Incommensurate Fillings Research Articles

Accessing the topological Mott insulator in cold atom quantum simulators with realistic Rydberg dressing

The interplay between many-body interactions and the kinetic energy gives rise to rich phase diagrams hosting, among others, interaction-induced topological phases. These phases are characterized by both a local order parameter and a global topological invariant, and can exhibit exotic ground states such as self-trapped polarons and interaction-induced edge states. In this work, we investigate a realistic scenario for the quantum simulation of such systems using cold Rydberg-dressed atoms in optical lattices. We consider spinless fermions on a checkerboard lattice, interacting via the tunable-range effective potential induced by the Rydberg dressing. We perform a detailed analysis of the phase diagram at half- and incommensurate fillings, in the mean-field approximation. We furthermore study the stability of the phases with respect to temperature within the mean-field approximation and with respect to quantum fluctuations using the density matrix renormalization group method. Finally, we propose an implementation protocol, and in particular identify attainable regimes of experimental parameters in which the topological properties of the model become accessible. Our work thereby opens a realistic pathway to the outstanding experimental observation of this predicted phase in state-of-the-art cold atom quantum simulators.

Commensuration effects on skyrmion Hall angle and drag for manipulation of skyrmions on two-dimensional periodic substrates

We examine the dynamics of an individually driven skyrmion moving through a background lattice of skyrmions coupled to a 2D periodic substrate as we vary the ratio of the number of skyrmions to the number of pinning sites across commensurate and incommensurate conditions. As the skyrmion density increases, the skyrmion Hall angle is nonmonotonic, dropping to low or zero values in commensurate states and rising to an enhanced value in incommensurate states. Under commensuration, the driven skyrmion is channeled by a symmetry direction of the pinning array and exhibits an increased velocity. At fillings for which the skyrmion Hall angle is zero, the velocity has a narrow band noise signature, while for incommensurate fillings, the skyrmion motion is disordered and the velocity noise is broad band. Under commensurate conditions, multi-step depinning transitions appear and the skyrmion Hall angle is zero at low drives but becomes finite at higher drives, while at incommensurate fillings there is only a single depinning transition. As the gyrotropic component of the skyrmion dynamics, called the Magnus force, increases, peaks in the velocity that appear in commensurate regimes cross over to dips, and new types of directional locking effects can arise in which the skyrmion travels along other symmetry directions of the background lattice. At large Magnus forces, and particularly at commensurate fillings, the driven skyrmion can experience a velocity boost in which the skyrmion moves faster than the applied drive due to the alignment of the Magnus-induced velocity with the driving direction. In some cases, an increase of the Magnus force can produce regimes of enhanced pinning when the skyrmion is forced to move along a nonsymmetry direction of the periodic pinning array. This is in contrast to systems with random pinning, where increasing the Magnus force generally reduces the pinning effect. We demonstrate these dynamics for both square and triangular substrates and map out the different regimes as a function of filling fraction, pinning force, and the strength of the Magnus force in a series of dynamic phase diagrams.

Charge-Order on the Triangular Lattice: A Mean-Field Study for the Lattice S = 1/2 Fermionic Gas.

The adsorbed atoms exhibit tendency to occupy a triangular lattice formed by periodic potential of the underlying crystal surface. Such a lattice is formed by, e.g., a single layer of graphane or the graphite surfaces as well as (111) surface of face-cubic center crystals. In the present work, an extension of the lattice gas model to fermionic particles on the two-dimensional triangular (hexagonal) lattice is analyzed. In such a model, each lattice site can be occupied not by only one particle, but by two particles, which interact with each other by onsite U and intersite and (nearest and next-nearest-neighbor, respectively) density-density interaction. The investigated hamiltonian has a form of the extended Hubbard model in the atomic limit (i.e., the zero-bandwidth limit). In the analysis of the phase diagrams and thermodynamic properties of this model with repulsive , the variational approach is used, which treats the onsite interaction term exactly and the intersite interactions within the mean-field approximation. The ground state () diagram for as well as finite temperature () phase diagrams for are presented. Two different types of charge order within unit cell can occur. At , for phase separated states are degenerated with homogeneous phases (but removes this degeneration), whereas attractive stabilizes phase separation at incommensurate fillings. For and only the phase with two different concentrations occurs (together with two different phase separated states occurring), whereas for small repulsive the other ordered phase also appears (with tree different concentrations in sublattices). The qualitative differences with the model considered on hypercubic lattices are also discussed.

