Tight-binding Hamiltonian Research Articles

Evolution of discrete symmetries.

Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a symmetry that holds only in a finite domain of space, can be either the result of a self-organization process or a structural ingredient into a synthetically prepared physical system. Applying local symmetry operations to extend a given finite chain we show that the resulting one-dimensional lattice consists of a transient followed by a subsequent periodic behavior. Due to the fact that, by construction, the implanted local symmetries strongly overlap the resulting lattice possesses a dense skeleton of such symmetries. We proof this behavior on the basis of a class of local symmetry operations allowing us to conclude upon the "asymptotic" properties such as the final period, decomposition of the unit cell and the length and appearance of the transient. As an example case, we explore the corresponding tight-binding Hamiltonians. Their energy eigenvalue spectra and eigenstates are analyzed in some detail, showing in particular the strong variability of the localization properties of the eigenstates due to the presence of a plethora of local symmetries.

Rényi negativities in non-equilibrium open free-boson chains

In this paper, we consider the dynamics of Rényi negativities after a quantum quench in the free-boson chain with homogeneous dissipation. Initially we prepare the system in the squeezed thermal state, and then let it evolves under the tight-binding bosonic Hamiltonian with local linear dissipation. We use the Lindblad equation to solve the time evolution of the covariance matrix, from which one can obtain the time dependence of Rényi negativities. We are interested in the weak dissipation hydrodynamic limit where a quasi-particle picture emerges. In this limit, exact results of non-equilibrium dynamics of Rényi negativities can be obtained using the stationary phase method. We consider the Rényi negativities between both adjacent and disjoint regions in a infinite chain. We numerically test our analytical predictions and perfect matches have found.

Realizing tight-binding Hamiltonians using site-controlled coupled cavity arrays

Analog quantum simulators rely on programmable and scalable quantum devices to emulate Hamiltonians describing various physical phenomenon. Photonic coupled cavity arrays are a promising alternative platform for realizing such simulators, due to their potential for scalability, small size, and high-temperature operability. However, programmability and nonlinearity in photonic cavities remain outstanding challenges. Here, using a silicon photonic coupled cavity array made up of 8 high quality factor (Q up to, sim 7.1times {10}^{4}) resonators and equipped with specially designed thermo-optic island heaters for independent control of cavities, we demonstrate a programmable photonic cavity array in the telecom regime, implementing tight-binding Hamiltonians with access to the full eigenenergy spectrum. We report a sim 50% reduction in the thermal crosstalk between neighboring sites of the cavity array compared to traditional heaters, and then present a control scheme to program the cavity array to a given tight-binding Hamiltonian. The ability to independently program high-Q photonic cavities, along with the compatibility of silicon photonics to high volume manufacturing opens new opportunities for scalable quantum simulation using telecom regime infrared photons.

Electric circuit simulation of Floquet topological insulators in Fourier space

We present a method for simulating any non-interacting and time-periodic tight-binding Hamiltonian in Fourier space using electric circuits made of inductors and capacitors. We first map the time-periodic Hamiltonian to a Floquet Hamiltonian, which converts the time dimension into a Floquet dimension. In electric circuits, this Floquet dimension is simulated as an extraspatial dimension without any time dependency in the electrical elements. The number of replicas needed in the Floquet Hamiltonian depends on the frequency and strength of the drive. We also demonstrate that we can detect the topological edge states (including the anomalous edge states in the dynamical gap) in an electric circuit by measuring the two-point impedance between the nodes. Our method paves a simple and promising way to explore and control Floquet topological phases in electric circuits.

