Broken Sublattice Symmetry Research Articles

Quantum simulator of extended bipartite Hubbard model with broken sublattice symmetry: Magnetism, correlations, and phase transitions

We describe here a quantum simulator of extended bipartite Hubbard model with broken sublattice symmetry. The simulator consists of a structured lateral gate confining two dimensional electrons in a quantum well into artificial minima arranged in a hexagonal lattice. The sublattice symmetry breaking is generated by forming an artificial triangular graphene quantum dot (ATGQD) with zigzag edges. The resulting extended Hubbard model generates tunable ratio of tunneling strength to electron-electron interactions and of sublattice symmetry with control over shape. The validity of the simulator is confirmed for small systems using mean-field and exact diagonalization many-body approaches which show that the ground state changes from a metallic to an antiferromagnetic (AF) phase by varying the distance between sites or depth of the confining potential. The one-electron spectrum of these triangular dots contains a macroscopically degenerate shell at the Fermi level. The shell persists at the mean-field level for weak interactions (metallic phase) but disappears for strong interactions, in the AF phase. We determine the effects of electron-electron interactions on the ground state, the total spin, and the excitation spectrum as a function of filling of the ATGQD. We find that the half-filled charge neutral shell leads to a partially spin polarized state in both metallic and AF regimes in accordance with Liebs theorem. In both regimes a relatively large gap separates the spin polarized ground state to the first excited many-body state at half filling of the degenerate shell. By adding or removing an electron, this gap drops dramatically, and alternate total spin states emerge with energies nearly degenerate to a spin polarized ground state.

Electrostatic interactions in twisted bilayer graphene

The effects of the long range electrostatic interaction in twisted bilayer graphene are described using the Hartree-Fock approximation. The results show a significant dependence of the band widths and shapes on electron filling, and the existence of broken symmetry phases at many densities, either valley/spin polarized, with broken sublattice symmetry, or both.

Strain-induced large injection current in twisted bilayer graphene

The electronic wavefunctions in moir\'e materials are highly sensitive to the details of the local atomic configuration enabling Bloch band geometry and topology to be controlled by stacking and strain. Here we predict that large injection currents (under circular polarized irradiation) can develop in strained twisted bilayer graphene (TBG) heterostructures with broken sublattice symmetry; such bulk photovoltaic currents flow even in the absence of a p-n junction and can be controlled by the helicity of incident light. As we argue, large injection current rates proceed from strong and highly peaked interband Berry curvature dipole distributions (arising from the texturing of Bloch wavefunctions in strained TBG heterostructures). Strikingly, we find that TBG injection current displays pronounced responses in the THz regime and can be tuned by chemical potential. These render injection currents a useful photocurrent probe of symmetry breaking in TBG heterostructures and make TBG a promising material for THz technology.

Anomalous and anisotropic nonlinear susceptibility in the proximate Kitaev magnet \u03b1-RuCl3

The leading order nonlinear (NL) susceptibility, χ3, in a paramagnet is negative and diverges as T → 0. This divergence is destroyed when spins correlate and the NL response provides unique insights into magnetic order. Dimensionality, exchange interaction, and preponderance of quantum effects all imprint their signatures in the NL magnetic response. Here, we study the NL susceptibilities in the proximate Kitaev magnet α-RuCl3, which differs from the expected antiferromagnetic behavior. For T < Tc = 7.5 K and field B in the ab-plane, we obtain contrasting NL responses in low (<2 T) and high field regions. For low fields, the NL behavior is dominated by a quadratic response (positive χ2), which shows a rapid rise below Tc. This large χ2 > 0 implies a broken sublattice symmetry of magnetic order at low temperatures. Classical Monte Carlo (CMC) simulations in the standard K − H − Γ model secure such a quadratic B dependence of M, only for T ≈ Tc with χ2 being zero as T → 0. It is also zero for all temperatures in exact diagonalization calculations. On the other hand, we find an exclusive cubic term (χ3) that describes the high field NL behavior well. χ3 is large and positive both below and above Tc crossing zero only for T > 50 K. In contrast, for B ∥ c-axis, no separate low/high field behaviors are measured and only a much smaller χ3 is apparent.