Stripe phases in WSe2/WS2 moiré superlattices.

Stripe phases, in which the rotational symmetry of charge density is spontaneously broken, occur in many strongly correlated systems with competing interactions1-11. However, identifying and studying such stripe phases remains challenging. Here we uncover stripe phases in WSe2/WS2 moiré superlattices by combining optical anisotropy and electronic compressibility measurements. We find strong electronic anisotropy over a large doping range peaked at 1/2 filling of the moiré superlattice. The 1/2 state is incompressible and assigned to an insulating stripe crystal phase. Wide-field imaging reveals domain configurations with a preferential alignment along the high-symmetry axes of the moiré superlattice. Away from 1/2 filling, we observe additional stripe crystals at commensurate filling 1/4, 2/5 and 3/5, and compressible electronic liquid crystal states at incommensurate fillings. Our results demonstrate that two-dimensional semiconductor moiré superlattices are a highly tunable platform from which to study the stripe phases and their interplay with other symmetry breaking ground states.

Dynamical Solitons and Boson Fractionalization in Cold-Atom Topological Insulators.

We study the Z_{2} Bose-Hubbard model, a chain of interacting bosons the tunneling of which is dressed by a dynamical Z_{2} field. The interplay between spontaneous symmetry breaking (SSB) and topological symmetry protection gives rise to interesting fractional topological phenomena when the system is doped to certain incommensurate fillings. In particular, we hereby show how topological defects in the Z_{2} field can appear in the ground state, connecting different SSB sectors. These defects are dynamical and can travel through the lattice carrying both a topological charge and a fractional particle number. In the hardcore limit, this phenomenon can be understood through a bulk-defect correspondence. Using a pumping argument, we show that it survives also for finite interactions, demonstrating how boson fractionalization induced by topological defects can occur in strongly correlated bosonic systems. Our results indicate the possibility of observing this phenomenon, which appears for fermionic matter in solid-state and high-energy physics, using ultracold atomic systems.

Self-Trapped Polarons and Topological Defects in a Topological Mott Insulator.

Many-body interactions in topological quantum systems can give rise to new phases of matter, which simultaneously exhibit both rich spatial features and topological properties. In this work, we consider spinless fermions on a checkerboard lattice with nearest and next-to-nearest neighbor interactions. We calculate the phase diagram at half filling, which presents, in particular, an interaction-induced quantum anomalous Hall phase. We study the system at incommensurate fillings using an unrestricted Hartree-Fock ansatz and report a rich zoo of solutions such as self-trapped polarons and domain walls above an interaction-induced topological insulator. We find that, as a consequence of the interplay between the interaction-induced topology and topological defects, these domain walls separate two phases with opposite topological invariants and host topologically protected chiral edge states. Finally, we discuss experimental prospects to observe these novel phenomena in a quantum simulator based on laser-dressed Rydberg atoms in an optical lattice.

Superconductor versus insulator in twisted bilayer graphene

We present a simple model that we believe captures the key aspects of the competition between superconducting and insulating states in twisted bilayer graphene. Within this model, the superconducting phase is primary, and arises at generic fillings, but is interrupted by the insulator at commensurate fillings. Importantly, the insulator forms because of electron-electron interactions, but the model is agnostic as to the superconducting pairing mechanism, which need not originate with electron-electron interactions. The model is composed of a collection of crossed one-dimensional quantum wires whose intersections form a superlattice. At each superlattice point, we place a locally superconducting puddle which can exchange Cooper pairs with the quantum wires. We analyze this model assuming weak wire-puddle and wire-wire couplings. We show that for a range of repulsive intrawire interactions, the system is superconducting at `generic' incommensurate fillings, with the superconductivity being `interrupted' by an insulating phase at commensurate fillings. We further show that the gapped insulating states at commensurate fillings give way to gapless states upon application of external Zeeman fields. These features are consistent with experimental observations in magic-angle twisted bilayer graphenes despite the distinct microscopic details. We further study the full phase diagram of this model and discover that it contains several distinct correlated insulating states, which we characterize herein.