Atomistic designing of 2D quantum materials heterostructures CdF/CrI3 for Berry curvature driven tunable intrinsic anomalous Hall state

The coupling between topology and magnetism can explore rich physics with fundamental interest. Passing through the phase of Bismuth-based topological insulators magnetized by the 3d/4f transition metal doping, currently the fabrication of quantum heterostructures by suitable new-generation 2D materials, has emerged as a prospective alternative. Following the current trends, the present investigation deals with the atomistic designing and investigation of the quantum heterostructures of the newly predicted massive Dirac semimetal CdF and well-known layered ferromagnetic insulator CrI3 using the first-principles density functional theory calculations supplemented by the low energy tight-binding model Hamiltonian. The designed strategy ensures the lattice mismatch should be within the permissible range. We have addressed the physical characteristics of heterostructures in terms of the non-trivial topological band inversion between Cd-5s and I-2p orbitals. Proximity effect induces magnetic interactions, breaks the time-reversal symmetry at the interface, and leads to Berry curvature-driven tunable intrinsic anomalous Hall conductance (AHC) at the Fermi energy. Our analysis reveals the electrons with high Fermi velocity (106 m s−1) in the heterostructures and the band topology at the Fermi level can be tuned effectively using very small external gate voltage or homogeneous electric field. Our investigation can open up new avenues for designing new topological phases in the heterostructure community and possible tailoring routes of the intrinsic AHC in moderate temperature.

Exploring valley polarized transport in graphene bilayer flakes

Valleytronics offers new routes to explore possible dual electronic responses related to the valley origin of the carriers. Graphene is known as an optimal material for devices based on valley-filter transport due to the double Dirac cones. Here we focus on understanding the role played by geometrical spatial details in the valley-dependent transport of bilayered graphene flakes, with long length, simulating nanoribbons. Flakes of different widths are considered at the stacking region. We also explore changing the valley transmission when a bias potential is applied. A tight-binding Hamiltonian is used to model the system, and the conductance is obtained by Landauer-Büttiker’s formalism and recursive Green’s function method. Our findings show that considering different bilayered graphene flake widths produces valley-polarized transmissions due to the presence of edge states. Furthermore, the corresponding energy range for which the valley filter occurs depends on the width asymmetries details. The theoretical analysis presented here indicates a potential route for valley-filter transmission scenarios of relatively easy engineering implementation.

PYATB: An efficient Python package for electronic structure calculations using ab initio tight-binding model

We present PYATB, a Python package designed for computing band structures and related properties of materials using the ab initio tight-binding Hamiltonian. The Hamiltonian is directly obtained after conducting self-consistent calculations with first-principles packages using numerical atomic orbital bases, such as ABACUS. The package comprises three modules: Bands, Geometric, and Optical. In the Bands module, one can calculate essential properties of band structures, including the partial density of states, fat bands, Fermi surfaces, and Weyl/Dirac points. The band unfolding method is utilized to obtain the energy band spectra of a supercell by projecting the electronic structure of the supercell onto the Brillouin zone of the primitive cell. With the Geometric module, one can compute the Berry phase and Berry curvature-related quantities, such as electric polarization, Wilson loops, Chern numbers, and anomalous Hall conductivities. The Optical module offers a range of optical property calculations, including optical conductivity and nonlinear optical responses, such as shift current and Berry curvature dipole. Program summaryProgram title: PYATBCPC Library link to program files:https://doi.org/10.17632/fsfpdy9t5r.1Developer's repository link:https://github.com/pyatb/pyatbCode Ocean capsule:https://codeocean.com/capsule/9408682Licensing provisions: GPLv3Programming language: C++, PythonNature of problem: This program is to study the electronic structure, electronic polarization, band topological properties, topological classification, linear and nonlinear optical response of solid crystal systems.Solution method: Based on the tight binding method to solve the band structure, the Wilson loop is used to classify the topological phases, and the optical response is calculated by Berry curvature and Berry connection.

Theoretical Study of Thermoelectric Properties of a Single Molecule of Diphenyl-Ether

Taking into consideration the research that has been conducted on the optical and electrical properties of molecular systems, especially the good thermoelectric energy conversion at a nanometric scale that such systems have presented, here we present a new alternative by using a particular diphenyl-ether molecule as a functional device. Such a molecular system is modeled as a planar segment coupled to two electrodes in the first-neighbor approximation within a tight-binding Hamiltonian. We study the electrical and thermal properties of diphenyl-ether molecules such as the electric current, electrical and thermal conductance, Seebeck coefficient, and figure of merit, in the strong and weak coupling regimes, considering different structural configurations and variations with temperature. Our results could be valuable for laboratory applications and/or verification since we characterize the diphenyl-ether molecule as a semiconductor device for different structural models.

