Anisotropic Hopping Research Articles

Tilted stripes origin in La1.88Sr0.12CuO4 revealed by anisotropic next-nearest neighbor hopping

Spin- and charge- stripe order has been extensively studied in the superconducting cuprates, among which underdoped La2−xSrxCuO4 (LSCO) is an archetype with static spin stripes at low temperatures. An intriguing, but not completely understood, phenomenon in LSCO is that the stripes are tilted away from the high-symmetry Cu-Cu directions. Using high-resolution neutron scattering on LSCO with x = 0.12, we find two coexisting phases at low temperatures, one with static spin stripes and the other with fluctuating ones, both sharing the same tilt angle. Our numerical calculations using the doped Hubbard model elucidate the tilting’s origin, attributing it to anisotropic next-nearest neighbor hopping t′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${t}^{{\\prime} }$$\\end{document}, consistent with the material’s slight orthorhombicity. Our results underscore the model’s success in describing specific details of the ground state of this real material and highlight the role of t′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${t}^{{\\prime} }$$\\end{document} in the Hamiltonian, revealing the delicate interplay between stripes and superconductivity across theoretical and experimental contexts.

Realizing Altermagnetism in Fermi-Hubbard Models with Ultracold Atoms.

Altermagnetism represents a type of collinear magnetism, that is in some aspects distinct from ferromagnetism and from conventional antiferromagnetism. In contrast to the latter, sublattices of opposite spin are related by spatial rotations and not only by translations and inversions. As a result, altermagnets have spin-split bands leading to unique experimental signatures. Here, we show theoretically how a d-wave altermagnetic phase can be realized with ultracold fermionic atoms in optical lattices. We propose an altermagnetic Hubbard model with anisotropic next-nearest neighbor hopping and obtain the Hartree-Fock phase diagram. The altermagnetic phase separates in a metallic and an insulating phase and is robust over a large parameter regime. We show that one of the defining characteristics of altermagnetism, the anisotropic spin transport, can be probed with trap-expansion experiments.

Coupling Antisite Defect and Lattice Tensile Stimulates Facile Isotropic Li-Ion Diffusion.

Despite widely used as a commercial cathode, the anisotropic 1D channel hopping of lithium ions along the [010] direction in LiFePO4 prevents its application in fast charging conditions. Herein, an ultrafast nonequilibrium high-temperature shock technology is employed to controllably introduce the Li-Fe antisite defects and tensile strain into the lattice of LiFePO4. This design makes the study of the effect of the strain field on the performance further extended from the theoretical calculation to the experimental perspective. The existence of Li-Fe antisite defects makes it feasible for Li+ to move from the 4a site of the edge-sharing octahedra across the ab plane to 4c site of corner-sharing octahedra, producing a new diffusion channel different from [010]. Meanwhile, the presence of a tensile strain field reduces the energy barrier of the new 2D diffusion path. In the combination of electrochemical experiments and first-principles calculations, the unique multiscale coupling structure of Li-Fe antisite defects and lattice strain promotes isotropic 2D interchannel Li+ hopping, leading to excellent fast charging performance and cycling stability (high-capacity retention of 84.4% after 2000 cycles at 10 C). The new mechanism of Li+ diffusion kinetics accelerated by multiscale coupling can guide the design of high-rate electrodes.

Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy. At low temperatures, theoretical predictions [Phys. Rev. A 72 053604 (2005)] and [arXiv: 0706.1609] indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering. However, due to ergodic difficulties faced by Monte Carlo methods at low temperatures, this topological phase has not been numerically explored. We propose a linear cluster updating Monte Carlo method, which flips spins without rejection in the anisotropy limit but does not change the energy. Using this scheme and conventional Monte Carlo methods, we succeed in revealing the nature of topological phases with half-vortices and domain walls. In the constructed global phase diagram, Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier. We also propose and explore a wide range of quantities, including magnetism, superfluidity, specific heat, susceptibility, and even percolation susceptibility, and obtain consistent and reliable results. Furthermore, we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes, as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections. The critical exponents of different types of phase transitions are reasonably fitted. The results are useful to help cold atom experiments explore the half-vortex topological phase.

