Hamiltonian Matrix Research Articles

Modeling and simulation of optical gain of GaP0.3Sb0.7/InP0.7Sb0.3 type-II heterostructure for IR optoelectronics under variable well width, temperature and external electric field

Abstract The type-II GaP0.3Sb0.7/InP0.7Sb0.3 nanoscale heterostructure is modelled and simulated for its optical properties in near-infrared lasing applications. The optical gain of GaP0.3Sb0.7/InP0.7Sb0.3 type-II heterostructure is analyzed under different external values of electric fields, temperatures and well widths at room temperature 300 K. The complete structure is grown on InP substrate. The effects of a varied temperature (290 K–320 K), quantum well width (2 nm, 3 nm, and 4 nm) and applied electric field (20 kV cm−1–8 0 kV cm−1) are explored regarding the band alignment, wavefunction, band dispersion, matrix elements, gain and wavelength. The Luttinger-Kohn model is utilized to compute the band structure. The gain computation involves the evaluation of the 6 × 6 k·p Hamiltonian matrix. The proposed heterostructure at 2 nm quantum well width exhibits a high optical gain of 14998 cm−1 in x-polarization and 16572 cm−1 in y-polarization for injected carrier concentration of 4 × 1012 cm2. Under variable temperature and electric field, a significant optical gain is achieved in x, y and z input polarizations. This heterostructure is regarded as new because of its very high optical gain in NIR regime, that makes it beneficial for optoelectronics.

Unraveling the Mechanisms of the Formations and Transformations of Metal-Ligand Charge Transfer States in [Ru(tpy)2]2+*: Consequences of Jahn-Teller Conical Intersections and the Pseudo-Jahn-Teller Effect.

This work investigates Jahn-Teller conical intersections (CoIns) and the pseudo-Jahn-Teller effect on the formations and transformations of the low-lying singlet metal-ligand charge transfer (1MLCT) excited states during the ultrafast evolution process of photoexcited [Ru(tpy)2]2+* (tpy = 2,2':6',2″-terpyridine). Longuet-Higgins' geometric phase analyses indicate that the potential energy surface (PES) crossing between charge transfer states 1MLCT1 and 1MLCT2 is a CoIn, originating from the change in diabatic Hamiltonian matrix elements around the CoIn. Moreover, an E⊗(b1 + b2) Jahn-Teller distortion can occur around the Franck-Condon and minimal energy CoIn (MECI) configurations, causing the molecule to distort spontaneously from the high-symmetry D2d configuration to C2v symmetry configurations that are close to it. Furthermore, the pseudo-Jahn-Teller effect can cause the molecule to distort further from C2v to C1 geometries since the former is a second-order saddle point on the whole dimensional PES but the latter is a true minimum. Eight minima in total are symmetrically distributed around the MECI. These minima are connected by the interligand electron transfer, the charge transfer, and the butterfly-like conformational inversion reactions, all of which have extremely small energy barriers.

Gate voltage dependence on the density of state of 30° twisted bilayer graphene using Trotter–Suzuki tight-binding time propagation method

Abstract Twisted multilayer structures are considered a helpful framework for exploring strongly correlated many-particle systems, where phenomena of physics correlation emerge. Here, we present the Trotter–Suzuki tight-binding time propagation method for computing the density of states (DOS) in a 30° twisted bilayer graphene (TBG). This method solves the time-dependent Schrödinger equation by decomposing Hamiltonian matrices to derive the correlation function. The Fourier transform of this correlation function yields the DOS of the system up to ≈ 1000 000 atoms. Our calculation proves that geometry makes an outstanding contribution to our final results. Additionally, applying additional gate voltage induces shifts in Van Hove singularities, potentially leading to the emergence of new states at the Fermi energy level. The results demonstrate that TBG systems can be easily adjusted and modified for further investigation of optoelectronic features.

Charge transport in two-dimensional system with massless Mexican-hat-like bands

We study the single-particle, DC and optical properties of a two-dimensional (2D) system with massless Mexican-hat-like (W-shaped) valence bands. A proposed 2 × 2 Hamiltonian matrix gives the W-bands and two ground state phases: a gapped phase and a nodal-loop phase. The intraband properties include the single particle density of states, the effective concentration of charge carriers (the Drude weight), the Hall coefficient and electron mobility, electronic heat capacity and thermopower. The real part of the interband conductivity is calculated for the gapped phase as it depends on doping and temperature. As for the undoped nodal-loop phase only the zero-frequency interband conductivity is finite. Among several results two most decisively stand out: By measuring the Hall coefficient as a function of doping at zero-temperature we can answer whether the bands are W-shaped. By measuring the square-root singularity in the finite-temperature optical conductivity, we identify the gapped phase.