Topological phases in coupled polyyne chains

We study the electronic properties of coupled parallel polyyne chains in a couple of symmetric stacking arrangements, namely the AA stacking and the AB stacking, with the single and triple carbon bonds of one chain aligned (AA) and anti-aligned (AB) with those of the other chain. Both these arrangements described by tight-binding Hamiltonians, whose parameters are calibrated by matching low energy dispersion provided by first principle calculations, fall in the BDI class of topological classification scheme. We calculate the topological invariants for all three topological phases of the system: one for the AA stacking and 2 for the AB one. In AA stacking, both the insulating and the metallic phase belongs to the same topological phase. Whereas, the model exhibits two different values of the topological invariant in the two different insulating phases (structurally differentiated by transverse strain). In this later stacking though the transition between two distinct topological phases with the closure of the gap is practically unachievable due to the requirement of the high transverse strain. We also show the existence of four non-zero energy edge modes in the AA stacking and that of two zero energy edge modes in one of the topological phases for the AB stacking.

DC and RF Performance of an N-channel Monolayer Black Phosphorus Nanoribbon Transistor

Two-dimensional black phosphorus is a relatively new discovery. There are numerous studies on black phosphorus two-dimensional transistors that focus on analog and RF performance. However, the RF performance of black phosphorus nanoribbon transistors is yet to be explored. We use a four-band tight binding Hamiltonian in conjunction with a non-equilibrium Green's function quantum transport simulator to investigate both the DC and RF performance of a monolayer black phosphorus nanoribbon transistor. We found that electron intra-band tunneling is responsible for current flow in the off-state, while in the on-state, the electrons flow over the top of the channel barrier potential. With a VDD of 0.4 volt and a gate length of 5 nm, our black phosphorus nanoribbon transistor has DC performance metrics of 510 µA/µm on-state current, 105 on/off current ratio, and 65 mV/dec inverse subthreshold slope. The device's RF performance characteristics are as follows: cut-off (unity current gain) frequency of 772.84 GHz, maximum oscillation (unity power gain) frequency of 1.15 THz, and open circuit voltage gain of 26.7 dB with transistor operating in the on-state. The RF performance of the device is found to be significantly impacted by the source and drain contact resistances. With source and drain resistances set to zero, the cut-off frequency increases to 995.23 GHz and the unity power gain frequency increases to 4.16 THz. The device shows unconditional stability above 893 GHz and it is conditionally stable below this frequency.

Exotic Electronic Properties of Twisted Bilayer Graphene-Emergence of Twistronics

In Twistronics we study the effect of relative twist between the layers of a material on the electronic properties of that layered materials. There are expected to be hundreds of layered materials which can give rise to thousands or even more layered materials with combination of layers and relative twist between the layers. There is a great possibility to encounter many exotic electronic properties in these rather less explored layered materials with relative twist between the layers. There is a lot to explore and understand, to unlock full potential of twistronics. A lot of theoretical and experimental studies have been done and are being done to explore the electronic properties of twisted bilayer graphene, making it a good material to start with to explore the hidden potential of twistronics. Here we present a simple theoretical model study for commensurate twisted bilayer graphene. Starting from understanding of moire pattern in twisted bilayer graphene our study goes through writing of tight binding Hamiltonian, computational codes to determine various model parameters, solution of Hamiltonian to obtain quasi particle energies and density of states near Fermi energy in twisted bilayer graphene. Our theoretical calculations have produced flat band near Dirac point and Van-Hove singularities near Fermi energy, which agree qualitatively with recent experimental studies.