Unusual magnetotransport in twisted bilayer graphene from strain-induced open Fermi surfaces

Anisotropic hopping in a toy Hofstadter model was recently invoked to explain a rich and surprising Landau spectrum measured in twisted bilayer graphene away from the magic angle. Suspecting that such anisotropy could arise from unintended uniaxial strain, we extend the Bistritzer-MacDonald model to include uniaxial heterostrain and present a detailed analysis of its impact on band structure and magnetotransport. We find that such strain strongly influences band structure, shifting the three otherwise-degenerate van Hove points to different energies. Coupled to a Boltzmann magnetotransport calculation, this reproduces previously unexplained nonsaturating [Formula: see text] magnetoresistance over broad ranges of density near filling [Formula: see text] and predicts subtler features that had not been noticed in the experimental data. In contrast to these distinctive signatures in longitudinal resistivity, the Hall coefficient is barely influenced by strain, to the extent that it still shows a single sign change on each side of the charge neutrality point-surprisingly, this sign change no longer occurs at a van Hove point. The theory also predicts a marked rotation of the electrical transport principal axes as a function of filling even for fixed strain and for rigid bands. More careful examination of interaction-induced nematic order versus strain effects in twisted bilayer graphene could thus be in order.

Spin filtration in generalized Sierpinski triangles in presence of Rashba spin–orbit interaction

In this work, we theoretically investigate the phenomenon of spin polarization in generalized Sierpinski gasket (SPG) triangles (, , , ) in the presence of Rashba spin–orbit interaction (RSOI) within a tight-binding framework. The geometrical construction is addressed for all four types of generalized SPG triangles using an iterative function system that begins with a fixed triangle of any arbitrary side length. The geometry of various types of fractal networks has a major impact on the degeneracy of the energy spectrum. It is shown that only the two-terminal setup in the presence of RSOI is incapable of breaking the spin degeneracy, which necessitates the use of a three-terminal setup to break the time-reversal symmetry. The effect of flip map induced anisotropic hopping integrals on three-terminal spin-resolved transmission probabilities is studied. In several cases, we find almost spin polarization in our considered lattices. We also analyze how spin polarization varies with RSOI strength and fractal generations. Our results indicate that fractal lattices might be suitable functional elements for designing future spin-based electronic devices.

Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit

We explore the quasi one-dimensional (thin torus, or TT) limit of fractional Chern insulators (FCIs) as a starting point for their adiabatic preparation in quantum simulators. Our approach is based on tuning the hopping amplitude in one direction as an experimentally amenable knob to dynamically change the effective aspect ratio of the system. Similar to the TT limit of fractional quantum Hall (FQH) systems in the continuum, we find that the hopping-induced TT limit adiabatically connects the FCI state to a trivial charge density wave (CDW) ground state. This adiabatic path may be harnessed for state preparation schemes relying on the initialization of a CDW state followed by the adiabatic decrease of a hopping anisotropy. Our findings are based on the calculation of the excitation gap in a number of FCI models, both on a lattice and consisting of coupled wires. By analytical calculation of the gap in the limit of strongly anisotropic hopping, we show that its scaling is compatible with the preparation of large size FCIs for sufficiently large hopping anisotropy. Our numerical simulations in the framework of exact diagonalization explore the full anisotropy range to corroborate these results.

Customizing topological phases in the twisted bilayer superconductors with even-parity pairings

We investigate the topological properties of twisted bilayer superconductors with different even-parity pairings in each layer. In the presence of spin–orbit coupling, the Hamiltonian is mapped into an effective odd-parity superconductor. Based on this, we deduce the topological properties by examining the relative configuration between Fermi surface and Dirac pairing node. We show that mixed Rashba and Dresselhaus spin–orbit coupling and anisotropic hopping terms, which break the C 4 symmetry of the Fermi surface, can induce first-order topological superconductors with non-zero bulk Chern number. This provides a versatile way to control the topological phases of bilayer superconductors by adjusting the twisted angle and chemical potential. We demonstrate our results using a typical twisted angle of 53.13°, at which the translation symmetry is restored and the Chern number and edge state are calculated using the Moiré momentum.