Molecular collapse in graphene: Sublattice symmetry effect

Atomic collapse can be observed in graphene because of its large "effective" fine structure constant, which enables this phenomenon to occur for an impurity charge as low as $Z_c\sim 1-2$. Here, we investigate the effect of the sublattice symmetry on molecular collapse in two spatially separated charge tunable vacancies, that are located on the same (A-A type) or different (A-B type) sublattices. We find that the broken sublattice symmetry: (1) does not affect the location of the main bonding and anti-bonding molecular collapse peaks, (2) but shifts the position of the satellite peaks, because they are a consequence of the breaking of the local sublattice symmetry, and (3) there are vacancy characteristic collapse peaks that only occur for A-B type vacancies, which can be employed to distinguish them experimentally from the A-A type. As the charge, energy, and separation distance increase, the additional collapse features merge with the main molecular collapse peaks. We show that the spatial distribution around the vacancy site of the collapse states allows us to differentiate the molecular from the frustrated collapse.

Flat Bands and Chiral Optical Response of Moiré Insulators.

We present a low-energy model describing the reconstruction of the electronic spectrum in twisted bilayers of honeycomb crystals with broken sublattice symmetry. The resulting moiré patterns are classified into two families with different symmetry. In both cases, flat bands appear at relatively large angles without any magic-angle condition. Transitions between them give rise to sharp resonances in the optical absorption spectrum at frequencies well below the gap of the monolayer. Owing to their chiral symmetry, twisted bilayers display circular dichroism, that is, different absorption of left and right circularly polarized light. This optical activity is a nonlocal property determined by the stacking. In hexagonal boron nitride, sensitivity to the stacking leads to strikingly different circular dichroism in the two types of moirés. Our calculations exemplify how subtle properties of the electronic wave functions, encoded in current correlations between the layers, control physical observables of moiré materials.

Spin-orbit torques in a Rashba honeycomb antiferromagnet

Recent experiments on switching antiferromagnetic domains by electric current pulses have attracted a lot of attention to spin-orbit torques in antiferromagnets. In this work, we employ the tight-binding model solver, kwant, to compute spin-orbit torques in a two-dimensional antiferromagnet on a honeycomb lattice with strong spin-orbit interaction of Rashba type. Our model combines spin-orbit interaction, local s-d-like exchange, and scattering of conduction electrons on on-site disorder potential to provide a microscopic mechanism for angular momentum relaxation. We consider two versions of the model: one with preserved and one with broken sublattice symmetry. A non-equilibrium staggered polarization, that is responsible for the so-called Neel spin-orbit torque, is shown to vanish identically in the symmetric model but may become finite if sublattice symmetry is broken. Similarly, anti-damping spin-orbit torques vanish in the symmetric model but become finite and anisotropic in a model with broken sublattice symmetry. As expected, anti-damping torques also reveal a sizable dependence on impurity concentration. Our numerical analysis also confirms symmetry classification of spin-orbit torques and strong torque anisotropy due to in-plane confinement of electron momenta.

Emergence of massless Dirac quasiparticles in correlated hydrogenated graphene with broken sublattice symmetry

Using the variational cluster approximation (VCA) and the cluster perturbation theory, we study the finite temperature phase diagram of a half-depleted periodic Anderson model on the honeycomb lattice at half filling for a model of graphone, i.e., single-side hydrogenated graphene. The ground state of this model is found to be ferromagnetic (FM) semi-metal. The spin wave dispersion in the FM state is linear in momentum at zero temperature but becomes quadratic at finite temperatures, implying that the FM state is fragile against thermal fluctuations. Indeed, our VCA calculations find that the paramagnetic (PM) state dominates the finite temperature phase diagram. More surprisingly, we find that massless Dirac quasiparticles with the linear energy dispersion emerge at the Fermi energy upon introducing the electron correlation $U$ at the impurity sites in the PM phase. The Dirac Fermi velocity is found to be highly correlated to the quasiparticle weight of the emergent massless Dirac quasiparticles at the Fermi energy and monotonically increases with $U$. These unexpected massless Dirac quasiparticles are also examined with the Hubbard-I approximation and the origin is discussed in terms of the spectral weight redistribution involving a large energy scale of $U$. Considering an effective quasiparticle Hamiltonian which reproduces the single-particle excitations obtained by the Hubbard-I approximation, we argue that the massless Dirac quasiparticles are protected by the electron correlation. Our finding is therefore the first example of the emergence of massless Dirac quasiparticles due to dynamical electron correlations without breaking any spatial symmetry. The experimental implications of our results for graphone as well as a graphene sheet on transition metal substrates are also briefly discussed.

