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arXiv:1904.00857 · Physical review. B./Physical review. B

Enhancement of local pairing correlations in periodically driven Mott insulators

Francesco Peronaci, Olivier Parcollet, Marco Schirò

Published Apr 1, 2020• 48 citations
arXivHTMLPDF

Abstract

Periodically driving strongly correlated systems offers new opportunities to control their properties. Heating effects, however, often hinder the actual realization of interesting states. Here, the authors study a model of a Mott insulator with a time-periodic Hubbard on-site potential $U$ coupled to a dissipative reservoir. Tuning the frequency above a characteristic value, they unveil a regime where the creation of doublon-holon excitations is greatly enhanced with respect to equilibrium. Below a certain effective temperature, this far-from-equilibrium state would give rise to the exotic $\ensuremath{\eta}$-pairing superconduting state.

DOI
10.1103/physrevb.101.161101

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Periodically driving strongly correlated systems offers new opportunities to control their properties. Heating effects, however, often hinder the actual realization of interesting states. Here, the authors study a model of a Mott insulator with a time-periodic Hubbard on-site potential UUU coupled to a dissipative reservoir. Tuning the frequency above a characteristic value, they unveil a regime where the creation of doublon-holon excitations is greatly enhanced with respect to equilibrium. Below a certain effective temperature, this far-from-equilibrium state would give rise to the exotic \ensuremathη\ensuremath{\eta}\ensuremathη-pairing superconduting state.
We demonstrate the existence of long-lived prethermalized states in the Mott insulating Hubbard model driven by periodic electric fields. These states, which also exist in the resonantly driven case with a large density of photo-induced doublons and holons, are characterized by a nonzero current and an effective temperature of the doublons and holons which depends sensitively on the driving condition. Focusing on the specific case of resonantly driven models whose effective time-independent Hamiltonian in the high-frequency driving limit corresponds to noninteracting fermions, we show that the time evolution of the double occupation can be reproduced by the effective Hamiltonian, and that the prethermalization plateaus at finite driving frequency are controlled by the next-to-leading–order correction in the high-frequency expansion of the effective Hamiltonian. We propose a numerical procedure to determine an effective Hubbard interaction that mimics the correlation effects induced by these higher-order terms.
Periodically driven systems can lead to a directed motion of particles. We investigate this ratchet effect for a bosonic Mott insulator where both a staggered hopping and a staggered local potential vary periodically in time. If driving frequencies are smaller than the interaction strength and the density of excitations is small, one obtains effectively a one-particle quantum ratchet describing the motion of doubly occupied sites (doublons) and empty sites (holes). Such a simple quantum machine can be used to manipulate the excitations of the Mott insulator. For suitably chosen parameters, for example, holes and doublons move in opposite directions. To investigate whether the periodic driving can be used to move particles ``uphill,'' i.e., against an external force, we study the influence of a linear potential $\ensuremath{-}gx$. For long times, transport is only possible when the driving frequency $\ensuremath{\omega}$ and the external force ggg are commensurate, ${n}_{0}g={m}_{0}\ensuremath{\omega}$, with $\frac{{n}_{0}}{2},{m}_{0}\ensuremath{\in}\mathbb{Z}$.
ηηη-pairing in metallic and particle-hole asymmetric systems
Light-induced superconducting-like states have been reported in several classes of correlated materials. From a theoretical point of view, the induction of ηηη-pairing is a promising route to nonthermal superconductivity. Numerical studies of photo-doped Mott systems revealed ηηη-pairing states with very high effective critical temperatures. These investigations were however restricted to particle-hole symmetric states in large-gap Mott insulators, while the experiments were performed on strongly correlated metallic systems. It is thus relevant to explore if ηηη-pairing also exists in non-particle-hole symmetric setups and in photo-excited metallic states. Here we use steady-state nonequilibrium dynamical mean field theory combined with a strong-coupling impurity solver up to third order to investigate this issue. We find that in the strongly correlated regime with large Mott gap, and for low effective doublon and holon temperatures, ηηη-pairing is robust against changes in the total filling and an imbalance in the doublon and holon density. An asymmetry in the effective doublon and holon temperatures can however strongly suppress the order parameter. In photo-doped metallic systems with a three-peak structure in the local density of states, ηηη-pairing can be realized in set-ups with positive doublon and holon temperatures and a population inversion in the low-energy quasi-particle band.
In the ionic Hubbard model, the on-site repulsion UUU, which drives a Mott insulator, and the ionic potential VVV, which drives a band insulator, compete with each other to open up a window of charge fluctuations when $U\ensuremath{\sim}V$. We study this model on square and cubic lattices in the limit of large UUU and VVV, with $V\ensuremath{\sim}U$. Using an effective Hamiltonian and a slave-boson approach with both doublons and holons, we find that the system undergoes a phase transition as a function of VVV from an antiferromagnetic Mott insulator to a paramagnetic insulator with strong singlet correlations, which is driven by a condensate of ``neutral'' doublon-holon pairs. On further increasing VVV, the system undergoes another phase transition to a superconducting phase driven by condensate of ``charged'' doublons and holons. The superfluid phase, characterized by the presence of a coherent (but gapped) fermionic quasiparticle and hc/ehc/ehc/e flux quantization, has a high ${T}_{c}\ensuremath{\sim}t$, which shows a dome-shaped behavior as a function of VVV. The paramagnetic insulator phase has a deconfined U(1) gauge field and associated gapless photon excitations. We also discuss how these phases can be detected in the ultracold-atom context.
In the strongly interacting limit of the Hubbard model localized double occupancies form effective hard-core bosonic excitations, called doublons, which are long lived due to energy conservation. Using time-dependent density-matrix renormalization group methods we investigate numerically the dynamics of doublons arising from the sudden expansion of a spatially confined band-insulating state in one spatial dimension. By analyzing the occupation scaling of the natural orbitals within the many-body state, we show that doublons dynamically quasicondense at the band edges, consistent with the spontaneous emergence of an $\ensuremath{\eta}$ quasicondensate. Building on this, we study the effect of periodically driving the system during the expansion. Floquet analysis reveals that doublon hopping and doublon repulsion are strongly renormalized by the drive, breaking the $\ensuremath{\eta}\text{\ensuremath{-}}\mathrm{SU}(2)$ symmetry of the Hubbard model. Numerical simulation of the driven expansion dynamics demonstrates that the momentum in which doublons quasicondense can be controlled by the driving amplitude. These results point to new pathways for engineering nonequilibrium condensates in fermionic cold-atom experiments and are potentially relevant to driven solid-state systems.
Recent experiments performed on cuprates and alkali-doped fullerides have demonstrated that key signatures of superconductivity can be induced above the equilibrium critical temperature by optical modulation. These observations in disparate physical systems may indicate a general underlying mechanism. Multiple theories have been proposed, but these either consider specific features, such as competing instabilities, or focus on conventional BCS-type superconductivity. Here we show that periodic driving can enhance electron pairing in strongly correlated systems. Focusing on the strongly repulsive limit of the doped Hubbard model, we investigate in-gap, spatially inhomogeneous, on-site modulations. We demonstrate that such modulations substantially reduce electronic hopping, while simultaneously sustaining superexchange interactions and pair hopping via driving-induced virtual charge excitations. We calculate real-time dynamics for the one-dimensional case, starting from zero- and finite-temperature initial states, and we show that enhanced singlet-pair correlations emerge quickly and robustly in the out-of-equilibrium many-body state. Our results reveal a fundamental pairing mechanism that might underpin optically induced superconductivity in some strongly correlated quantum materials.