Optical properties of twisted bilayer graphene with magnetic defects

Even when fabricated under ideal conditions twisted bilayer graphene (TBG) inevitably contains various defects which may significantly affect its physical properties. Here we comprehensively analyze the impact of typical point defects, represented by adsorbed hydrogen atoms, on the electronic and optical properties of TBG. It is shown using self-consistent tight-binding Hamiltonians that such point defects make TBG ferromagnetic, and that its ground state comprises a pair of nearly dispersionless spin-polarized energy bands around the Fermi level. Transitions to and from these bands strongly modify the infrared absorption of TBG and result in a sharp low-energy peak in its spectrum. It is also revealed that the adsorption of hydrogen atoms suppresses the circular dichroism of TBG due to the weakening of the electronic coupling between the graphene layers. Our findings will guide future experimental studies on the optical properties of TBG in realistic, impurity-rich environments.

Treatment of symmetry in the tight-binding method for crystals with several atoms per unit cell

Consistent treatment of symmetry in the tight-binding method, developed by Egorov et al [Phys. Stat. Sol. 26, 391 (1968)] for crystals with two atoms per unit cell, is generalized to crystals with several atoms per unit cell. A method is presented for expressing the matrix components of the tight-binding Hamiltonian in terms of independent parameters using group-theoretical techniques. The method is demonstrated by obtaining an analytical form for the low-dimensional effective Hamiltonian describing the electronic structure of the 2H-TaSe2 conduction band with quasi 2D hexagonal crystal structure.

Low- and high-energy localization landscapes for tight-binding Hamiltonians in two-dimensional lattices

Low- and high-energy localization landscapes for tight-binding Hamiltonians in two-dimensional lattices

Numerical simulation of non-Abelian anyons

Two-dimensional systems such as quantum spin liquids or fractional quantum Hall systems exhibit anyonic excitations that possess more general statistics than bosons or fermions. This exotic statistics makes it challenging to solve even a many-body system of non-interacting anyons. We introduce an algorithm that allows to simulate anyonic tight-binding Hamiltonians on two-dimensional lattices. The algorithm is directly derived from the low energy topological quantum field theory and is suited for general Abelian and non-Abelian anyon models. As concrete examples, we apply the algorithm to study the energy level spacing statistics, which reveals level repulsion for free semions, Fibonacci anyons, and Ising anyons. Additionally, we simulate nonequilibrium quench dynamics, where we observe that the density distribution becomes homogeneous for large times---indicating thermalization.

Quasiclassical theory for antiferromagnetic metals

Unlike ferromagnetism, antiferromagnetism cannot readily be included in the quasiclassical Keldysh theory because of the rapid spatial variation in the directions of the magnetic moments. The quasiclassical framework is useful because it separates the quantum effects occurring at length scales comparable to the Fermi wavelength from other length scales, and has successfully been used to study a wide range of phenomena involving both superconductivity and ferromagnetism. Starting from a tight-binding Hamiltonian, we develop general quasiclassical equations of motion and boundary conditions, which can be used to describe two-sublattice metallic antiferromagnets in the dirty limit. The boundary conditions are applicable also for spin-active boundaries that can be either compensated or uncompensated. Additionally, we show how nonuniform or dynamic magnetic textures influence the equations and we derive a general expression for observables within this framework.

Detecting topological phases in the square–octagon lattice with statistical methods

Electronic systems living on Archimedean lattices such as kagome and square–octagon networks are presently being intensively discussed for the possible realization of topological insulating phases. Coining the most interesting electronic topological states in an unbiased way is however not straightforward due to the large parameter space of possible Hamiltonians. A possible approach to tackle this problem is provided by a recently developed statistical learning method (Mertz and Valentí in Phys Rev Res 3:013132, 2021. https://doi.org/10.1103/PhysRevResearch.3.013132), based on the analysis of a large data sets of randomized tight-binding Hamiltonians labeled with a topological index. In this work, we complement this technique by introducing a feature engineering approach which helps identifying polynomial combinations of Hamiltonian parameters that are associated with non-trivial topological states. As a showcase, we employ this method to investigate the possible topological phases that can manifest on the square–octagon lattice, focusing on the case in which the Fermi level of the system lies at a high-order van Hove singularity, in analogy to recent studies of topological phases on the kagome lattice at the van Hove filling.