Tunable anisotropic superfluidity in an optical kagome superlattice

We study the phase diagram of the Bose-Hubbard model on the kagome lattice with a broken sublattice symmetry. Such a superlattice structure can naturally be created and tuned by changing the potential offset of one sublattice in the optical generation of the frustrated lattice. The superstructure gives rise to a rich quantum phase diagram, which is analyzed by combining Quantum Monte Carlo simulations with the Generalized Effective Potential Landau Theory. Mott phases with non-integer filling and a characteristic order along stripes are found, which show a transition to a superfluid phase with an anisotropic superfluid density. Surprisingly, the direction of the superfluid anisotropy is changing between different symmetry directions as a function of the particle number or the hopping strength. Finally, we discuss characteristic signatures of anisotropic phases in time-of-flight absorption measurements.

Four-Coloring Model and Frustrated Superfluidity in the Diamond Lattice

We propose a novel four-coloring model which describes "frustrated superfluidity" of p-band bosons in the diamond optical lattice. The superfluid phases of the condensate wave functions on the diamond-lattice bonds are mapped to four distinct colors at low temperatures. The fact that a macroscopic number of states satisfy the constraints that four differently colored bonds meet at the same site leads to an extensive degeneracy in the superfluid ground state at the classical level. We demonstrate that the phase of the superfluid wave function as well as the orbital angular momentum correlations exhibit a power-law decay in the degenerate manifold that is described by an emergent magnetostatic theory with three independent flux fields. Our results thus provide a novel example of critical superfluid phase with algebraic order in three dimensions. We further show that quantum fluctuations favor a Néel ordering of orbital angular moments with broken sublattice symmetry through the order-by-disorder mechanism.

Broken Symmetries, Zero-Energy Modes, and Quantum Transport in Disordered Graphene: From Supermetallic to Insulating Regimes

The role of defect-induced zero-energy modes on charge transport in graphene is investigated using Kubo and Landauer transport calculations. By tuning the density of random distributions of monovacancies either equally populating the two sublattices or exclusively located on a single sublattice, all conduction regimes are covered from direct tunneling through evanescent modes to mesoscopic transport in bulk disordered graphene. Depending on the transport measurement geometry, defect density, and broken sublattice symmetry, the Dirac-point conductivity is either exceptionally robust against disorder (supermetallic state) or suppressed through a gap opening or by algebraic localization of zero-energy modes, whereas weak localization and the Anderson insulating regime are obtained for higher energies. These findings clarify the contribution of zero-energy modes to transport at the Dirac point, hitherto controversial.

Carrier-mediated long-range ferromagnetism in electron-doped Fe-C4and Fe-N4incorporated graphene

Graphene magnetism has been proposed but based on thermodynamically unstable zigzag edges and dangling electrons with broken sublattice symmetry. From results of first-principles calculations, we propose a way to realize thermodynamically stable graphene ferromagnetism by seamlessly incorporating transition metals into the graphene honeycomb network. An Fe atom substituting a carbon-carbon dimer of graphene can result in nearly square-planar covalent bonding between the spin-polarized Fe 3$d$ orbitals and graphene dangling bond states. Dangling bond passivation of the divacancy pore with N and O strongly affects the Fe incorporation into the graphene network in terms of energetics and electronic structure. The Fe-N${}_{4}$ or Fe-C${}_{4}$ incorporated graphene is predicted to show long-range ferromagnetism particularly due to carrier mediation when electron doped.

Rotationally symmetric ordered phase in the three-state antiferromagnetic Potts model.

We investigate the three-state antiferromagnetic Potts model on a simple cubic lattice with a cluster flipping Monte Carlo simulation algorithm in the temperature region below the transition into disorder at ${\mathit{T}}_{\mathit{c}1}$. We find both the well-established broken-sublattice-symmetry (BSS) phase at low temperature and a rotationally symmetric phase at higher temperature, but below ${\mathit{T}}_{\mathit{c}1}$. The properties of the second phase and the transition temperature to the BSS phase are in disagreement with recent cluster-variation and Monte Carlo simulation results, but in agreement with simulations by Kolesik and Suzuki. \textcopyright{} 1996 The American Physical Society.