Generalizing deep learning electronic structure calculation to the plane-wave basis.

Deep neural networks capable of representing the density functional theory (DFT) Hamiltonian as a function of material structure hold great promise for revolutionizing future electronic structure calculations. However, a notable limitation of previous neural networks is their compatibility solely with the atomic-orbital (AO) basis, excluding the widely used plane-wave (PW) basis. Here we overcome this critical limitation by proposing an accurate and efficient real-space reconstruction method for directly computing AO Hamiltonian matrices from PW DFT results. The reconstruction method is orders of magnitude faster than traditional projection-based methods to convert PW results to the AO basis, and the reconstructed Hamiltonian matrices can faithfully reproduce the PW electronic structure, thus bridging the longstanding gap between the AO basis deep learning electronic structure approach and PW DFT. Advantages of the PW methods, such as high accuracy, high flexibility and wide applicability, thus can be all integrated into deep learning electronic structure methods without sacrificing these methods' inherent benefits. This allows for the construction of large-scale and high-fidelity training datasets with the help of PW DFT results towards the development of precise and broadly applicable deep learning electronic structure models.

Unified Implementation of Relativistic Wave Function Methods: 4C-iCIPT2 as a Showcase.

In parallel to the unified construction of relativistic Hamiltonians based solely on physical arguments (J. Chem. Phys. 2024, 160, 084111), a unified implementation of relativistic wave function methods is achieved here via programming techniques (e.g., template metaprogramming and polymorphism in C++). That is, once the code for constructing the Hamiltonian matrix is made ready, all the rest can be generated automatically from existing templates used for the nonrelativistic counterparts. This is facilitated by decomposing a second-quantized relativistic Hamiltonian into diagrams that are topologically the same as those required for computing the basic coupling coefficients between spin-free configuration state functions (CSF). Moreover, both time reversal and binary double point group symmetries can readily be incorporated into molecular integrals and Hamiltonian matrix elements. The latter can first be evaluated in the space of (randomly selected) spin-dependent determinants and then transformed to that of spin-dependent CSFs, thanks to simple relations in between. As a showcase, we consider here the no-pair four-component relativistic iterative configuration interaction with selection and perturbation correction (4C-iCIPT2), which is a natural extension of the spin-free iCIPT2 (J. Chem. Theory Comput. 2021, 17, 949), and can provide near-exact numerical results within the manifold of positive energy states (PES), as demonstrated by numerical examples.

How symmetry helps to improve the estimation of the hyperfine splitting of torsional levels due to tunneling. The case of the HSSSH molecule

In this study, we analyze a series of molecules belonging to the C2V(M) molecular symmetry group which are characterized by several conformers. The use of molecular symmetry at each stage of calculating the energy of stationary torsional states is demonstrated. In particular, the importance is shown of preliminary symmetrization of physical characteristics of the molecules obtained by quantum chemical calculations. For the first time, symmetry-adapted basis functions for the diagonal kinetic coefficients are presented, which for the analyzed molecules do not satisfy all symmetry operations of the C2V(M) group. Using the HSSSH molecule as an example, it is shown how the full or partial accounting for molecular symmetry influences the calculated values of ultra-small tunneling splittings of the ground torsional states of the trans- and cis-conformers. It has also been established that the Hamiltonian matrix is characterized by symmetry which, when taken into account, makes it possible to halve the time of calculation of its elements.

Dimers for type D relativistic Toda model

We construct dimer graphs for type D relativistic Toda models by introducing impurities into the Y2N,0 square dimer graphs. By properly placing the impurities and changing the canonical variables assigned to the 1-loops on the dimer graph, we perform a “folding” of the graphs, which yields the type D relativistic Toda lattice Hamiltonian and monodromy matrix.

Structure of Multi-State Correlation in Electronic Systems.

