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arXiv:2207.13973 · SciPost Physics

Enhancement of chiral edge currents in (ddd+1)-dimensional atomic Mott-band hybrid insulators

Matteo Ferraretto, Andrea Richaud, Lorenzo Del Re, L. Fallani, Massimo Capone

Published Mar 24, 2023• 15 citations
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Abstract

We consider the effect of a local interatomic repulsion on synthetic heterostructures where a discrete synthetic dimension is created by Raman processes on top of SU(N) S U ( N ) -symmetric two-dimensional lattice systems. At a filling of one fermion per site, increasing the interaction strength, the system is driven towards a Mott state which is adiabatically connected to a band insulator. The chiral currents associated with the synthetic magnetic field increase all the way to the Mott transition, where they reach the maximum value, and they remain finite in the whole insulating state. The transition towards the Mott-band insulator is associated with the opening of a gap within the low-energy quasiparticle peak, while a mean-field picture is recovered deep in the insulating state.

DOI
10.21468/scipostphys.14.3.048

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We consider the effect of a local interatomic repulsion on synthetic heterostructures where a discrete synthetic dimension is created by Raman processes on top of SU(N) S U ( N ) -symmetric two-dimensional lattice systems. At a filling of one fermion per site, increasing the interaction strength, the system is driven towards a Mott state which is adiabatically connected to a band insulator. The chiral currents associated with the synthetic magnetic field increase all the way to the Mott transition, where they reach the maximum value, and they remain finite in the whole insulating state. The transition towards the Mott-band insulator is associated with the opening of a gap within the low-energy quasiparticle peak, while a mean-field picture is recovered deep in the insulating state.
Under the influence of an external magnetic field and spin-changing collisions, the band insulator state of one-dimensional sss-wave repulsively interacting four-component fermions at half-filling transforms into Mott insulator states with a spontaneously doubled unit cell: a dimerized state for shallow lattices and a N\'eel state for deep lattices via an intermediate topological state. These Mott insulator phases could be of special interest for experiments as they can be reached starting from band insulator state and changing magnetic field adiabatically.
We study a model of a covalent band insulator with on-site Coulomb repulsion at half filling using dynamical mean-field theory. Upon increasing the interaction strength the system undergoes a discontinuous transition from a correlated band insulator to a Mott insulator with hysteretic behavior at low temperatures. Increasing the temperature in the band insulator close to the insulator-insulator transition we find a crossover to a Mott insulator at elevated temperatures. Remarkably, correlations decrease the energy gap in the correlated band insulator. The gap renormalization can be traced to the low-frequency behavior of the self-energy, analogously to the quasiparticle renormalization in a Fermi liquid. While the uncorrelated band insulator is characterized by a single gap for both charge and spin excitations, the spin gap is smaller than the charge gap in the correlated system.
We address how the nature of linearly dispersing edge states of two-dimensional (2D) topological insulators evolves with increasing electron-electron correlation engendered by a Hubbard-like on-site repulsion UUU in finite ribbons of two models of topological band insulators. Using an inhomogeneous cluster slave-rotor mean-field method developed here, we show that electronic correlations drive the topologically nontrivial phase into a Mott insulating phase via two different routes. In a synchronous transition, the entire ribbon attains a Mott insulating state at one critical UUU that depends weakly on the width of the ribbon. In the second, asynchronous route, Mott localization first occurs on the edge layers at a smaller critical value of electronic interaction, which then propagates into the bulk as UUU is further increased until all layers of the ribbon become Mott localized. We show that the kind of Mott transition that takes place is determined by certain properties of the linearly dispersing edge states which characterize the topological resilience to Mott localization.
We investigate a quarter-filled two-band Hubbard model involving a crystal-field splitting, which lifts the orbital degeneracy as well as an interorbital hopping (interband hybridization). Both terms are relevant to the realistic description of correlated materials such as transition-metal oxides. The nature of the Mott metal-insulator transition is clarified and is found to depend on the magnitude of the crystal-field splitting. At large values of the splitting, a transition from a two-band to a one-band metal is first found as the on-site repulsion is increased and is followed by a Mott transition for the remaining band, which follows the single-band (Brinkman-Rice) scenario well documented previously within dynamical mean-field theory. At small values of the crystal-field splitting, a direct transition from a two-band metal to a Mott insulator with partial orbital polarization is found, which takes place simultaneously for both orbitals. This transition is characterized by a vanishing of the quasiparticle weight for the majority orbital but has a first-order character for the minority orbital. It is pointed out that finite-temperature effects may easily turn the metallic regime into a bad metal close to the orbital polarization transition in the metallic phase.
We study the filling-driven Mott transition involving the metallic and paramagnetic insulating phases in SU(N)\mathrm{SU}(N)SU(N) Fermi-Hubbard models, using the dynamical mean-field theory and the numerical renormalization group as its impurity solver. The compressibility shows a striking temperature dependence: near the critical end-point temperature, it is strongly enhanced in the metallic phase close to the insulating phase. We demonstrate that this compressibility enhancement is associated with the thermal suppression of the quasiparticle peak in the local spectral functions. We also explain that the asymmetric shape of the quasiparticle peak originates from the asymmetry in the dynamics of the generalized doublons and holons.
We study Mott phases and superfluid-insulator (SI) transitions of ultracold bosonic atoms in a two-dimensional square optical lattice at commensurate filling and in the presence of a synthetic periodic vector potential characterized by a strength ppp and a period l=qal=qal=qa, where qqq is an integer and aaa is the lattice spacing. We show that the Schr\"odinger equation for the noninteracting bosons in the presence of such a periodic vector potential can be reduced to an one-dimensional Harper-like equation which yields qqq energy bands. The lowest of these bands have either single or double minima whose position within the magnetic Brillouin zone can be tuned by varying ppp for a given qqq. Using these energies and a strong-coupling expansion technique, we compute the phase diagram of these bosons in the presence of a deep optical lattice. We chart out the ppp and qqq dependence of the momentum distribution of the bosons in the Mott phases near the SI transitions and demonstrate that the bosons exhibit several reentrant field-induced SI transitions for any fixed period qqq. We also predict that the superfluid density of the resultant superfluid state near such a SI transition has a periodicity qqq (q/2)(q/2)(q/2) in real space for odd (even) qqq and suggest experiments to test our theory.