Hopping Integrals Research Articles

Realization of Yin–Yang kagome bands and tunable quantum anomalous Hall effect in monolayer V3Cl6

Kagome materials serve as crucial platforms for investigating the quantum anomalous Hall effect (QAHE) due to the presence of kagome bands in their electronic structures. However, despite the theoretical predictions being proposed, kagome band material realizations have been limited. In this work, through tight-binding (TB) model analysis, by setting the nearest-neighbor hopping integrals with opposite signs, we propose a Yin–Yang kagome band structure characterized by two stable enantiomorphic kagome bands. Furthermore, we design a monolayer V3Cl6 to confirm the TB model. Three V atoms are located in different coordination environments in V3Cl6, so opposite signs of the hopping integrals between two of their orthogonal d orbitals can be achieved, which is the key to realize Yin–Yang kagome band structures. The calculated band structures obtained from first principles are consistent with those from the TB model. Additionally, we find that the two enantiomorphic flat bands in monolayer V3Cl6 possess opposite Chern number after spin–orbit coupling is considered, which can also be confirmed from symmetry index analysis. The Chern numbers as well as the topological properties can be modulated by doping hole or adjusting the magnetization directions, so the QAHE can be tuned in monolayer V3Cl6. Our results provide a practicable pathway for realizing Yin–Yang kagome band structures and achieving tunable QAHE in them.

Two-Dimensional Moiré Polaronic Electron Crystals.

Two-dimensional moiré materials have emerged as the most versatile platform for realizing quantum phases of electrons. Here, we explore the stability origins of correlated states in WSe_{2}/WS_{2} moiré superlattices. We find that ultrafast electronic excitation leads to partial melting of the Mott states on timescales 5 times longer than predictions from the charge hopping integrals and that the melting rates are thermally activated, with activation energies of 18±3 and 13±2 meV for the one- and two-hole Mott states, respectively, suggesting significant electron-phonon coupling. A density functional theory calculation of the one-hole Mott state confirms polaron formation and yields a hole-polaron binding energy of 16meV. These findings reveal a close interplay of electron-electron and electron-phonon interactions in stabilizing the polaronic Mott insulators at transition metal dichalcogenide moiré interfaces.

Doping dependence of superconductivity on a honeycomb lattice within the framework of kinetic-energy-driven superconductivity

Unconventional superconductivity on a honeycomb lattice has received increasing interest since the discovery of graphene primarily due to the similarities between materials with a honeycomb lattice and cuprate superconductors. Many theoretical studies have been conducted on superconductivity on a honeycomb lattice, however, a consistent picture is still lacking. In this paper, we have extended the theory of kinetic-energy-driven superconductivity, which has been developed to investigate unconventional superconductivity in cuprate superconductors, to explore superconductivity on a honeycomb lattice within the t-J model. Our results demonstrate that the charge-carrier pair gap parameter with [Formula: see text]-wave symmetry exhibits a dome-like shape as a function of doping, with superconductivity emerging at a certain doping concentration and disappearing at high doping levels, similar to what has been observed in cuprate and cobaltate superconductors. Furthermore, the charge-carrier pair gap parameter decreases with increasing the value of [Formula: see text] (the ratio between the antiferromagnetic exchange coupling constant and the nearest-neighbor hopping integral), and approaches zero when [Formula: see text] reaches a sufficiently large value. This indicates that the antiferromagnetic order will suppress the superconducting state and a sufficiently strong exchange coupling will completely destroy the superconductivity. Taking into account our present results together with the corresponding results of cuprate and cobaltate superconductors, it appears that the dome-like shape of the doping dependence of the charge-carrier pair gap parameter may be a common feature in doped Mott insulators.

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.