Beyond the Hohenberg-Kohn density functional theory for the ground state, it has been established that the Hamiltonian matrix for a finite number (N) of lowest eigenstates is a matrix density functional. Its fundamental variable─the matrix density D(r)─can be represented by, or mapped to, a set of auxiliary, multiconfigurational wave functions expressed as a linear combination of no more than N2 determinant configurations. The latter defines a minimal active space (MAS), which naturally leads to the introduction of the correlation matrix functional, responsible for the electronic correlation effects outside the MAS. In this study, we report a set of rigorous conditions in the Hamiltonian matrix functional, derived by enforcing the symmetry of a Hilbert subspace, namely the subspace invariance property. We further establish a fundamental theorem on the correlation matrix functional. That is, given the correlation functional for a single state in the N-dimensional subspace, all elements of the correlation matrix functional for the entire subspace are uniquely determined. These findings reveal the intricate structure of electronic correlation within the Hilbert subspace of lowest eigenstates and suggest a promising direction for efficient simulation of excited states.

Random matrix theory approach to quantum Fisher information in quantum ergodic systems.

We theoretically investigate quantum parameter estimation in quantum chaotic systems. Our analysis is based on an effective description of quantum ergodic systems in terms of a random matrix Hamiltonian. Based on this approach, we derive an analytical expression for the time evolution of the quantum Fisher information (QFI), which we find to have three distinct timescales. Initially, the QFI increase is quadratic in time, characterizing the timescale over which initial information is extractable from local measurements only. This quickly passes into linear increase with slope determined by the decay rate of the measured spin observable. When the information is fully spread among all degrees of freedom, a second quadratic timescale determines the long-time behavior of the QFI. We test our random matrix theory prediction with the exact diagonalization of a nonintegrable spin system, focusing on the estimation of a local magnetic field by measurements of the many-body state. Our numerical calculations agree with the effective random matrix theory approach and show that the information on the local Hamiltonian parameter is distributed throughout the quantum system during the quantum thermalization process.

Accelerating the calculation of electron-phonon coupling strength with machine learning.

The calculation of electron-phonon couplings (EPCs) is essential for understanding various fundamental physical properties, including electrical transport, optical and superconducting behaviors in materials. However, obtaining EPCs through fully first-principles methods is notably challenging, particularly for large systems or when employing advanced functionals. Here we introduce a machine learning framework to accelerate EPC calculations by utilizing atomic orbital-based Hamiltonian matrices and gradients predicted by an equivariant graph neural network. We demonstrate that our method not only yields EPC values in close agreement with first-principles results but also enhances calculation efficiency by several orders of magnitude. Application to GaAs using the Heyd-Scuseria-Ernzerhof functional reveals the necessity of advanced functionals for accurate carrier mobility predictions, while for the large Kagome crystal CsV3Sb5, our framework reproduces the experimentally observed double domes in pressure-induced superconducting phase diagrams. This machine learning framework offers a powerful and efficient tool for the investigation of diverse EPC-related phenomena in complex materials.

Using nested tensor train contracted basis functions with group theoretical techniques to compute (ro)-vibrational spectra of molecules with non-Abelian groups.

In this paper, we use nested tensor-train contractions to compute vibrational and ro-vibrational energy levels of molecules with five and six atoms. At each step, we fully exploit symmetry by using symmetry adapted basis functions obtained from an irreducible tensor method. Contracted basis functions are determined by diagonalizing reduced dimensional Hamiltonian matrices. The size of matrices of eigenvectors, used to account for coupling between groups of coordinates, is reduced by discarding rows and columns. The size of the matrices that must be diagonalized is thus substantially reduced, making it possible to use direct eigensolvers, even for molecules with five and six atoms. The symmetry-adapted contracted vibrational basis functions have been used to compute J = 0 energy levels of the CH3CN (C3v) and J > 0 levels of CH4.

Eigenstructure Perturbations for a Class of Hamiltonian Matrices and Solutions of Related Riccati Inequalities

Eigenstructure Perturbations for a Class of Hamiltonian Matrices and Solutions of Related Riccati Inequalities

Analytical Solutions of Symmetric Isotropic Spin Clusters Using Spin and Point Group Projectors

Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually required to find exact or approximate eigenstates, but for small clusters with spatial symmetry, analytical solutions exist, and a few Heisenberg systems have been solved in closed form. This paper presents a simple, generally applicable approach to analytically solve isotropic spin clusters, based on adapting the basis to both total spin and point group symmetry to factor the Hamiltonian matrix into sufficiently small blocks. We demonstrate applications to small rings and polyhedra, some of which are straightforward to solve by successive spin-coupling for Heisenberg terms only; additional interactions, such as biquadratic exchange or multi-center terms necessitate symmetry adaptation.