Tunning the tilt of the Dirac cone by atomic manipulations in 8Pmmn borophene

Two dimensional quantum materials possessing Dirac cones in their spectrum are fascinating due to their emergent low-energy Dirac fermions. In 8Pmmn borophene the Dirac cone is furthermore tilted, which is a proxy for spacetime geometry, since the future light-cone depends on the underlying metric. Therefore it is important to understand the microscopic origin of the tilt. Here, based on ab-initio calculations, we decipher the atomistic mechanism of the formation of tilt. First, nearest-neighbor hopping on a buckled honeycomb lattice forms an upright Dirac cone. Then, the difference in the renormalized anisotropic second-neighbor hopping, formed by virtual hoppings on one-dimensional chains of atoms, tilts the Dirac cone. We construct an accurate tight-binding model on honeycomb graph for analytical investigation, and we find that substitution of certain boron atoms by carbon provides a way to change the tilt of the cone.

Hund's coupling and spin-orbit interaction in the three-band Hubbard model: Anomalous mass renormalization in Sr2RuO4

We study electronic correlation effects in the three-band Hubbard model in presence of Hund's and spin-orbit couplings using slave-spin mean-field theory. We consider three different regimes of hopping parameter values for the model on a square lattice. For orbital diagonal and isotropic hopping, we show that spin-orbit coupling (SOC), in general, enhances electronic correlations via the reduction of orbital degeneracy. In presence of Hund's coupling $J$, SOC tends to oppose the effect of $J$ on electronic correlations. Considering symmetry allowed anisotropic hopping, we find that the quasiparticle weights become orbital selective in presence of interaction. The effect of $J$ is particularly interesting for the band filling of two particles per site. Here, the Janus-faced effect of $J$ on correlation is obtained only in the narrower band, whereas electronic correlation in the wider band get reduced by $J$ for all values of Hubbard repulsion $U$. For model parameters corresponding to ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, interestingly, we find that the mass renormalizations in the bands become anomalous in presence of strong $U$ and $J$. The effective mass enhancement in the wider band becomes greater compared to that in the narrower band. We show that it originates in the peculiar electronic band structure of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$, in which the spinon Fermi surface topology changes in a particular way in the presence of interactions.

Effects of spin-orbit interaction and electron correlations in strontium titanate

We show that the Bloch states in the conduction band of SrTiO$_3$ arise from the interplay between highly anisotropic hopping in sub-bands derived from the Ti $t_{2g}$ orbitals and spin-orbit coupling that mixes these orbitals. Because of the nearly flat-band characteristics for one of the principal axes, at sufficiently high doping these Bloch states become unstable with respect to electron interactions, resulting in Mott-like singlet correlations. These findings may be relevant to the anomalous electronic properties of SrTiO$_3$, including its unusual superconductivity.

Anisotropic Melting Path of Charge-Ordering Insulator in LSMO/STO Superlattice.

Multiple phases coexist in manganite with simultaneously active couplings, and the transition among them depends on the relative intensities of different interactions. However, the melting path with variable intensities is unclear. The concentration and the ordering of oxygen vacancy in previous work are found to induce ferromagnetic charge-ordering insulator phase in [(La0.7 Sr0.3 MnO3 )10 /(SrTiO3 )5 ]n superlattice, which translates into metallic phase with magnetic field H and temperature T. In the current work, the H-T phase diagram for current I//[100] and I//[110] shows a large difference with H normal to the film plane, which is ascribed to the response of a variable range of hopping process to H with the in-plane anisotropic hopping probability of charge carrier. With H rotating from the out-of-plane to the in-plane direction, the preferred occupancy of the orbital causes a decrease of spin-orbital coupling and lowers the activation energy, inducing a gentler melting process of a charge-ordering insulator. This work shows that the melting path of a charge-ordering insulator phase can be largely modulated in manganite with anisotropy.

Topological Floquet bands in a circularly shaken dice lattice

The hoppings of noninteracting particles in the optical dice lattice result in the gapless dispersions in the band structure formed by the three lowest minibands. In our research, we find that once a periodic driving force is applied to this optical dice lattice, the original spectral characteristics could be changed, forming three gapped quasienergy bands in the quasienergy Brillouin zone. The topological phase diagram containing the Chern number of the lowest quasienergy band shows that when the hopping strengths of the nearest-neighbor hoppings are isotropic, the system persists in the topologically nontrivial phases with Chern number $C=2$ within a wide range of the driving strength. Accompanied by the anisotropic nearest-neighbor hopping strengths, a topological phase transition occurs, making the Chern number change from $C=2$ to $C=1$. This transition is further verified by our analytical method. Our theoretical work implies that it is feasible to realize the nontrivially topological characteristics of optical dice lattices by applying periodic shaking and that topological phase transition can be observed by independently tuning the strength of a type of nearest-neighbor hopping.

