Tight-binding Basis Research Articles

Machine learned environment-dependent corrections for a spds∗ empirical tight-binding basis

Abstract Empirical tight-binding (ETB) methods have become a common choice to simulate electronic and transport properties for systems composed of thousands of atoms. However, their performance is profoundly dependent on the way the empirical parameters were fitted, and the found parametrizations often exhibit poor transferability. In order to mitigate some of the the criticalities of this method, we introduce a novel Δ-learning scheme, called MLΔTB. After being trained on a custom data set composed of ab-initio band structures, the framework is able to correlate the local atomistic environment to a correction on the on-site ETB parameters, for each atom in the system. The converged algorithm is applied to simulate the electronic properties of random GaAsSb alloys, and displays remarkable agreement both with experimental and ab-initio test data. Some noteworthy characteristics of MLΔTB include the ability to be trained on few instances, to be applied on 3D supercells of arbitrary size, to be rotationally invariant, and to predict physical properties that are not exhibited by the training set.

Superexchange coupling of donor qubits in silicon

Atomic engineering in a solid-state material has the potential to functionalize the host with novel phenomena. STM-based lithographic techniques have enabled the placement of individual phosphorus atoms at selective lattice sites of silicon with atomic precision. Here we show that by placing four phosphorus donors spaced 10–15 nm apart from their neighbors in a linear chain, one can realize coherent spin coupling between the end dopants of the chain, analogous to the superexchange interaction in magnetic materials. Since phosphorus atoms are a promising building block of a silicon quantum computer, this enables spin coupling between their bound electrons beyond nearest neighbors, allowing the qubits to be separated by 30–45 nm. The added flexibility in architecture brought about by this long-range coupling not only reduces gate densities but can also reduce correlated noise between qubits from local noise sources that are detrimental to error-correction codes. We base our calculations on a full-configuration-interaction technique in the atomistic tight-binding basis, solving the four-electron problem exactly, over a domain of a million silicon atoms. Our calculations show that superexchange can be tuned electrically through gate voltages where it is less sensitive to charge noise and donor-placement errors. Published by the American Physical Society 2024

Optically active cross-band transition in double-walled carbon nanotube and its impact on Raman resonances

Double-walled carbon nanotubes (DWNTs), often regarded as the simplest one-dimensional (1D) van der Waals moiré superlattices, are the ideal structures to explore the interlayer coupling, including mechanical and electronical coupling, at the nanoscale in 1D systems. By combining spatial modulation spectroscopy (SMS) and resonant Raman scattering (RRS) experiments on well-identified individual free-standing DWNTs with the calculations of their optical absorption by using the recursion method with non-orthogonal tight-binding (NTB) basis functions, we are able to unambiguously assign the nature, namely mirror transition or cross transition, of each optical transitions in DWNTs. Our study identifies and allows to determine the conditions of the mixing of the electronic states leading to the appearance of cross transitions in the optical absorption of DWNTs, beyond of the so-called Koshino's criteria previously derived. On the other hand, the striking behavior of the resonant excitation profile (REP) of the Raman active modes around the cross transition reveals the strong sensitivity of the modes intensity on the electronic interlayer coupling in DWNTs, emphasizing the relevance of Raman spectroscopy for studying the electronic and mechanical coupling at the nanoscale.

Nonlocal sidewall response and deviation from exact quantization of the topological magnetoelectric effect in axion-insulator thin films

Topological insulator (TI) thin films with surface magnetism are expected to exhibit a quantized anomalous Hall effect (QAHE) when the magnetizations on the top and bottom surfaces are parallel, and a quantized topological magnetoelectric (QTME) response when the magnetizations have opposing orientations (axion insulator phase) and the films are sufficiently thick. We present a unified picture of both effects that associates deviations from exact quantization of the QTME caused by finite thickness with non-locality in the side-wall current response function. Using realistic tight-binding model calculations, we show that in $Bi_2Se_3$ TI thin films deviations from quantization in the axion insulator-phase are reduced in size when the exchange coupling of tight-binding model basis states to the local magnetization near the surface is strengthened. Stronger exchange coupling also reduces the effect of potential disorder, which is unimportant for the QAHE but detrimental for the QTME, which requires that the Fermi energy lie inside the gap at all positions.