Classifying topology in photonic crystal slabs with radiative environments

In the recent years, photonic Chern materials have attracted substantial interest as they feature topological edge states that are robust against disorder, promising to realize defect-agnostic integrated photonic crystal slab devices. However, the out-of-plane radiative losses in those photonic Chern slabs has been previously neglected, yielding limited accuracy for predictions of these systems’ topological protection. Here, we develop a general framework for measuring the topological protection in photonic systems, such as in photonic crystal slabs, while accounting for in-plane and out-of-plane radiative losses. Our approach relies on the spectral localizer that combines the position and Hamiltonian matrices of the system to draw a real-picture of the system’s topology. This operator-based approach to topology allows us to use an effective Hamiltonian directly derived from the full-wave Maxwell equations after discretization via finite-elements method (FEM), resulting in the full account of all the system’s physical processes. As the spectral FEM-localizer is constructed solely from FEM discretization of the system’s master equation, the proposed framework is applicable to any physical system and is compatible with commonly used FEM software. Moving forward, we anticipate the generality of the method to aid in the topological classification of a broad range of complex physical systems.

On the symplectic self-adjointness and residual spectral emptiness of upper triangular Hamiltonian operator matrices

This paper deals with the symplectic self-adjointness and residual spectral emptiness of upper triangular Hamiltonian operator matrices H=AB0-A∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H=\\left( {\\begin{matrix}A&{}B\\\\ 0&{}-A^*\\end{matrix}}\\right) $$\\end{document}. First, for symplectic self-adjoint Hamiltonian operator H, based on detailed classification of point spectrum σp(H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _p(H)$$\\end{document} and residual spectrum σr(H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _r(H)$$\\end{document}, the symmetry about imaginary axis is given between σp(H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _p(H)$$\\end{document}, σr(H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _r(H)$$\\end{document}, deficiency spectrum σδ(H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _{\\delta }(H)$$\\end{document}, compression spectrum σcom(H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _\\mathrm{{com}}(H)$$\\end{document} and approximate point spectrum σapp(H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _\\mathrm{{app}}(H)$$\\end{document}. Second, by means of the spectral symmetry, the sufficient and necessary conditions are given for σr(H)=∅\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _r(H)=\\varnothing $$\\end{document}, σr1(H)=∅\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _{r_1}(H)=\\varnothing $$\\end{document} and σr2(H)=∅\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _{r_2}(H)=\\varnothing $$\\end{document}, respectively. Then, for H=AB0-A∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H=\\left( {\\begin{matrix}A&{}B\\\\ 0&{}-A^*\\end{matrix}}\\right) $$\\end{document}, it is proved that H is symplectic self-adjoint, if H is defined with diagonal domain D(H)=D(A)⊕D(A∗)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {D}}(H)={\\mathcal {D}}(A)\\oplus {\\mathcal {D}}(A^*)$$\\end{document}. Finally, for H=AB0-A∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H=\\left( {\\begin{matrix}A&{}B\\\\ 0&{}-A^*\\end{matrix}}\\right) $$\\end{document} defined with diagonal domain, using the space decomposition, the sufficient and necessary conditions for σr(H)=∅\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _r(H)=\\varnothing $$\\end{document} and σr1(H)=∅\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma _{r_1}(H)=\\varnothing $$\\end{document} are described in detail, respectively, by line operator, null space, and range of inner elements.

Continuous Time Algebraic Riccati Equation Solution for Second Order Systems

Abstract The continuous time algebraic Riccati equation (ARE) is often utilized in control, estimation, and optimization. For a linear system with a second order structure, the ARE required to be solved to get the control values in standard control problems results in complex sub-equations in terms of the second order system matrices. The computational costs of solving the algebraic Riccati equation through standard methods such as the Hamiltonian matrix pencil approach increase substantially as matrix sizes increase for a second order system, due to the eigendecomposition of the 2n x 2n system matrices involved. This work introduces a new solution that does not require the eigendecomposition of the 2n x 2n system matrices, while satisfying all of the requirements of the solution to the Riccati equation (e.g., detectability, stabilizability, positive semi-definite solution matrix).