Optical lattices as a tool to study defect-induced superfluidity

We study the superfluid response, the energetic and structural properties of a one-dimensional ultracold Bose gas in an optical lattice of arbitrary strength. We use the Bose-Fermi mapping in the limit of infinitely large repulsive interaction and the diffusion Monte Carlo method in the case of finite interaction. For slightly incommensurate fillings we find a superfluid behavior, which is discussed in terms of vacancies and interstitials. It is shown that both the excitation spectrum and static structure factor are different for the cases of microscopic and macroscopic fractions of defects. This system provides an extremely well-controlled model for studying defect-induced superfluidity.

Phases of one-dimensional SU([formula omitted]) cold atomic Fermi gases—From molecular Luttinger liquids to topological phases

Alkaline-earth and ytterbium cold atomic gases make it possible to simulate SU(N)-symmetric fermionic systems in a very controlled fashion. Such a high symmetry is expected to give rise to a variety of novel phenomena ranging from molecular Luttinger liquids to (symmetry-protected) topological phases. We review some of the phases that can be stabilized in a one dimensional lattice. The physics of this multi-component Fermi gas turns out to be much richer and more exotic than in the standard SU(2) case. For N>2, the phase diagram is quite rich already in the case of the single-band model, including a molecular Luttinger liquid (with dominant superfluid instability in the N-particle channel) for incommensurate fillings, as well as various Mott-insulating phases occurring at commensurate fillings. Particular attention will be paid to the cases with additional orbital degree of freedom (which is accessible experimentally either by taking into account two atomic states or by putting atoms in the p-band levels). We introduce two microscopic models which are relevant for these cases and discuss their symmetries and strong coupling limits. More intriguing phase diagrams are then presented including, for instance, symmetry protected topological phases characterized by non-trivial edge states.

Polar molecules in frustrated triangular ladders

Polar molecules in geometrically frustrated lattices may result in a very rich landscape of quantum phases, due to the non-trivial interplay between frustration, and two- and possibly three-body inter-site interactions. In this paper, we illustrate this intriguing physics for the case of hard-core polar molecules in frustrated triangular ladders. Whereas commensurate lattice fillings result in gapped phases with bond-order and/or density-wave order, at incommensurate fillings we find chiral-, two-component-, and pair-superfluids. We show as well that, remarkably, polar molecules in frustrated lattices allow, for the first time to our knowledge, for the observation of bond-ordered supersolids.

Dynamic regimes for driven colloidal particles on a periodic substrate at commensurate and incommensurate fillings

We numerically examine colloidal particles driven over a muffin tin substrate. Previous studies of this model identified a variety of commensurate and incommensurate static phases in which topological defects can form domain walls, ordered stripes, superlattices, or disordered patchy regimes as a function of the filling fraction. Here, we show that the addition of an external drive to these static phases can produce distinct dynamical responses. At incommensurate fillings the flow occurs in the form of localized pulses or solitons correlated with topological defect structures. Transitions between different modes of motion can occur as a function of increasing drive. We measure the average particle velocity for specific ranges of external drive and show that changes in the velocity response correlate with changes in the topological defect arrangements. We also demonstrate that in the different dynamic phases, the particles have distinct trajectories and velocity distributions. Dynamic transitions between ordered and disordered flows exhibit hysteresis, while in strongly disordered regimes there is no hysteresis and the velocity-force curves are smooth. When stripe patterns are present, transport can occur at an angle to the driving direction.

Mott transitions in three-component Falicov-Kimball model

Metal-insulator transitions are studied within a three-component Falicov-Kimball model which mimics a mixture of one-component and two-component fermionic particles with local repulsive interactions in optical lattices. Within the model the two-component fermionic particles are able to hop in the lattice, while the one-component fermionic particles are localized. The model is studied by using the dynamical mean-field theory with exact diagonalization. Its homogeneous solutions establish Mott transitions for both commensurate and incommensurate fillings between one third and two thirds. At commensurate one third and two thirds fillings the Mott transition occurs for any density of hopping particles, while at incommensurate fillings the Mott transition can occur only for density one half of hopping particles. At half filling, depending on the repulsive interactions the reentrant effect of the Mott insulator is observed. As increasing local interaction of hopping particles, the first insulator-metal transition is continuous, whereas the second metal-insulator transition is discontinuous. The second metal-insulator transition crosses a finite region where both metallic and insulating phase coexist. At third filling the Mott transition is established only for strong repulsive interactions. A phase separation occurs together with the phase transition.