Manipulating the optimal transport orbital and virtual states in a supramolecular transistor

Supramolecular electronics bridges the gap between single-molecule electronics and bulk, plastic electronics, and is embodied as one of the biggest promises of nanometer electronics made by supramolecular functional materials. Within this field, the way in which electrons propagate through the supramolecule plays a profound role both in designing supramolecular devices and in understanding the structure–property relationships at the molecular level. Herein, we consider a supramolecular transistor, which contains bipartite molecular monomers, with one molecular orbital is non-interacting, whereas the other one is strongly correlated. Modeling this device using the two-impurity Anderson model, we unravel the orbital selections and the virtual states in the electronic transport process with the aid of the celebrated numerical renormalization group method. We demonstrate that if both orbitals are in their particle-hole symmetric regimes, electrons favor to transmit through the non-interacting molecular orbital via the resonant tunneling process, rather than through the strongly correlated molecular orbital via the Kondo effect, despite the energy of the strongly correlated orbital is lower. This phenomenon indicates that if the Kondo effect occurs, it experiences a temporarily doubly occupied virtual state. Interestingly, the situation reverses if the inter-molecule hopping integral is applied, where the strongly correlated orbital becomes optimal and the virtual state turns to be an empty state. To understand these behaviors, both the static and the dynamical properties, as well as those thermodynamic quantities are studied in detail, and necessary physical arguments are given. Our findings afford deep insights into the manipulations of the optimal transport orbital and the Kondo behaviors within quantum impurity devices.

Ground-state and spectral properties of the doped one-dimensional optical Hubbard-Su-Schrieffer-Heeger model

We present a density matrix renormalization group study of the doped one-dimensional (1D) Hubbard-Su-Schrieffer-Heeger (Hubbard-SSH) model, where the atomic displacements linearly modulate the nearest-neighbor hopping integrals. Focusing on an optical variant of the model in the strongly correlated limit relevant for cuprate spin chains, we examine how the SSH interaction modifies the model's ground- and excited-state properties. The SSH coupling weakly renormalizes the model's single- and two-particle response functions for electron-phonon $(e\text{\ensuremath{-}}\mathrm{ph})$ coupling strengths below a parameter-dependent critical value ${g}_{\mathrm{c}}$. For larger $e\text{\ensuremath{-}}\mathrm{ph}$ coupling, the sign of the effective hopping integrals changes for a subset of orbitals, which drives a lattice dimerization distinct from the standard nesting-driven picture in 1D. The spectral weight of the one- and two-particle dynamical response functions are dramatically rearranged across this transition, with significant changes in the ground-state correlations. We argue that this dimerization results from the breakdown of the linear approximation for the $e\text{\ensuremath{-}}\mathrm{ph}$ coupling and thus signals a fundamental limitation of the linear SSH interaction. Our results have consequences for our understanding of how SSH-like interactions can enter the physics of strongly correlated quantum materials, including the recently synthesized doped cuprate spin chains.

Interplay between hopping dimerization and quasi-periodicity on flux-driven circular current in an incommensurate Su–Schrieffer–Heeger ring

We report for the first time the phenomenon of flux-driven circular current in an isolated Su–Schrieffer–Heeger (SSH) quantum ring in presence of cosine modulation in the form of the Aubry–André–Harper (AAH) model. The quantum ring is described within a tight-binding framework, where the effect of magnetic flux is incorporated through Peierls substitution. Depending on the arrangements of AAH site potentials we have two different kinds of ring systems that are referred to as staggered and non-staggered AAH SSH rings. The interplay between the hopping dimerization and quasiperiodic modulation leads to several new features in the energy band spectrum and persistent current which we investigate critically. An atypical enhancement of current with increasing AAH modulation strength is obtained that gives a clear signature of transition from a low conducting phase to a high conducting one. The specific roles of AAH phase, magnetic flux, electron filling, intra- and inter-cell hopping integrals, and ring size are discussed thoroughly. We also study the effect of random disorder on persistent current with hopping dimerization to compare the results with the uncorrelated ones. Our analysis can be extended further in studying magnetic responses of similar kinds of other hybrid systems in presence of magnetic flux.

Realization of quasi-1D topological magnetism at the V-alloyed MoS2 zigzag edge.