Universal Machine Learning Kohn–Sham Hamiltonian for Materials

Abstract While density functional theory (DFT) serves as a prevalent computational approach in electronic structure calculations, its computational demands and scalability limitations persist. Recently, leveraging neural networks to parameterize the Kohn–Sham DFT Hamiltonian has emerged as a promising avenue for accelerating electronic structure computations. Despite advancements, challenges such as the necessity for computing extensive DFT training data to explore each new system and the complexity of establishing accurate machine learning models for multi-elemental materials still exist. Addressing these hurdles, this study introduces a universal electronic Hamiltonian model trained on Hamiltonian matrices obtained from first-principles DFT calculations of nearly all crystal structures on the Materials Project. We demonstrate its generality in predicting electronic structures across the whole periodic table, including complex multi-elemental systems, solid-state electrolytes, Moiré twisted bilayer heterostructure, and metal-organic frameworks. Moreover, we utilize the universal model to conduct high-throughput calculations of electronic structures for crystals in GNoME datasets, identifying 3940 crystals with direct band gaps and 5109 crystals with flat bands. By offering a reliable efficient framework for computing electronic properties, this universal Hamiltonian model lays the groundwork for advancements in diverse fields, such as easily providing a huge data set of electronic structures and also making the materials design across the whole periodic table possible.

Approximate Analytical Solution of the Ground State Problem of He and He-like Ions using Symmetrized-Hydrogenic States

The matrix method using three symmetrized-hydrogenic basis states has been applied to analytically obtain an approximate solution to the Schrödinger equation of the Helium atom and some He-like ions (2<Z<10). This study aims at obtaining more accurate ground state energies of the systems compared to our previous calculation using un-symmetrized basis states and some other simple calculations in the literature. The contribution of the symmetrized basis states on the ground state energies of the systems is also investigated. The time-independent Schrödinger equation involving a 3×3 Hamiltonian matrix, formed by hydrogenic s-states, was analytically solved to obtain three energy eigenvalues of the systems as well as their corresponding eigenvectors. Results showed that the 1s2 energies of the systems were more accurate than our previous unsymmetrized basis calculations, with significant error reduction observed for He and Li+. With the same matrix size, the ground state energies of He and He-like ions obtained from three symmetrized basis states in this study were found to be closer to the exact and experimental energies than those obtained from unsymmetrized basis states. It was also demonstrated that the |100;100> state made the largest contribution to the ground state energies of the systems, i.e. about 90.9% for He and around 99.9% for Ne8+, and consequently the smallest contribution came from the other two symmetrized states (less than 1%). To conclude, the calculated ground state energies were more accurate than some other simple calculations reported in the literature.

Jiezi: An open-source Python software for simulating quantum transport based on non-equilibrium Green's function formalism

We present a Python-based open-source library named Jiezi, which provides the means of simulating the electronic transport properties of nanoscaled devices on the atomistic level. The key feature of Jiezi lies in its core algorithm, i.e., self-consistent orchestration between the non-equilibrium Green's function (NEGF) method and a Poisson's equation solver. Beyond the construction of the tight-binding (TB) Hamiltonian with empirical parameters for conventional materials, the package offers a comprehensive framework for constructing the Wannier-based Hamiltonian matrix, enabling the investigation of novel materials and their heterostructures. To expedite the solution of NEGF systems, a methodology based on renormalization theory is proposed for reducing the dimension of the Hamiltonian matrix. Additionally, we adopt a non-linear Poisson equation solver with no analytical approximation in this software. The software facilitates seamless integration with external tools for geometry and mesh generation and post-processing. In this paper, we present the main capabilities and workflow by demonstrating with a simulation for the carbon nanotube field-effect transistor (CNTFET). Program summaryProgram Title: JieziCPC Library link to program files:https://doi.org/10.17632/nk79kbtww4.1Developer's repository link:https://github.com/Jiezi-negf/JieziLicensing provisions: GPLv3Programming language: PythonNature of problem: Simulates the quantum transport property of nano-scaled transistors based on the predefined device structure and the material composition.Solution method: Solves the coupled Schrödinger equation and Poisson equation by NEGF and finite element method.