Effective Lattice Model Research Articles

Concentrated subradiant modes in a one-dimensional atomic array coupled with chiral waveguides

Non-Hermitian systems have recently attracted broad interest and exhibited intriguing physical phenomena, in which the non-Hermitian skin effect is one of the most remarkable quantum phenomena desiring detailed investigations and has been widely studied in various fermionic and bosonic systems. Here we propose a non-Hermitian atom-waveguide system composed of a tilted one-dimensional atomic array coupled with two identical waveguides with opposite chiralities. Such system creates an effective lattice model including nonreciprocal long-range hoppings through the chiral-waveguide photon-mediated interactions. We find the excitation of the collective atomic states concentrates in the middle interface, pointing towards the non-Hermitian skin effect associated with subradiant modes, while, on the contrary, superradiant modes exhibit extended features. Simulation results present subradiant funneling effect, with robustness against small atomic position disorders. Our work underpins the fundamental comprehension towards the non-Hermitian skin effect in open quantum systems and also provide prospective paths to study non-Hermitian systems in the area of quantum optics.

Dynamic control of octahedral rotation in perovskites by defect engineering

Engineering oxygen octahedra rotation patterns in $ABO_3$ perovskites is a powerful route to design functional materials. Here we propose a strategy that exploits point defects that create local electric dipoles and couple to the oxygen sublattice, enabling direct actuation on the rotational degrees of freedom. This approach, which relies on substituting an $A$ site with a smaller ion, paves a way to couple dynamically octahedra rotations to external electric fields. A common antisite defect, $\mathrm{Al_{La}}$ in rhombohedral LaAlO$_3$ is taken as a prototype to validate the idea, with atomistic density functional theory calculations supported with an effective lattice model to simulate the dynamics of switching of the local rotational degrees of freedom to long distances. Our simulations provide an insight of the main parameters that govern the operation of the proposed mechanism, and allow to define guidelines for screening other systems where this approach could be used for tuning the properties of the host material.

Edge states of a diffusion equationin one dimension: Rapid heat conduction to the heat bath.

We propose a one-dimensional diffusion equation(heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period a. We solve the time evolution of the field (temperature) profile from a given initial distribution, by diagonalizing the Hamiltonian, i.e., the Laplacian with alternating diffusion constants, and expanding the temperature profile by its eigenstates. We show that there are basically phases with or without edge states. The edge states affect the heat conduction around heat baths. In particular, rapid heat transfer to heat baths would be observed in a short-time regime, which is estimated to be t<10^{-2}s for the a∼10^{-3}m system and t<1s for the a∼10^{-2}m system composed of two kinds of familiar metals such as titanium, zirconium, and aluminium, gold, etc. We also discuss the effective lattice model which simplifies the calculation of edge states up to high energy. It is suggested that these high-energy edge states also contribute to very rapid heat conduction in a very short-time regime.

Effective Floquet model for minimally twisted bilayer graphene

We construct an effective Floquet lattice model for the triangular network that emerges in interlayer-biased minimally twisted bilayer graphene and which supports two chiral channels per link for a given valley and spin. We introduce the Floquet scheme with the one-channel triangular network and subsequently extend it to the two-channel case. From the bulk topological index (winding number) and finite system calculations, we find that both cases host anomalous Floquet insulators (AFIs) with a different gap-opening mechanism. In the one-channel network, either time-reversal or in-plane inversion symmetry has to be broken to open a gap. In contrast, in the two-channel network, interchannel coupling can open a gap without breaking these symmetries yielding a valley AFI with counterpropagating edge states. This phase is topologically trivial with respect to the total winding number but robust in the absence of intervalley scattering. Finally, we demonstrate the applicability of the Floquet model with magnetotransport calculations.

Anomalous Quantum Oscillations in a Heterostructure of Graphene on a Proximate Quantum Spin Liquid.

The quasi-two-dimensional Mott insulator α-RuCl_{3} is proximate to the sought-after Kitaev quantum spin liquid (QSL). In a layer of α-RuCl_{3} on graphene, the dominant Kitaev exchange is further enhanced by strain. Recently, quantum oscillation (QO) measurements of such α-RuCl_{3} and graphene heterostructures showed an anomalous temperature dependence beyond the standard Lifshitz-Kosevich (LK) description. Here, we develop a theory of anomalous QO in an effective Kitaev-Kondo lattice model in which the itinerant electrons of the graphene layer interact with the correlated magnetic layer via spin interactions. At low temperatures, a heavy Fermi liquid emerges such that the neutral Majorana fermion excitations of the Kitaev QSL acquire charge by hybridizing with the graphene Dirac band. Using abinitio calculations to determine the parameters of our low-energy model, we provide a microscopic theory of anomalous QOs with a non-LK temperature dependence consistent with our measurements. We show how remnants of fractionalized spin excitations can give rise to characteristic signatures in QO experiments.