Hybrid Atomic Orbital Basis from First Principles: Bottom-Up Mapping of Self-Energy Correction to Large Covalent Systems.

Construction of hybrid atomic orbitals is proposed as the approximate common eigenstates of finite first moment matrices. Their hybridization and orientation can be a priori tuned as per their anticipated neighborhood. Their Wannier function counterparts constructed from the Kohn-Sham (KS) single particle states constitute an orthonormal multiorbital tight binding (TB) basis resembling hybrid atomic orbitals locked to their immediate atomic neighborhood, while spanning the subspace of KS states. The proposed basis thus renders predominantly single TB parameters from first principles for each nearest neighbor bond involving no more than two orbitals irrespective of their orientation and also facilitates an easy route for the transfer of such TB parameters across isostructural systems exclusively through mapping of neighborhoods and projection of orbital charge centers. With hybridized 2s, 2p and 3s, 3p valence electrons, the spatial extent of the self-energy correction (SEC) to TB parameters in the proposed basis is found to be localized mostly within the third nearest neighborhood, thus allowing effective transfer of self-energy-corrected TB parameters from smaller reference systems to much larger target systems, with nominal additional computational cost beyond that required for explicit computation of SEC in the reference systems. The proposed approach promises inexpensive estimation of the quasi-particle structures of large covalent systems with workable accuracy.

Transferability of self-energy correction in tight-binding basis constructed from first principles.

We demonstrate in this work the transferability of self-energy (SE) correction (SEC) of Kohn-Sham (KS) single particle states from smaller to larger systems, when mapped through localized orbitals constructed from the KS states. The approach results in a SE corrected TB framework within which the mapping of SEC of TB parameters is found to be transferable from smaller to larger systems of similar morphology, leading to a computationally inexpensive approach for the estimation of SEC in large systems with reasonably high accuracy. The scheme has been demonstrated in insulating, semiconducting, and magnetic nanoribbons of graphene and hexagonal boron nitride, where the SEC tends to strengthen the individual π bonds, leading to transfer of charges from the edge to bulk. Additionally, in magnetic bipartite systems, the SEC tends to enhance inter-sublattice spin separation. The proposed scheme thus promises to enable the estimation of SEC of bandgaps of large systems without the need to explicitly calculate the SEC of KS single particle levels, which can be computationally prohibitively expensive.

Theoretical evidence of a significant modification of the electronic structure of double-walled carbon nanotubes due to the interlayer interaction

The recently reported experimental optical spectra of double-walled carbon nanotubes exhibit more peaks than it could be expected based on the layers alone. The appearance of excess peaks has been attributed to the interlayer interaction. In order to elucidate the origin of the excess peaks, we perform calculations of the optical absorption of a particular nanotube using the recursion method with non-orthogonal tight-binding basis functions. Our study shows that the interlayer interaction can give rise to major changes in the electronic structure of this nanotube, manifesting themselves with shifts of the optical transitions and appearance of new optical transitions. The derived absorption spectrum is found to be in excellent agreement with the available experimental data, which justifies the use of the proposed approach for double-walled carbon nanotubes.

Topological classification of molecules and chemical reactions with a perplectic structure

In this paper, a topological classification of molecules and their chemical reactions is proposed on a single particle level . We consider zero-dimensional electronic Hamiltonians in a real-space tight-binding basis with spinless time-reversal symmetry and an additional spatial reflection symmetry. The symmetry gives rise to a perplectic structure and suggests a $\mathbb{Z}_2$ invariant in form of a pfaffian, which can be captured by an entanglement cut. We apply our findings to a class of chemical reactions studied by Woodward and Hoffmann, where a reflection symmetry is preserved along a one-dimensional reaction path and argue that the topological classification should contribute to the rate constants of these reactions. More concretely, we find that a reaction takes place experimentally whenever the reactants and products can be adiabatically deformed into each other, while reactions that require a change of topological invariants have not been observed experimentally.

