Abstract Non-equilibrium engineering is becoming a seminal way for realising novel quantum phases that are unimaginable in equilibrium. In particular, Floquet theory applied to quantum mechanics revealed that we can even control the band topology in semimetallic/insulating systems, while the straightforward application to topological superconductivity fails for typical superconductors because the supercondicting gap function does not couple to the electromagnetic field in a direct manner. Here we show that we can overcome this difficulty by taking account of correlation effects. Namely, we study how a d-wave superconductivity is changed when illuminated by circularly-polarised light (CPL) in the repulsive Hubbard model in the strong-coupling regime. We adopt the Floquet formalism for the Gutzwiller-projected effective Hamiltonian with the time-periodic Schrieffer-Wolff transformation. We find that CPL induces a topological superconductivity with a d + id pairing, which arises from the chiral spin coupling and the three-site term generated by the CPL. The latter term remains significant even for low frequencies and low intensities of the CPL. This is clearly reflected in the obtained phase diagram against the laser intensity and temperature for various frequencies red-detuned from the Hubbard U, with the transient dynamics also examined. The phenomenon revealed here can open a novel, dynamical way to induce a topological superconductivity.
Abstract Non-equilibrium engineering is becoming a seminal way for realising novel quantum phases that are unimaginable in equilibrium. In particular, Floquet theory applied to quantum mechanics revealed that we can even control the band topology in semimetallic/insulating systems, while the straightforward application to topological superconductivity fails for typical superconductors because the supercondicting gap function does not couple to the electromagnetic field in a direct manner. Here we show that we can overcome this difficulty by taking account of correlation effects. Namely, we study how a d-wave superconductivity is changed when illuminated by circularly-polarised light (CPL) in the repulsive Hubbard model in the strong-coupling regime. We adopt the Floquet formalism for the Gutzwiller-projected effective Hamiltonian with the time-periodic Schrieffer-Wolff transformation. We find that CPL induces a topological superconductivity with a d + id pairing, which arises from the chiral spin coupling and the three-site term generated by the CPL. The latter term remains significant even for low frequencies and low intensities of the CPL. This is clearly reflected in the obtained phase diagram against the laser intensity and temperature for various frequencies red-detuned from the Hubbard U, with the transient dynamics also examined. The phenomenon revealed here can open a novel, dynamical way to induce a topological superconductivity.
Abstract Periodically driven systems provide a novel route to control the topology of quantum materials. In particular, Floquet theory allows an effective band description of periodically-driven systems through the Floquet Hamiltonian. Here, we study the time evolution of d-wave superconductors irradiated with intense circularly-polarized laser light. We consider the Floquet t–J model with time-periodic interactions, and investigate its mean-field dynamics by formulating the time-dependent Gutzwiller approximation. We observe the development of the idxy-wave pairing amplitude along with the original dx2−y2 d x 2 − y 2 -wave order upon gradual increasing of the field amplitude. We further numerically construct the Floquet Hamiltonian for the steady state, with which we identify the system as the fully-gapped d + id superconducting phase with a nonzero Chern number. We explore the low-frequency regime where the perturbative approaches in the previous studies break down, and find that the topological gap of an experimentally-accessible size can be achieved at much lower laser intensities.
In this thesis, we theoretically investigate exotic quantum phenomena underlying periodically-driven systems.We discuss three distinct systems, noninteracting Dirac systems, lattice systems with a strong repulsive interaction, and lattice systems with a strong attractive interaction.We reveal various novel phenomena underlying these systems, and provide clear understanding of them.Periodically-driven systems, i.e., systems with a discrete time-translational symmetry, are described by the Floquet formalism, which maps the time-dependent Hamiltonian to a static "photon-dressed Hamiltonian".While a perturbative expansion of this Hamiltonian from the limit of high driving frequency has clarified various novel phenomena peculiar to periodically-driven systems, such an approach suffers from serious heating or damage when it is applied to realistic condensed matters.In this thesis, we focus on a lower-frequency regime, especially when the heating should be suppressed due to the small driving amplitude or an energy gap larger than the driving frequency.There, the high-frequency expansion cannot capture the relevant physics, so that we first formulate various perturbative expansions for three distinct regimes, i.e., high-frequency, small-amplitude, and strong-coupling regimes.We apply the small-amplitude expansion to two-and three-dimensional Dirac electrons driven by a circularly-polarized light to explore their behavior in the lowfrequency regime.We find an emergence of infinite numbers of topological gaps for the former and Weyl nodes for the latter.We also discuss how a regularization of the model affects this topological structure.We then introduce a strong repulsive interaction, and discuss behaviors of spins using the strong-coupling expansion.We predict an emergence of scalar spin chirality when a circularly-polarized light is illuminated, and discuss possible applications to photo-induced chiral spin liquids, and optical probing of spin chirality.Finally we turn to a strong attractive interaction to discuss the fate of the ordinary s-wave superconductivity under the periodic driving.We demonstrate an emergence of long sought-after η-pairing superconductivity, first as a ground state of the photon-dressed Hamiltonian, and then as a consequence of a dynamical phase transition in an isolated system such as an optical lattice system.