Topological magnetism in quasi-1D systems can be interesting because of the significant quantum confinement. However, the realization is missing. In this letter, we propose the use of 3× periodicities related edge reconstructions of MoS2 zigzag edges to construct a topological quasi-1D spin chain. Specifically, a trimer Su-Schrieffer-Heeger model can be applied to illustrate the topological and spin order when the inter-cell hopping integral is larger than the intra-cell ones. As a result, topological ferromagnetic order is achieved for S-oriented edge states magnetized by V atoms and confirmed by first-principles calculations and Wannier functions analysis. Finally, gap opening and spin-polarized end states are realized.

Bardeen's tunneling theory applied to intraorbital and interorbital hopping integrals between dopants in silicon

We utilize Bardeen's tunneling theory to calculate intra- and interorbital hopping integrals between phosphorus donors in silicon using known orbital wave functions. While the two-donor problem can be solved directly, the knowledge of hoppings for various pairs of orbitals is essential for constructing multi-orbital Hubbard models for chains and arrays of donors. To assure applicability to long-range potentials, we rederive Bardeen's formula for the matrix element without assuming non-overlapping potentials. Moreover, we find a correction to the original expression allowing us to use it at short distances. We also show that accurate calculation of the lowest donor-pair eigenstates is possible based on these tunnel couplings, and we characterize the obtained states. The results are in satisfactory quantitative agreement with those obtained with the standard H\"uckel tight-binding method. The calculation relies solely on the wave functions in the barrier region and does not explicitly involve donor or lattice potentials, which has practical advantages. We find that neglecting the central correction potential in the standard method may lead to qualitatively incorrect results, while its explicit inclusion raises severe numerical problems, as it is contained in a tiny volume. In contrast, using wave functions obtained with this correction in the proposed method does not raise such issues. Nominally, the computational cost of the method is to calculate a double integral along the plane that separates donors. For donor separation in directions where valley interference leads to oscillatory behavior, additional averaging over the position of the integration plane is needed. Despite this, the presented approach offers a competitive computational cost as compared to the standard one. This work may be regarded as a benchmark of a promising method for calculating hopping integrals in lattice models.

Fractional Spin Excitations in the Infinite-Layer Cuprate CaCuO2

We use resonant inelastic x-ray scattering (RIXS) to investigate the magnetic dynamics of the infinite-layer cuprate CaCuO2. We find that close to the (1/2,0) point, the single magnon decays into a broad continuum of excitations accounting for about 80% of the total magnetic spectral weight. Polarization-resolved RIXS spectra reveal the overwhelming dominance of the spin-flip (ΔS=1) character of this continuum with respect to the ΔS=0 multimagnon contributions. Moreover, its incident-energy dependence is identical to that of the magnon, supporting a common physical origin. We propose that the continuum originates from the decay of the magnon into spinon pairs, and we relate it to the exceptionally high ring exchange Jc∼J1 of CaCuO2. In the infinite-layer cuprates, long-range and multisite hopping integrals are very important, and they amplify the 2D quantum magnetism effects in spite of the 3D antiferromagnetic Néel order.Received 12 October 2021Accepted 30 March 2022DOI:https://doi.org/10.1103/PhysRevX.12.021041Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAntiferromagnetismExchange interactionMagnonsSpinonPhysical SystemsAntiferromagnetsCharge-transfer insulatorsHigh-temperature superconductorsTechniquesResonant inelastic x-ray scatteringCondensed Matter, Materials & Applied Physics

Enhancement of pairing correlations due to nearly flat bands in the plaquette-Lieb Hubbard model

Motivated by recent research works on the flat-band correlated electron systems, we construct a plaquette-Lieb lattice, which exhibits nearly flat bands close to the Fermi level around half-filling, when the inter-plaquette hopping integral is much smaller than the intra-plaquette one. A detailed comparison study with the well-known checkerboard lattice indicates that there exist significant differences for the pairing property between the two lattices, and the nearly flat bands on the plaquette-Lieb lattice strongly enhance the [Formula: see text]-wave pairing correlation for repulsive on-site Hubbard interaction and [Formula: see text]-wave pairing correlation for attractive on-site Hubbard interaction. Our study not only provides a new lattice with nearly flat bands, but also deepens the understanding of electronic structure on superconductivity.