Superconductivity from collective excitations in magic-angle twisted bilayer graphene

A purely electronic mechanism is proposed for the unconventional superconductivity recently observed in twisted bilayer graphene (tBG) close to the magic angle. Using the Migdal-Eliashberg framework on a one parameter effective lattice model for tBG we show that a superconducting state can be achieved by means of collective electronic modes in tBG. We posit robust features of the theory, including an asymmetrical superconducting dome and the magnitude of the critical temperature that are in agreement with experiments.

Effective lattice model of graphene moiré superlattices on hexagonal boron nitride

We propose an effective lattice model of graphene moir\'e superlattices on hexagonal boron nitride (MLG/BN) based on ab initio calculations to study the evolution of electronic properties of relaxed MLG/BN superlattices with relative twist angle ($\ensuremath{\theta}$). The parameters for obtaining hopping terms and on-site energies in the lattice Hamiltonian are directly extracted from the ab initio electronic structure of shifted commensurate bilayers. The effect of the in-plane strain induced by the structural relaxation can be taken into account straightforwardly for the lattice model. We consider completely free MLG/BN heterostructures and those with constant interlayer distances. We find that the structural distortion due to the relaxation exhibits similar magnitude for $\ensuremath{\theta}$ smaller than about $0.{5}^{\ensuremath{\circ}}$. The gap at the primary Dirac points (${\mathrm{\ensuremath{\Delta}}}_{P}$) is maintained for $\ensuremath{\theta}l0.{5}^{\ensuremath{\circ}}$, while the gap at the secondary Dirac points (${\mathrm{\ensuremath{\Delta}}}_{S}$) decreases rapidly with small $\ensuremath{\theta}$, and such distinct behavior of ${\mathrm{\ensuremath{\Delta}}}_{P}$ and ${\mathrm{\ensuremath{\Delta}}}_{S}$ is roughly consistent with recent experimental observations. In addition, decreasing interlayer distance can significantly enhance ${\mathrm{\ensuremath{\Delta}}}_{P}$. This lattice model is sufficiently transparent and flexible to be employed to investigate various configurations of MLG/BN moir\'e superlattices.

Fully Spin-Polarized Nodal Loop Semimetals in Alkaline Metal Monochalcogenide Monolayers.

Topological semimetals in ferromagnetic materials have attracted an enormous amount of attention due to potential applications in spintronics. Using first-principles density functional theory together with an effective lattice model, here we present a new family of topological semimetals with a fully spin-polarized nodal loop in alkaline metal monochalcogenide MX (M = Li, Na, K, Rb, or Cs; X = S, Se, or Te) monolayers. The half-metallic ferromagnetism can be established in MX monolayers, in which one nodal loop formed by two crossing bands with the same spin components is found at the Fermi energy. This nodal loop half-metal survives even when considering the spin-orbit coupling owing to the symmetry protection provided by the mirror plane. The quantum anomalous Hall state and Weyl-like semimetal in this system can be also achieved by rotating the spin from the out-of-plane to the in-plane direction. The MX monolayers hosting rich topological phases thus offer an excellent platform for realizing advanced spintronic concepts.

Mirror protected multiple nodal line semimetals and material realization

The conventional k.p method fails to capture the full and essential physics of many symmetry enriched multiple nodal line structures in the three dimensional Brillouin zone. Here we present a new and systematical method to construct the effective lattice model of mirror symmetry protected three-dimensional multiple nodal line semimetals, when the spin-orbit interaction is ignored. For systems with a given pair of perpendicular nodal rings, we obtain all the effective lattice models and eleven inequivalent nodal line Fermi surfaces together with their related constraints. By means of first-principles calculations, we first propose a family of real materials, beta phase of ternary nitrides X2GeN2 (X = Ca; Sr; Ba), that support one kind of these novel Fermi surfaces. Therefore, our work deepens the understanding of the nodal line structures and promotes the experimental progress of topological nodal line semimetals.

Topology in single-wall carbon nanotube of zigzag and armchair type

Single-wall carbon nanotubes can be one-dimensional (1D) topological insulators except for armchair nanotubes. The electronic states are characterized by a non-zero topological invariant, winding number, which is related to the number of 0D edge states via the bulk-edge correspondence. In the present study, we theoretically examine zigzag and armchair nanotubes to elucidate the emergence and absence of edge states. The effective 1D lattice model is employed in order to describe the fine structures due to the finite curvature of tube surface and spin-orbit interaction. We show that the lattice model for a zigzag nanotube is equivalent to the Su-Schrieffer-Heeger model, by which the formation of edge states is explained. An armchair nanotube is described by a ladder model, on the other hand, which does not host any edge states owing to the σh symmetry.