We study the interplay of magnetic order and superconductivity in the square-lattice Hubbard model under periodic driving with circularly polarized light. Formulating diagrammatic techniques based on the random-phase approximation in terms of Floquet Green's functions, allows us to analyze fluctuation-driven unconventional pairing for weak to moderate interactions. The interplay of repulsive interactions and photoassisted hopping of electrons gives rise to a rich magnetic phase diagram featuring an antiferromagnetic-to-ferromagnetic transition prior to a Floquet Lifshitz transition. Close to the antiferromagnetic transition, topological d + i d -wave superconductivity prevails in the phase diagram for a wide range of drive parameters. At intermediate- to high-frequency driving near the Floquet Lifshitz transition, superconducting orders are tuned from spin-singlet d -wave to spin-triplet p -wave character, providing an effective protocol for Floquet engineering topological superconductivity.
Intense time-periodic laser fields can transform the electronic structure of a solid into strongly modified Floquet-Bloch bands. While this suggests multiple pathways to induce electronic orders such as superconductivity or charge density waves, the possibility of preparing low-energy phases of Floquet Hamiltonians remains unclear because of the energy absorption at typical experimentally accessible driving frequencies. Here we investigate a realistic pathway towards laser control of electronic orders, which is the transient enhancement of fluctuating orders. Using a conserving Keldysh Green's function formalism, we simulate the buildup of short range Cooper-pair correlations out of a normal metal in the driven attractive Hubbard model. Even for frequencies only slightly above or within the bandwidth, a substantial enhancement of correlations can be achieved before the system reaches a high electronic temperature. This behavior relies on the nonthermal nature of the driven state. The effective temperature of the electrons at the Fermi surface, which more closely determines the superconducting correlations, remains lower than an estimate from the global energy density. Even though short ranged, the fluctuations can have marked signatures in the electronic spectra.
Scalar spin chirality, a three-body spin correlation that breaks time-reversal symmetry, is revealed to couple directly to circularly polarized laser. This is shown by the Floquet formalism for the periodically driven repulsive Hubbard model with a strong-coupling expansion. A systematic derivation of the effective low-energy Hamiltonian for a spin degree of freedom reveals that the coupling constant for scalar spin chirality can become significant for a situation in which the driving frequency and the on-site interaction are comparable. This implies that the scalar chirality can be induced by circularly polarized lights, or that it can be used conversely for probing the chirality in Mott insulators as a circular dichroism.
We review methods for using time-periodic fields (e.g., laser or microwave fields) to induce non-equilibrium topological phenomena in quantum many-body systems. We discuss how such fields can be used to change the topological properties of the single particle spectrum, and key experimental demonstrations in solid state, cold atomic, and photonic systems. The single particle Floquet band structure provides a stage on which the system's dynamics play out; the crucial question is then how to obtain robust topological behaviour in the many-particle setting. In the regime of mesoscopic transport, we discuss manifestations of topological edge states induced in the Floquet spectrum. Outside the context of mesoscopic transport, the main challenge of inducing stable topological phases in many-body Floquet systems is their tendency to absorb energy from the drive and thereby to heat up. We discuss three routes to overcoming this challenge: long-lived transient dynamics and prethermalization, disorder-induced many-body localization, and engineered couplings to external baths. We discuss the types of phenomena that can be explored in each of these regimes, and their experimental realizations.