SU(4) Valley+Spin Fluctuation Interference Mechanism for Nematic Order in Magic-Angle Twisted Bilayer Graphene: The Impact of Vertex Corrections.

In the magic-angle twisted bilayer graphene (MATBG), one of the most remarkable observations is the C_{3}-symmetry-breaking nematic state. We identify that the nematicity in MATBG is the E-symmetry ferro bond order, which is the modulation of correlated hopping integrals owing to the E-symmetry particle-hole pairing condensation. The nematicity in MATBG originates from prominent quantum interference among SU(4) valley+spin composite fluctuations. This novel "valley+spin fluctuation interference mechanism" is revealed by the density wave equation analysis for the realistic multiorbital Hubbard model for MATBG. We find that the nematic state is robust once three van Hove singularity points exist in each valley. This interference mechanism also causes novel time-reversal-symmetry-broken valley polarization accompanied by a charge loop current. We discuss interesting similarities and differences between MATBG and Fe-based superconductors.

Competing multipolar orders in a face-centered cubic lattice: Application to the osmium double perovskites

In 5$d^2$ Mott insulators with strong spin-orbit coupling, the lowest pseudospin states form a non-Kramers doublet, which carries quadrupolar and octupolar moments. A family of double perovskites where magnetic ions form a face-centered cubic (fcc) lattice was suggested to unveil an octupolar order offering a rare example in $d$-orbital systems. The proposed order requires a ferromagnetic (FM) octupolar interaction, since the antiferromagnetic (AFM) Ising model is highly frustrated on the fcc lattice. A microscopic model was recently derived for various lattices: for an edge-sharing octahedra geometry, AFM Ising octupolar and bond-dependent quadrupolar interactions were found when only dominant inter- and intraorbital hopping integrals were taken into account. Here we investigate all possible intra- and interorbital exchange processes and report that interference of two intraorbital exchanges generates a FM octupolar interaction. Applying the strong-coupling expansion results together with tight-binding parameters obtained by density functional theory, we estimate the exchange interactions for the osmium double perovskites, Ba$_2$BOsO$_6$ (B=Mg,Cd, and Ca). Using classical Monte Carlo simulations, we find that these systems are close to the phase boundary between AFM type-I quadrupole and FM octupole orders. We also find that exchange processes beyond second-order perturbation theory including virtual processes via pseudospin-triplet states may stabilize an octupolar order.

Polarization-dependent magnetic properties of periodically driven α−RuCl3

We study magnetic properties of a periodically driven Mott insulator with strong spin-orbit coupling and show some properties characteristic of linearly polarized light. We consider a $t_{2g}$-orbital Hubbard model driven by circularly or linearly polarized light with strong spin-orbit coupling and derive its effective Hamiltonian in the strong-interaction limit for a high-frequency case. We show that linearly polarized light can change not only the magnitudes and signs of the exchange interactions, but also their bond anisotropy even without the bond-anisotropic hopping integrals. Because of this property, the honeycomb-network spin system could be transformed into weakly coupled zigzag or step spin chains for the light field polarized along the $b$- or $a$-axis, respectively. Then, analyzing how the light fields affect several magnetic states in a mean-field approximation, we show that linearly polarized light can change the relative stability of the competing magnetic states, whereas such a change is absent for circularly polarized light. We also analyze the effects of both the bond anisotropy of nearest-neighbor hopping integrals and a third-neighbor hopping integral on the magnetic states and show that the results obtained in a simple model, in which the bond-averaged nearest-neighbor hopping integrals are considered, remain qualitatively unchanged except for the stability of zigzag states in the non-driven case and the degeneracy lifting of the zigzag or stripy states.