Questaal: A package of electronic structure methods based on the linear muffin-tin orbital technique

This paper summarises the theory and functionality behind Questaal, an open-source suite of codes for calculating the electronic structure and related properties of materials from first principles. The formalism of the linearised muffin-tin orbital (LMTO) method is revisited in detail and developed further by the introduction of short-ranged tight-binding basis functions for full-potential calculations. The LMTO method is presented in both Green’s function and wave function formulations for bulk and layered systems. The suite’s full-potential LMTO code uses a sophisticated basis and augmentation method that allows an efficient and precise solution to the band problem at different levels of theory, most importantly density functional theory, LDA+U, quasi-particle self-consistent GW and combinations of these with dynamical mean field theory. This paper details the technical and theoretical bases of these methods, their implementation in Questaal, and provides an overview of the code’s design and capabilities. Program summaryProgram Title: QuestaalProgram Files doi:http://dx.doi.org/10.17632/35jxxtzpdn.1Code Ocean Capsule:https://doi.org/10.24433/CO.3778701.v1Licensing provisions: GNU General Public License, version 3Programming language: Fortran, C, Python, ShellNature of problem: Highly accurate ab initio calculation of the electronic structure of periodic solids and of the resulting physical, spectroscopic and magnetic properties for diverse material classes with different strengths and kinds of electronic correlation.Solution method: The many electron problem is considered at different levels of theory: density functional theory, many body perturbation theory in the GW approximation with different degrees of self consistency (notably quasiparticle self-consistent GW) and dynamical mean field theory. The solution to the single-particle band problem is achieved in the framework of an extension to the linear muffin-tin orbital (LMTO) technique including a highly precise and efficient full-potential implementation. An advanced fully-relativistic, non-collinear implementation based on the atomic sphere approximation is used for calculating transport and magnetic properties.

Locally self-consistent embedding approach for disordered electronic systems

We present a new embedding scheme for the locally self-consistent method to study disordered electron systems. We test this method in a tight-binding basis and apply it to the single band Anderson model. The local interaction zone is used to efficiently compute the local Green's function of a supercell embeded into a local typical medium. We find a quick convergence as the size of the local interaction zone which reduces the computational costs as expected. This method captures the Anderson localization transition and accurately predicts the critical disorder strength. The present work opens the path towards the development of a typical medium embedding scheme for the $O(N)$ multiple scattering methods.

Lazy electrons in graphene

Within a tight-binding approximation, we numerically determine the time evolution of graphene electronic states in the presence of classically vibrating nuclei. There is no reliance on the Born-Oppenheimer approximation within the p-orbital tight-binding basis, although our approximation is "atomically adiabatic": the basis p-orbitals are taken to follow nuclear positions. Our calculations show that the strict adiabatic Born-Oppenheimer approximation fails badly. We find that a diabatic (lazy electrons responding weakly to nuclear distortions) Born-Oppenheimer model provides a much more accurate picture and suggests a generalized many-body Bloch orbital-nuclear basis set for describing electron-phonon interactions in graphene.