Effective lattice model for the collective modes in a Fermi liquid with spin-orbit coupling

A Fermi-liquid (FL) with spin-orbit coupling (SOC) supports a special type of collective modes--chiral spin waves--which are oscillations of magnetization even in the absence of the external magnetic field. We study the chiral spin waves of a two-dimensional FL in the presence of both the Rashba and Dresselhaus types of SOC and also subject to the in-plane magnetic field. We map the system of coupled kinetic equations for the angular harmonics of the occupation number onto an effective one-dimensional tight-binding model, in which the lattice sites correspond to angular-momentum channels. Linear-in-momentum SOC ensures that the effective tight-binding model has only nearest-neighbor hopping on a bipartite lattice. In this language, the continuum of spin-flip particle-hole excitations becomes a conduction band of the lattice model, whereas electron-electron interaction, parameterized by the harmonics of the Landau function, is mapped onto lattice defects of both on-site and bond type. Collective modes correspond to bound states formed by such defects. All the features of the collective-mode spectrum receive natural explanation in the lattice picture as resulting from the competition between on-site and bond defects.

Microscopic derivation of multichannel Hubbard models for ultracold nonreactive molecules in an optical lattice

Recent experimental advances in the cooling and manipulation of bialkali dimer molecules have enabled the production of gases of ultracold molecules that are not chemically reactive. It has been presumed in the literature that in the absence of an electric field the low-energy scattering of such nonreactive molecules (NRMs) will be similar to atoms, in which a single $s$-wave scattering length governs the collisional physics. However, in Ref. [1], it was argued that the short-range collisional physics of NRMs is much more complex than for atoms, and that this leads to a many-body description in terms of a multi-channel Hubbard model. In this work, we show that this multi-channel Hubbard model description of NRMs in an optical lattice is robust against the approximations employed in Ref. [1] to estimate its parameters. We do so via an exact, albeit formal, derivation of a multi-channel resonance model for two NRMs from an ab initio description of the molecules in terms of their constituent atoms. We discuss the regularization of this two-body multi-channel resonance model in the presence of a harmonic trap, and how its solutions form the basis for the many-body model of Ref. [1]. We also generalize the derivation of the effective lattice model to include multiple internal states (e.g., rotational or hyperfine). We end with an outlook to future research.

Devil's staircases in synthetic dimensions and gauge fields

We study interacting bosonic or fermionic atoms in a high synthetic magnetic field in two dimensions spanned by continuous real space and a synthetic dimension. Here, the synthetic dimension is provided by hyperfine spin states, and the synthetic field is created by laser-induced transitions between them. While the interaction is short-range in real space, it is long-range in the synthetic dimension in sharp contrast with fractional quantum Hall systems. Introducing an analog of the lowest-Landau-level approximation valid for large transition amplitudes, we derive an effective one-dimensional lattice model, in which density-density interactions turn out to play a dominant role. We show that in the limit of a large number of internal states, the system exhibits a cascade of crystal ground states, which is known as devil's staircase, in a way analogous to the thin-torus limit of quantum Hall systems.

Angular momentum and topology in semiconducting single-wall carbon nanotubes

Semiconducting single-wall carbon nanotubes are classified into two types by means of orbital angular momentum of valley state, which is useful to study their low energy electronic properties in finite-length. The classification is given by an integer $d$, which is the greatest common divisor of two integers $n$ and $m$ specifying the chirality of nanotubes, by analyzing cutting lines. For the case that $d$ is equal to or greater than four, two lowest subbands from two valleys have different angular momenta with respect to the nanotube axis. Reflecting the decoupling of two valleys, discrete energy levels in finite-length nanotubes exhibit nearly fourfold degeneracy and its small lift by the spin-orbit interaction. For the case that $d$ is less than or equal to two, in which two lowest subbands from two valleys have the same angular momentum, discrete levels exhibit lift of fourfold degeneracy reflecting the coupling of two valleys. Especially, two valleys are strongly coupled when the chirality is close to the armchair chirality. An effective one-dimensional lattice model is derived by extracting states with relevant angular momentum, which reveals the valley coupling in the eigenstates. A bulk-edge correspondence, relationship between number of edge states and the winding number calculated in the corresponding bulk system, is analytically shown by using the argument principle, which enables us to estimate the number of edge states from the bulk property. The number of edge states depends not only on the chirality but also on the shape of boundary.