Bond versus charge disproportionation and nature of the holes in s−p ABX3 perovskites

We use density functional theory methods to study the electronic structures of a series of $s\text{\ensuremath{-}}p$ cubic perovskites, $AB{X}_{3}$: the experimentally available $\mathrm{Sr}\mathrm{Bi}{\mathrm{O}}_{3}, \mathrm{Ba}\mathrm{Bi}{\mathrm{O}}_{3}, \mathrm{Ba}\mathrm{Sb}{\mathrm{O}}_{3}, \mathrm{Cs}\mathrm{Tl}{\mathrm{F}}_{3}$, and $\mathrm{Cs}\mathrm{Tl}{\mathrm{Cl}}_{3}$, as well as the hypothetical $\mathrm{Mg}{\mathrm{PO}}_{3}, \mathrm{Ca}\mathrm{As}{\mathrm{O}}_{3}, \mathrm{Sr}\mathrm{Sb}{\mathrm{O}}_{3}$, and $\mathrm{Ra}\mathrm{Mc}{\mathrm{O}}_{3}$. We use tight-binding modeling to calculate the interatomic hopping integrals ${t}_{sp\ensuremath{\sigma}}$ between the $B\phantom{\rule{4pt}{0ex}}s$ and $X\phantom{\rule{4pt}{0ex}}p$ atomic orbitals and charge-transfer energies $\mathrm{\ensuremath{\Delta}}$, which are the two most important parameters that determine the low-energy electron and hole states of these systems. Our calculations elucidate several trends in ${t}_{sp\ensuremath{\sigma}}$ and $\mathrm{\ensuremath{\Delta}}$ as one moves across the periodic table, such as the relativistic energy lowering of the $B\phantom{\rule{4pt}{0ex}}s$ orbital in heavy $B$ cations, leading to strongly negative $\mathrm{\ensuremath{\Delta}}$ values. Our results are discussed in connection with the general phase diagram for $s\text{\ensuremath{-}}p$ cubic perovskites proposed by Khazraie et al. [Phys. Rev. B 98, 205104 (2018)], who find the parent superconductors $\mathrm{Sr}\mathrm{Bi}{\mathrm{O}}_{3}$ and $\mathrm{Ba}\mathrm{Bi}{\mathrm{O}}_{3}$ to be in the regime of negative $\mathrm{\ensuremath{\Delta}}$ and large ${t}_{sp\ensuremath{\sigma}}$. Here, we explore this further and search for different materials with similar parameters, which could lead to the discovery of new superconductors. Also, some considerations are offered regarding a possible relation between the physical properties of a given $s\text{\ensuremath{-}}p$ compound (such as its tendency to bond disproportionate and the maximal achievable superconducting transition temperature) and its electronic structure.

New route to enhanced figure of merit at nano scale: effect of Aubry–Andre–Harper modulation

We report, for the first time, the phenomenon of thermoelectricity at quantum level, considering a correlated disordered tight-binding one-dimensional lattice where site energies and/or nearest-neighbor hopping integrals are modulated in the cosine form following the well known Aubry–Andre–Harper (AAH) model. The atypical gapped and fragmented energy spectrum yields a transmission function whose steepness is not symmetrical around the Fermi energy, and because of this fact, we obtain a reasonably large figure of merit, a quantity that measures the thermoelectric energy conversion efficiency. The efficiency can be further monitored by means of AAH phase(s) which undoubtedly gives a possible route of designing controlled thermoelectric devices. Evaluating transmission probabilities using the Green’s function formalism, we compute all the thermoelectric quantities based on the Landauer integrals. The diagonal, off-diagonal and generalized versions of the AAH model are taken into account, and in all the cases we find favorable thermoelectric response. At the end of our analysis, we discuss briefly the specific role of phonon thermal conductance on thermoelectric efficiency to make the present investigation a self-contained one. Our theoretical study may shed some light in analyzing thermoelectric phenomena in similar kind of quasicrystals and other related systems.