Resonantly enhanced tunneling and transport of ultracold atoms on tilted optical lattices

We investigate the resonantly enhanced tunneling dynamics of ultracold bosons loaded on a tilted 1-D optical lattice, which can be used to simulate a chain of Ising spins and associated quantum phase transitions. The center of mass motion after a sudden tilt both at commensurate and incommensurate fillings is obtained via analytic, time-dependent exact diagonalization and density matrix renormalization group methods (adaptive t-DMRG). We identify a maximum in the amplitude of the center of mass oscillations at the quantum critical point of the effective spin system. For the dynamics of incommensurate systems, which cannot be mapped to a spin model, we develop an analytical approach in which the time evolution is obtained by projecting onto resonant families of small clusters. We compare the results of this approach at low fillings to the exact time evolution and find good agreement even at filling factors as large as 2/3. Using this projection onto small clusters, we propose a controllable transport scheme applicable in the context of Atomtronic devices on optical lattices (`slinky scheme').

Two distinct Mott-insulator to Bose-glass transitions and breakdown of self-averaging in the disordered Bose-Hubbard model

We investigate the instabilities of the Mott-insulating phase of the weakly disordered Bose-Hubbard model within a renormalization group analysis of the replica field theory obtained by a strong-coupling expansion around the atomic limit. We identify an order parameter and associated correlation length scale that are capable of capturing the transition from a state with zero compressibility, the Mott insulator, to one in which the compressibility is finite, the Bose glass. The order parameter is the relative variance of the disorder-induced mass distribution. In the Mott insulator, the relative variance renormalizes to zero, whereas it diverges in the Bose glass. The divergence of the relative variance signals the breakdown of self-averaging. The length scale governing the breakdown of self-averaging is the distance between rare regions. This length scale is finite in the Bose glass but diverges at the transition to the Mott insulator with an exponent of $\ensuremath{\nu}=1/D$ for incommensurate fillings. Likewise, the compressibility vanishes with an exponent of $\ensuremath{\gamma}=4/D\ensuremath{-}1$ at the transition. At commensurate fillings, the transition is controlled by a different fixed point at which both the disorder and interaction vertices are relevant.

Semiclassical solitons in strongly correlated systems of ultracold bosonic atoms in optical lattices

We investigate theoretically soliton excitations and dynamics of their formation in strongly correlated systems of ultracold bosonic atoms in two and three dimensional optical lattices. We derive equations of nonlinear hydrodynamics in the regime of strong interactions and incommensurate fillings, when atoms can be treated as hard core bosons. When parameters change in one direction only we obtain Korteweg–de Vries type equation away from half-filling and modified KdV equation at half-filling. We apply this general analysis to a problem of the decay of the density step. We consider stability of one dimensional solutions to transverse fluctuations. Our results are also relevant for understanding nonequilibrium dynamics of lattice spin models.

Momentum Distribution in a One-Dimensional Bose–Hubbard Model at Incommensurate Fillings

We study the momentum distribution of the hard-core extended Bose–Hubbard model at incommensurate fillings in one dimension. From the finite-size scaling behavior of the zero-momentum occupancy, the Luttinger liquid parameters are obtained as a function of interaction strength and filling. The curvature of the momentum distribution shows distinction between the easy-plane and the easy-axis region, and the occupancy at the zone boundary indicates the filling fraction.

Anomalous suppression of the Bose glass at commensurate fillings in the disordered Bose-Hubbard model

We study the weakly disordered Bose-Hubbard model on a cubic lattice through a one-loop renormalization-group analysis of the corresponding effective-field theory which is explicitly derived by combining a strong-coupling expansion with a replica average over the disorder. The method is applied not only to generic uncorrelated on-site disorder but also to simultaneous hopping-disorder correlated with the differences of adjacent disorder potentials. Such correlations are inherent in fine-grained optical speckle potentials used as a source of disorder in optical lattice experiments. As a result of strong coupling, the strength of the replica-mixing disorder vertex, responsible for the emergence of a Bose glass, crucially depends on the chemical potential and the Hubbard repulsion and vanishes to leading order in the disorder at commensurate boson fillings. As a consequence, at such fillings a direct transition between the Mott insulator and the superfluid in the presence of disorder cannot be excluded on the basis of a one-loop calculation. At incommensurate fillings, at a certain length scale, the Mott insulator will eventually become unstable toward the formation of a Bose glass. Phase diagrams as a function of the microscopic parameters are presented and the finite-size crossover between the Mott-insulating state and the Bose glass is analyzed.