Kinetic specific features of singlet fission in highly anisotropic organic semiconductors.

Kinetics of singlet fission (SF) in molecular semiconductors, i.e., spontaneous splitting of the excited singlet state into a pair of triplet (T) excitons, is known to be strongly affected by geminate annihilation of created TT-pairs. In our work, we analyze in detail the specific properties of SF-kinetics in highly anisotropic molecular crystals (in which T-excitons undergo strongly anisotropic hopping migration) within the earlier proposed two-state model (TSM). This model allows for accurate treatment of the characteristic effects of anisotropic relative migration of T-excitons and TT-interaction on SF-kinetics, describing these effects within the approximation, that assumes kinetic coupling of two states: the [TT]-state of interacting TT-pairs and the [T + T]-state of freely migrating T-excitons. The TSM makes it possible to represent the TT-migration and interaction effects in terms of lattice-migration Green's functions, accurate analytical formulas that are obtained in this work. The TSM is applied to the analysis of SF-kinetics in rubrene single crystals, recently measured in a wide range of times (0.1ns < t < 104ns). The analysis enables one to obtain important information on specific properties of SF-kinetics in highly anisotropic crystals. In particular, the observed specific "hump" of SF-kinetics at intermediate times can be treated as a manifestation of the TT-coupling in the [TT]-state. It is also found that the characteristic asymptotic time-dependence of SF-kinetics (∼t-3/2) can markedly be distorted by spin relaxation in TT-pairs.

Quantum phase transition of the Bose-Hubbard model with anisotropic hopping on a cubic lattice

In quantum many-body system, dimensionality plays a critical role on type of the quantum phase transition. In order to study the quantum system during dimensional crossover, we studied the Bose-Hubbard model on cubic lattice with anisotropic hopping by using the high order symbolic strong coupling expansion method. The analytic series expanded boundaries between the Mott-insulator and superfluid phase up to eighth order are calculated. The critical exponents are extracted by Pad\'{e} re-summation method, which clearly shows the dimensional crossover behavior. Meanwhile, the critical points at commensurate filling can also be obtained, and they match well with the prediction of renormalization group theory. The scaling of the gap energy and whole phase diagram are given at last, and they can be taken as the benchmark for experiment and numerical simulations in the future study.

Collective modes in excitonic insulators: Effects of electron-phonon coupling and signatures in the optical response

We consider a two-band spinless model describing an excitonic insulator (EI) on the two-dimensional square lattice with anisotropic hopping parameters and electron-phonon (el-ph) coupling, inspired by the EI candidate Ta$_2$NiSe$_5$. We systematically study the nature of the collective excitations in the ordered phase which originates from the interband Coulomb interaction and the el-ph coupling. When the ordered phase is stabilized only by the Coulomb interaction (pure EI phase), its collective response exhibits a massless phase mode in addition to the amplitude mode. We show that in the BEC regime, the signal of the amplitude mode becomes less prominent and that the anisotropy in the phase mode velocities is relaxed compared to the model bandstructure. Through coupling to the lattice, the phase mode acquires a mass and the signal of the amplitude mode becomes less prominent. Importantly, character of the softening mode at the boundary between the normal semiconductor phase and the ordered phase depends on the parameter condition. In particular, we point out that even for el-ph coupling smaller than the Coulomb interaction the mode that softens to zero at the boundary can have a phonon character. We also discuss how the collective modes can be observed in the optical conductivity. Furthermore, we study the effects of nonlocal interactions on the collective modes and show the possibility of realizing a coexistence of an in-gap mode and an above-gap mode split off from the single amplitude mode in the system with the local interaction only.

