases compared to thermal equilibrium, even when a system appears locally thermal due to electron-electron scattering, provides a general perspective to control intertwined orders out of equilibrium.
Recently, a flurry of works have found strong competition between charge density wave (CDW) and superconductivity (SC) in the doped Hubbard and $t\text{\ensuremath{-}}J$ models on the square lattice. Interestingly, some recent results suggest that the electron-phonon coupling may suppress CDW order and enhance SC. In this work, we consider the square-lattice Hubbard model with the Holstein or Su-Schrieffer-Heeger electron-phonon coupling at the large-
U and antiadiabatic (infinite phonon frequency) limits, which gives an effective $t\text{\ensuremath{-}}J$ model with either a density attractive interaction
V or a
JP term that contributes a larger spin exchange and a density repulsive interaction. To explore how these effective couplings may tune the competition between CDW and SC, we implement the density matrix renormalization group simulations on the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J$ model with
V or
JP coupling. We focus on the six-leg cylinder system with the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$, which hosts partially filled stripe and
d-wave SC in phase diagram. By tuning ${t}^{\ensuremath{'}}/t>0$ and
V or
JP, we establish two quantum phase diagrams at
121 doping ratio. In the SC phases, the increased
V or
JP coupling can enhance the quasi-long-range SC order, consistent with some previous findings. Nonetheless, no SC emerges when the partially filled stripe phase disappears with increased
V or
JP. Instead, the system has a transition to either a phase-separation-like regime or a filled stripe phase. On the other hand, with increased ${t}^{\ensuremath{'}}/t$, not only the partially filled stripe but the phase separation and filled stripe can also be tuned to SC phase. Our results suggest that although
V and
JP couplings may strengthen hole binding, the hole dynamics controlled by ${t}^{\ensuremath{'}}/t$ appears to play a more crucial role for obtaining a SC in the $t\text{\ensuremath{-}}J$ model.
We investigate the laser-induced dynamics of electronically driven charge-density-wave (CDW) order. A comprehensive mean-field analysis of the attractive Hubbard model in the weak-coupling regime reveals ultrafast switching and ultrafast melting of the order via a nonthermal pathway. The resulting nonequilibrium phase diagram exhibits multiple distinct regimes of the order parameter dynamics upon increasing field strength, indicative of multiple dynamical phase transitions. Using an intuitive pseudospin picture, we show how the distinct dynamical regimes can be connected to the spin precession angle. We furthermore study the effects of electron-electron interactions beyond mean field to show that the main features of the phase diagram are robust against scattering or thermalization processes. For example, the nonthermal state with switched order is characterized by a particularly slow relaxation. The nonthermal phases can be stabilized by tailoring the pulse shape with optimal control theory. We also demonstrate how the dynamics allows to distinguish an electron-electron interaction driven CDW from an electron-phonon interaction driven CDW.
We show that a resonant pulsed field can induce a steady superconducting state even in the deep Mott insulating phase of the dimerized Hubbard model. The superconductivity found here in the nonequilibrium steady state is due to the $\ensuremath{\eta}$-pairing mechanism, characterized by the existence of the off-diagonal long-range order (ODLRO), and is absent in the ground-state phase diagram. The key of the scheme lies in the generation of the field-induced charge density wave (CDW) state that is from the valence bond solid. The dynamics of this state resides in the highly excited subspace of the dimerized Hubbard model and is dominated by a $\ensuremath{\eta}$-spin ferromagnetic model. The decay of such long-living excitation is suppressed because of energy conservation. We also develop a dynamical method to detect the ODLRO of the nonequilibrium steady state. Our finding demonstrates that the nonequilibrium many-body dynamics induced by the interplay between the resonant external field and electron-electron interaction is an alternative pathway to access a new exotic quantum state, and also provides an alternative mechanism for enhancing superconductivity.