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arXiv:1008.2594 · Physical Review Letters

Dynamical Band Flipping in Fermionic Lattice Systems: An ac-Field-Driven Change of the Interaction from Repulsive to Attractive

Naoto Tsuji, Takashi Oka, Philipp Werner, Hideo Aoki

Published Jun 6, 2011• 135 citations
arXivHTMLPDF

Abstract

We show theoretically that the sudden application of an appropriate ac field to correlated lattice fermions flips the band structure and effectively switches the interaction from repulsive to attractive. The nonadiabatically driven system is characterized by a negative temperature with a population inversion. We numerically demonstrate the converted interaction in an ac-driven Hubbard model with the nonequilibrium dynamical mean-field theory solved by the continuous-time quantum Monte Carlo method. Based on this, we propose an efficient ramp-up protocol for ac fields that can suppress heating, which leads to an effectively attractive Hubbard model with a temperature below the superconducting transition temperature of the equilibrium system.

DOI
10.1103/physrevlett.106.236401

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We show theoretically that the sudden application of an appropriate ac field to correlated lattice fermions flips the band structure and effectively switches the interaction from repulsive to attractive. The nonadiabatically driven system is characterized by a negative temperature with a population inversion. We numerically demonstrate the converted interaction in an ac-driven Hubbard model with the nonequilibrium dynamical mean-field theory solved by the continuous-time quantum Monte Carlo method. Based on this, we propose an efficient ramp-up protocol for ac fields that can suppress heating, which leads to an effectively attractive Hubbard model with a temperature below the superconducting transition temperature of the equilibrium system.
We show theoretically that the sudden application of an appropriate ac field to correlated lattice fermions flips the band structure and effectively switches the interaction from repulsive to attractive.The nonadiabatically driven system is characterized by a negative temperature with a population inversion.We numerically demonstrate the converted interaction in an ac-driven Hubbard model with the nonequilibrium dynamical mean-field theory solved by the continuous-time quantum Monte Carlo method.Based on this, we propose an efficient ramp-up protocol for ac fields that can suppress heating, which leads to an effectively attractive Hubbard model with a temperature below the superconducting transition temperature of the equilibrium system.
We investigate the possibility to control dynamically the interactions between repulsively bound pairs of fermions (doublons) in correlated systems with off-resonant ac fields. We introduce an effective Hamiltonian that describes the physics of doublons up to second order in the high-frequency limit. It unveils that the doublon interaction, which is attractive in equilibrium, can be completely suppressed and then switched to repulsive by varying the power of the ac field. We show that the signature of the dynamical repulsion between doublons can be found in the single-fermion density of states averaged in time. Our results are further supported by nonequilibrium dynamical mean-field theory simulations for the half-filled Fermi-Hubbard model.
We study the time evolution of the Hubbard model driven by a half-cycle or monocycle pulsed electric field F(t)F(t)F(t) using the nonequilibrium dynamical mean-field theory. We find that for properly chosen pulse shapes the electron-electron interaction can be effectively and permanently switched from repulsive to attractive if there is no energy dissipation. The physics behind the interaction conversion is a nonadiabatic shift $\ensuremath{\delta}$ of the population in momentum space. When $\ensuremath{\delta}\ensuremath{\sim}\ensuremath{\pi}$, the shifted population relaxes to a negative-temperature state, which leads to the interaction switching. Due to electron correlation effects $\ensuremath{\delta}$ deviates from the dynamical phase $\ensuremath{\varphi}=\ensuremath{\int}dtF(t)$, which enables the seemingly counterintuitive repulsion-to-attraction transition by a monocycle pulse with $\ensuremath{\varphi}=0$.
We propose a novel possibility of dynamically changing the pairing of superconductors from sss wave to $\ensuremath{\eta}$ pairing (where the pairs condense at the Brillouin-zone corner momenta) by driving the system with ac fields. We consider a periodically-driven attractive Hubbard model in the strong-coupling regime and show that the pair-hopping and pair-repulsion terms in the effective Hamiltonian in the Floquet formalism are drastically renormalized in different manners between the two terms, which can change the ground states from an sss-wave superconductivity to an $\ensuremath{\eta}$-pairing superconductivity or a charge-ordered phase. While in isolated systems such as cold atoms a simple quench scheme would not realize the dynamical phase transition into $\ensuremath{\eta}$ pairing, we show that there are pathways that realize the dynamical transition, where the field amplitude is varied via a charge-ordered phase as an intermediate state.
The recent experimental implementation of condensed matter models in optical lattices has motivated research on their non-equilibrium behavior. Predictions about the dynamics of superconductors following a sudden quench of the pairing interaction have been made based on the effective Bardeen–Cooper–Schrieffer (BCS) Hamiltonian; however, their experimental verification requires the preparation of a suitable excited state of the Hubbard model along a twofold constraint: (i) a sufficiently non-adiabatic ramping scheme is essential to excite the non-equilibrium dynamics and (ii) overheating beyond the critical temperature of superconductivity must be avoided. For commonly discussed interaction ramps, there is no clear separation of the corresponding energy scales. Here we show that the matching of both conditions is simplified by the intrinsic relaxation behavior of ultracold fermionic systems: for the particular example of a linear ramp we examine the transient regime of prethermalization (Moeckel and Kehrein 2008 Phys. Rev. Lett. 100 175702) under the crossover from sudden to adiabatic switching using Keldysh perturbation theory. A real-time analysis of the momentum distribution exhibits a temporal separation of an early energy relaxation and its later thermalization by scattering events. For long but finite ramping times this separation can be large. In the prethermalization regime, the momentum distribution resembles a zero-temperature Fermi liquid as the energy inserted by the ramp remains located in high-energy modes. Thus ultracold fermions prove to be robust to heating, which simplifies the observation of non-equilibrium BCS dynamics in optical lattices.
We consider the multiband, purely repulsive Hubbard model on a class of systems in which there are two (or more) kinds of orbitals per unit cell such that one metallic band interacts with the other insulating band. From both perturbational canonical transformation and quantum Monte Carlo studies we have shown that superconductivity due to nonretarded attraction (negative U) is a generic feature of this class of metal-insulator composite many-body systems. Remarkably, the superconductivity arises, under appropriate conditions, for various types of insulating bands (a charge-transfer insulator, Mott-Hubbard insulator, etc.). Superconductivity is unambiguously identified from the pairing correlation function, which agrees with that of the attractive Hubbard model surprisingly well even in the nonperturbative regime. The superconductivity revealed here is in a sense an opposite limit to conventional superconductivity with retarded attraction from boson-exchange mechanisms. We also show that the present mechanism is distinct from existing multiband models such as d-${\mathit{p}}_{\mathrm{\ensuremath{\sigma}}}$ models. As we increase the magnitude of the attraction in the present model by changing some parameters (e.g., to make the accompanying band metallic), the similarity with the attractive Hubbard model becomes eventually degraded, so that the optimum condition for superconductivity is determined by this kind of tradeoff. We also discuss the relevance of the present model to high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductivity in cuprates and fullerenes.