Bosons in one-dimensional incommensurate superlattices

We investigate numerically the zero-temperature physics of the one-dimensional Bose-Hubbard model in an incommensurate cosine potential, recently realized in experiments with cold bosons in optical superlattices [L. Fallani et al., Phys. Rev. Lett. 98, 130404 (2007)]. An incommensurate cosine potential has intermediate properties between a truly periodic and a fully random potential, displaying a characteristic length scale (the quasiperiod) which is shown to set a finite lower bound to the excitation energy of the system at special incommensurate fillings. This leads to the emergence of gapped incommensurate band-insulator (IBI) phases along with gapless Bose-glass (BG) phases for strong quasiperiodic potential for both hard-core and soft-core bosons. Enriching the spatial features of the potential by the addition of a second incommensurate component appears to remove the IBI regions, stabilizing a continuous BG phase over an extended parameter range. Moreover, we discuss the validity of the local-density approximation in the presence of a parabolic trap, clarifying the notion of a local BG phase in a trapped system; we investigate the behavior of first- and second-order coherence upon increasing the strength of the quasiperiodic potential; and we discuss the ab initio derivation of the Bose-Hubbard Hamiltonian with quasiperiodic potential starting from the microscopic Hamiltonian of bosons in an incommensurate superlattice.

Modulating the Framework Negative Charge Density in the System [BDT−TTP•+]/[Re6S5Cl91-]/[Re6(S/Se)6Cl82-]/[Re6S7Cl73-]: Templating by Isosteric Cluster Anions of Identical Symmetry and Shape, Variations of Incommensurate Band Filling, and Electronic Structure in 2D Metals

A series of 2D metals, beta-(BDT-TTP)6[Re6Se6Cl8] x (CHCl2-CHCl2)2, 2; beta-(ST-TTP)6[Re6S6Cl8] x (CH2Cl-CHCl2)2, 3; beta-(BDT-TTP)7[Re6S6Cl8]0.5[Re6S7Cl7]0.5 x (CH2Cl2), 4; beta-(BDT-TTP)7[Re6Se6Cl8]0.5[Re6S7Cl7]0.5 x (CH2Cl2), 5; beta-(BDT-TTP)8[Re6S7Cl7] x (CH2Cl2)4, 6 (BDT-TTP and ST-TTP are 2,5-bis(1,3-dithiol-2-ylidene)-1,3,4,6-tetrathiapentalene and 2-(1,3-diselenol-2-ylidene)-5(1,3-dithiol-2-ylidene)-1,3,4,6-tetrathiapentalene, respectively) is reported to have one single beta-slab layered topology despite successive increases of the cluster anion negative charge. The charge density within the templating composite inorganic-neutral molecule slab is shown to remain above a threshold of ca. one negative charge per square nanometer, that is, for cluster anions with two negative charges and higher. Conversely, discrete stacks are shown to be stabilized instead in the semiconducting salts (BDT-TTP)2[Re6S5Cl9], 1 where the cluster anion bears one negative charge only. The electronic structure of salts 2-6 is shown to be very stable and kept almost intact across the series. The templating strategy is shown to fulfill its anticipated potential for deliberate installment of incommensurate band fillings in molecular metals. The deliberate admixture of the 6:1 and 8:1 structures yields novel phases with a 7:1 stoichiometry with the anticipated crystal and electronic structures. The action at the organic-inorganic interface triggered by changing the anion charge yet keeping its shape and volume identical, which ultimately governs the shape of the unit cell, is of paramount importance in defining the Fermi surface of these metallic salts. The present BDT-TTP salts thus provide a series of materials with strongly related but subtly different Fermi surfaces worthy of many physical studies. Shubnikov-de Haas measurements are expected to be particularly interesting since they are especially sensitive to the details of the Fermi surface.

Phase separation in a two-species Bose mixture

We study the ground state quantum phase diagram for a two species Bose mixture in a one-dimensional optical lattice using the finite size density matrix renormalization group(FSDMRG) method. We discuss our results for different combinations of inter and intra species interaction strengths with commensurate and incommensurate fillings of the bosons. The phases we have obtained are superfluid, Mott insulator and a novel phase separation, where different species reside in spatially separate regions. The spatially separated phase is further classified into phase separated superfluid(PS-SF) and Mott insulator(PS-MI). The phase separation appears for all the fillings we have considered, whenever the inter-species interaction is slightly larger than the intra-species interactions.