Valley coupling in finite-length metallic single-wall carbon nanotubes

Degeneracy of discrete energy levels of finite-length, metallic single-wall carbon nanotubes depends on the type of nanotubes, boundary condition, length of nanotubes, and spin-orbit interaction. Metal-1 nanotubes, in which two nonequivalent valleys in the Brillouin zone have different orbital angular momenta with respect to the tube axis, exhibit nearly fourfold degeneracy and small lift of the degeneracy by the spin-orbit interaction reflecting the decoupling of two valleys in the eigenfunctions. In metal-2 nanotubes, in which the two valleys have the same orbital angular momentum, vernier-scale-like spectra appear for boundaries of orthogonal-shaped edge or cap termination reflecting the strong valley coupling and the asymmetric velocities of the Dirac states. Lift of the fourfold degeneracy by parity splitting overcomes the spin-orbit interaction in shorter nanotubes with a so-called minimal boundary. Slowly decaying evanescent modes appear in the energy gap induced by the curvature of nanotube surface. Effective one-dimensional lattice model reveals the role of boundary on the valley coupling in the eigenfunctions.

Coexistence and Competition of Magnetic and Charge Orders in an Extended Kondo Lattice Model for Sm Skutterudite

The properties of possible ordered phases in Sm skutterudite are studied in the framework of an effective Kondo lattice model derived from the p–f hybridization. In particular, the stable region of coexisting magnetic and charge orders is investigated in detail by changing the strength of crystal and magnetic fields in an Sm J = 5/2 multiplet. It is demonstrated that the coexisting phase does take place when the crystal field splitting is small, whereas it does not for an isolated Γ7 or Γ8 crystal field ground state. Although the phase usually appears under a finite magnetic field, the mean field theory predicts its existence at zero field in a case of the Γ8 ground state. The relationship of these theoretical results with experimental results of SmRu4P12 is discussed.

Flat band electrons and interactions in rhombohedral trilayer graphene

Multilayer graphene systems with a rhombohedral stacking order harbor nearly flat bands in their single-particle spectrum. We propose ansatz states to describe the surface-localized states of flat band electrons. The absence of kinetic dispersion near the fermi level leaves the interaction as a dominate mechanism to govern the low energy physics of a low density electron system. We build up an effective lattice model in two interacting low-energy bands, where the full terms of the Coulomb interaction, including those long-range and off-diagonal parts, have been considered. The interaction matrix coefficients in the many-body Hamiltonian model are directly calculated for a trilayer system using orthonormal Wannier basis. We then present a flat-band projection to yield an interaction-only lattice model for flat band electrons. We find that this limited model might energetically favor a ferromagnetic quantum crystal under certain conditions.

Lattice model for the surface states of a topological insulator with applications to magnetic and exciton instabilities

A surface of a strong topological insulator (STI) is characterized by an odd number of linearly dispersing gapless electronic surface states. It is well known that such a surface cannot be described by an effective two-dimensional lattice model (without breaking the time-reversal symmetry), which often hampers theoretical efforts to quantitatively understand some of the properties of such surfaces, including the effect of strong disorder, interactions and various symmetry-breaking instabilities. Here we formulate a lattice model that can be used to describe a {\em pair} of STI surfaces and has an odd number of Dirac fermion states with wavefunctions localized on each surface. The Hamiltonian consists of two planar tight-binding models with spin-orbit coupling, representing the two surfaces, weakly coupled by terms that remove the extra Dirac points from the low-energy spectrum. We illustrate the utility of this model by studying the magnetic and exciton instabilities of the STI surface state driven by short-range repulsive interactions and show that this leads to results that are consistent with calculations based on the continuum model as well as three-dimensional lattice models. We expect the model introduced in this work to be widely applicable to studies of surface phenomena in STIs.

Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model

We study the collective states of interacting non-Abelian anyons that emerge in Kitaev's honeycomb lattice model. Vortex–vortex interactions are shown to lead to the lifting of topological degeneracy and the energy is found to exhibit oscillations that are consistent with Majorana fermions being localized at vortex cores. We show how to construct states corresponding to the fusion channel degrees of freedom and obtain the energy gaps characterizing the stability of the topological low-energy spectrum. To study the collective behavior of many vortices, we introduce an effective lattice model of Majorana fermions. We find the necessary conditions for the model to approximate the spectrum of the honeycomb lattice model, and show that bi-partite interactions are responsible for the lifting of degeneracy also in many-vortex systems.

Birefringent breakup of Dirac fermions on a square optical lattice

We generalize a proposal by Sorensen et al. [Phys. Rev. Lett. 94, 086803 (2005)] for creating an artificial magnetic field in a cold atom system on a square optical lattice. This leads us to an effective lattice model with tunable spatially periodic modulation of the artificial magnetic field and the hopping amplitude. When there is an average flux of half a flux quantum per plaquette the spectrum of low-energy excitations can be described by massless Dirac fermions in which the usually doubly degenerate Dirac cones split into cones with different "speeds of light" which can be tuned to give a single Dirac cone and a flat band. These gapless birefringent Dirac fermions arise because of broken chiral symmetry in the kinetic energy term of the effective low energy Hamiltonian. We characterize the effects of various perturbations to the low-energy spectrum, including staggered potentials, interactions, and domain wall topological defects.