Generation of circular spin current in an AB magnetic ring with vanishing net magnetization: a new prescription

In this work we report for the first time the appearance of non-decaying circular spin current in a magnetic ring with vanishing net magnetization, even in absence of any spin chirality. Breaking the symmetry in hopping integrals we can misalign up and down spin electronic energy levels which yields a net spin current in the magnetic quantum ring, threaded by an Aharonov–Bohm flux. Along with spin current, a net charge current also appears, and we compute both these currents using the second quantized approach. A tight-binding framework is employed to describe the magnetic ring where each site of the ring contains a finite magnetic moment. Itinerant electrons get scattered from the localized magnetic moments at different lattice sites, and the moments are arranged in such a way that the net magnetization vanishes. The interplay between magnetic moments and asymmetric hopping integrals leads to several atypical features in energy spectra, especially the existence of vanishing current carrying energy eigenstates together with the current carrying ones. The formation of such states those do not contribute any current is the artifact of different kinds of on-site energies and/or hopping integrals in different segments of the magnetic ring. The atypical signatures of energy levels are directly reflected into the charge and spin currents, and here we critically investigate the behaviors of circular currents as functions of electron filling, hopping integrals, strength of spin-moment interaction and ring size. Finally, we discuss briefly the possible experimental realization to implement our proposed magnetic system. The present analysis may provide a new route of generating persistent spin current in magnetic quantum rings with vanishing net magnetization, circumventing the use of spin–orbit coupled systems.

Synthetic gravitational horizons in low-dimensional quantum matter

We propose a class of lattice models realizable in a wide range of setups whose low-energy dynamics exactly reduces to Dirac fields subjected to (1+1)-dimensional gravitational backgrounds, including (anti-)de Sitter spacetime. Wave-packets propagating on the lattice exhibit an eternal slowdown for power-law position-dependent hopping integrals $t(x)\propto x^\gamma$ when $\gamma\geq 1$, signalling the formation of black hole event horizons. For $\gamma< 1$ instead the wave-packets behave radically different and bounce off the horizon. We show that the eternal slowdown relates to a zero-energy spectral singularity of the lattice model and that the semiclassical wave packets trajectories coincide with the geodesics on (1+1)D dilaton gravity, paving the way for new and experimentally feasible routes to mimic black hole horizons and realize (1+1)D spacetimes as they appear in certain gravity theories.

Atomistic Band-Structure Computation for Investigating Coulomb Dephasing and Impurity Scattering Rates of Electrons in Graphene.

In this paper, by introducing a generalized quantum-kinetic model which is coupled self-consistently with Maxwell and Boltzmann transport equations, we elucidate the significance of using input from first-principles band-structure computations for an accurate description of ultra-fast dephasing and scattering dynamics of electrons in graphene. In particular, we start with the tight-binding model (TBM) for calculating band structures of solid covalent crystals based on localized Wannier orbital functions, where the employed hopping integrals in TBM have been parameterized for various covalent bonds. After that, the general TBM formalism has been applied to graphene to obtain both band structures and wave functions of electrons beyond the regime of effective low-energy theory. As a specific example, these calculated eigenvalues and eigen vectors have been further utilized to compute the Bloch-function form factors and intrinsic Coulomb diagonal-dephasing rates for induced optical coherence of electron-hole pairs in spectral and polarization functions, as well as the energy-relaxation time from extrinsic impurity scattering of electrons for non-equilibrium occupation in band transport.

Influence of electric and magnetic fields andσ-edge bands on the electronic and optical spectra of graphene nanoribbons

The unusual electronic and optical properties of armchair and zigzag graphene nanoribbons (GNRs) subject to in-plane transverse electric and perpendicular magnetic fields have been systematically investigated. Our calculations were carried out within the generalized multi-orbital tight-binding model based on a Hamiltonian which takes into account hopping integrals among the (s, $p_x$, $p_y$, $p_z$) atomic orbitals as well as the external electric and magnetic fields. The electronic structure consists of $\pi$ bands arising from the $p_z$ orbital and $\sigma$ bands originating from the (s, $p_x$, $p_y$) orbitals. The energy bands and optical spectra are diversified by both the nature of the edge of the nanoribbon and strength of the external fields. Armchair GNRs display a width-dependent energy gap in addition to low-energy $\sigma$ bands while the zigzag system has the unfilled flat band with $\pi$ edge states at zero energy and partially filled wide-range $\sigma$ bands. An applied in-plane electric field leads to the splitting of energy bands and shifted Fermi level, thereby enriching the inter-band and intra-band optical conductivities. The interplay between an external magnetic field and the edge geometry gives rise to extraordinary quantized Landau levels and special optical spectra.