Trion formation and unconventional superconductivity in a three-dimensional model with short-range attraction

A three-fermion problem in a three-dimensional lattice with anisotropic hopping is solved by discretizing the Schrödinger equation in momentum space. Interparticle interaction comprises on-site Hubbard repulsion and in-plane nearest-neighbor attraction. By comparing the energy of three-fermion bound clusters (trions) with the energy of one pair plus one free particle, a trion formation threshold is accurately determined, and the region of pair stability is mapped out. It is found that the “close-packed” density of fermion pairs, which is associated with a maximum pair condensation temperature in this model, is the highest in a strongly anisotropic case. It is also argued that pair superconductivity with the highest critical temperature is always close to trion formation, which makes the system prone to phase separation and local charge ordering.

Effect of strain on charge density wave order in the Holstein model

We investigate charge ordering in the Holstein model in the presence of anisotropic hopping, $t_x, t_y=1-\delta, 1 + \delta$, as a model of the effect of strain on charge density wave (CDW) materials. Using Quantum Monte Carlo simulations, we show that the CDW transition temperature is relatively insensitive to moderate anisotropy $\delta \lesssim 0.3$, but begins to decrease more rapidly at $\delta \gtrsim 0.4$. However, the density correlations, as well as the kinetic energies parallel and perpendicular to the compressional axis, change significantly for moderate $\delta$. Accompanying mean-field theory calculations show a similar qualitative structure, with the transition temperature relatively constant at small $\delta$ and a more rapid decrease for larger strains. We also obtain the density of states $N(\omega)$, which provides clear signal of the charge ordering transition at large strain, where finite size scaling of the charge structure factor is extremely difficult because of the small value of the order parameter.

Tunable topological semimetallic phases in Kondo lattice systems

We exploit topological semi-metallic phases resulting from the Kondo screening in Anderson lattice models. It is shown that by including spin-orbit interactions both in the bulk electrons and in the hybridization between the conduction electrons and electrons in $f$ orbit, all types of topological semi-metallic phases can be realized in Anderson lattice models. Specifically, upon either time-reversal symmetry broken or inversion symmetry broken, we find that either Weyl semi-metallic phase, Dirac semi-metallic phase or nodal-ring semi-metallic phases always emerge between insulating phases and can be accessed by tuning either temperature or spin-orbit interaction. For Anderson lattice models with general 3D spin-orbit hybridization between the conduction electrons and electrons in $f$ orbit, we find that Weyl nodal-ring semi-metallic phases emerges between strong and weak topological insulating phases. Furthermore, in the presence of an exchange field, Weyl semi-metallic phases forms after two Weyl points of charge $\pm1$ split off from a Dirac point at time-reversal momenta. On the other hand, when the spin-orbit interaction is included in the conduction electron, we find that upon the rotation symmetry being broken with anisotropic hopping amplitudes, Weyl semi-metallic phase emerges with double Weyl node of charges of $\pm2$. Furthermore, the Weyl semi-metallic phases with charges of $\pm2$ can be tuned into Weyl semi-metallic phases with charges of $\pm1$ through the inclusion of the Rashba spin-orbit interaction. Our analyses indicate that Anderson lattices with appropriate spin-orbit interactions provide a platform for realizing all types of topological semi-metallic phase

Effect of the anisotropy of long-range hopping on localization in three-dimensional lattices

It has become widely accepted that particles with long-range hopping do not undergo Anderson localization. However, several recent studies demonstrated localization of particles with long-range hopping. In particular, it was recently shown that the effect of long-range hopping in 1D lattices can be mitigated by cooperative shielding, which makes the system behave effectively as one with short-range hopping. Here, we show that cooperative shielding, demonstrated previously for 1D lattices, extends to 3D lattices with isotropic long-range $r^{-\alpha}$ hopping, but not to 3D lattices with dipolar-like anisotropic long-range hopping. We demonstrate the presence of localization in 3D lattices with uniform ($\alpha=0$) isotropic long-range hopping and the absence of localization with uniform anisotropic long-range hopping by using the scaling behaviour of eigenstate participation ratios. We use the scaling behaviour of participation ratios and energy level statistics to show that the existence of delocalized, non-ergodic extended, or localized states in the presence of disorder depends on both the exponents $\alpha$ and the isotropy of the long-range hopping amplitudes.