Calculation method for the conductance of mesoscopic systems: assembly of Tight Binding Hamiltonians with spin effects—revisited

We discretize the Schrödinger equation in the approximation of the effective mass for the two-dimensional electron gas of GaAs, without magnetic field and on the other hand, with magnetic field. This discretization leads naturally to Tight Binding (TB) Hamiltonians in the approximation of the effective mass. An analysis of this discretization allows us to gain insight into the role of site and hopping energies, which allows us to model the TB Hamiltonian assembly with spin: Zeeman and spin–orbit coupling effects, especially the case Rashba. With this tool we can assemble Hamiltonians of quantum boxes, Aharanov–Bohm interferometers, anti-dots lattices and effects of imperfections, as well as disorder in the system. The extension to mount quantum billiards is natural. We also explain here how to adapt the recursive equations of Green’s functions for the case of spin modes, apart from transverse modes, for the calculation of conductance in these mesoscopic systems. The assembled Hamiltonians allow to identify the matrix elements (depending on the different parameters of the system) associated with splitting or spin flipping, which gives a starting point to model specific systems of interest, manipulating certain parameters. In general, the approach of this work allows us to clearly see the relationship between the wave and matrix description of quantum mechanics. We discuss here also, the extension of the method for 1D and 3D systems, for the extension apart from the first neighbors and for the inclusion of other types of interaction. The way we approach the method, has the objective of showing how specifically the site and hopping energies change in the presence of new interactions. This is very important in the case of spin interactions, because by looking at the matrix elements (site or hopping) we can directly identify the conditions that can lead to splitting, flipping or a mixture of these effects. Which is essential for the design of devices based on spintronics. Finally, we discuss spin-conductance modulation (Rashba spin precession) for the states of an open quantum dot (resonant states). Unlike the case of a quantum wire, the spin-flipping observed in the conductance is not perfectly sinusoidal, there is an envelope that modulates the sinusoidal component, which depends on the discrete-continuous coupling of the resonant states.

Electronic frustration, Berry’s phase interference and slow dynamics in some tight-binding systems coupled to harmonic baths

Conical intersections in two-state systems require a coordinate-dependent coupling. This paper identifies and investigates conical intersections in cyclic tight-binding system-bath Hamiltonians with an odd number of sites and a constant site-to-site coupling. In the absence of bath degrees of freedom, such tight-binding systems with a positive coupling parameter exhibit electronic frustration and a doubly-degenerate ground state. When these systems interact with a harmonic bath, the degeneracy becomes a conical intersection between the adiabatic ground and first excited states. Under weak system-bath coupling, overlapping wavefunctions associated with different sites give rise to distinct pathways with interfering geometric phases, which lead to considerably slower transfer dynamics. The effect is most pronounced in the presence of low-temperature dissipative baths characterized by a continuous spectral density. It is found that the transfer dynamics and equilibration time of a cyclic dissipative three-site system with a positive coupling exceeds that of a similar three-site system with a negative coupling, as well as that of cyclic four-site systems, by an order of magnitude.

Truncated atomic plane wave method for subband structure calculations of moiré systems

We propose a highly efficient and accurate numerical scheme named the truncated atomic plane wave method to determine the subband structure of twisted bilayer graphene (TBG) inspired by the Bistritzer-MacDonald model. Our method utilizes real-space information of carbon atoms in the moir\'e unit cell and projects the full tight-binding Hamiltonian into a much smaller subspace using atomic plane waves. Using our method, we are able to present accurate electronic band structures of TBG in a wide range of twist angles together with the detailed moir\'e potential and screened Coulomb interaction at the first magic angle. Furthermore, we generalize our formalism to solve the problem of low-frequency moir\'e phonons in TBG.