Unusual bandgap bowing in highly mismatched ZnOS alloys: Atomistic tight-binding band anti-crossing model

An atomistic band anticrossing (BAC) model is developed and used to study “unusual bowing” in energy bandgap and its dependence on the material composition in minority O anion-alloyed ZnS (ZnS1−xOx) and minority S anion-alloyed ZnO (ZnO1−xSx) highly mismatched alloys. For dilute O in ZnS1−xOx, it is found that the bandgap decreases as the O composition is increased. A “down-shift” in the conduction band edge (CBE) of host ZnS, which arises from an interaction between the CBE and the localized O defect state, is identified as the root cause. However, the reduction in bandgap as a function of dilute S composition in the ZnO1−xSx alloy follows an “up-shift” in the valence band edge (VBE) of host ZnO, which arises from an interaction between the VBE and the localized S defect state. The BAC model captures the E+ and E− splitting in the sub-bands, which are found to be an admixture of the extended CBE (VBE) of ZnS (ZnO) and the localized O (S) state. A fully atomistic 8-band sp3-spin tight-binding basis set is used to construct the Hamiltonian for the wurtzite host materials as well as their alloy supercells. For alloy supercells, a strain is computed via the valence force-field formalism using Keating potentials. The O and S energy states are found to be approximately 199 meV below the CBE of ZnS and 190 meV above the VBE of ZnO, respectively. Overall, the calculated energy bandgaps using the BAC model are in good agreement with corrected local density approximation (LDA+U) calculations and experimental results.

Two-electron states of a group-V donor in silicon from atomistic full configuration interactions

Two-electron states bound to donors in silicon are important for both two-qubit gates and spin readout. We present a full configuration interaction technique in the atomistic tight-binding basis to capture multielectron exchange and correlation effects taking into account the full band structure of silicon and the atomic-scale granularity of a nanoscale device. Excited $s$-like states of ${A}_{1}$ symmetry are found to strongly influence the charging energy of a negative donor center. We apply the technique on subsurface dopants subjected to gate electric fields and show that bound triplet states appear in the spectrum as a result of decreased charging energy. The exchange energy, obtained for the two-electron states in various confinement regimes, may enable engineering electrical control of spins in donor-dot hybrid qubits.

Comprehensive Simulation Study of Direct Source-to-Drain Tunneling in Ultra-Scaled Si, Ge, and III-V DG-FETs

As the scaling of transistors approaches the 7-/5-nm technology nodes, direct source-to-drain tunneling (SDT) is becoming increasingly important with the shrinking gate lengths. In this paper, we present a comprehensive simulation study on the effects of SDT in ultrascaled FETs with various channel materials (Si, Ge, SiGe, InGaAs, and so on), surface/channel orientation configurations, gate lengths, body thicknesses, doping concentrations, stress levels, and temperatures. The nonequilibrium Green’s function formalism with the atomistic tight-binding basis is used to accurately model both the quantum-mechanical tunneling and the bandstructure effects. To quantify the strength of SDT, we propose a current ratio ( $\beta $ ), which essentially illustrates the difference between a full quantum transport model and a semiclassical model for calculating the FET OFF-current. The results clearly show that SDT strongly depends on orientations and stress levels in the FET channel, and for materials with a small transport effective-mass (e.g., Ge and InAs), SDT dominates the total OFF-current, making it difficult to achieve a low OFF-current target at a scaled gate length. In addition, it is found that the temperature dependence of the FET OFF-current decreases with the strength of SDT, which may have an implication on the technology definition and device targeting for the 7-/5-nm nodes.

Diameter dependent polarization in ZnO/MgO disk-in-wire emitters: Multiscale modeling of optical quantum efficiency

A multiscale computational study is performed to investigate how electronic structure, optical transitions, and terminal characteristics of nanostructured ZnO/MgO disk-in-wire emitters are governed by an intricate coupling of size-quantization, atomicity, and built-in structural and polarization fields. As for the models, an 8-band sp3 (with spin) atomistic tight-binding basis set was used to construct the Hamiltonian of the device in wurtzite crystal symmetry. Strain and the associated distortions of bond directions and bond lengths were modeled via the valence force-field (VFF) molecular mechanics framework. Specifically, in this work, a recently proposed ab initio based diameter-dependent model for the piezoelectric fields was implemented, which, as compared to the conventional diameter-independent model, was found to curb the influence of spontaneous (pyroelectric) polarization significantly. This particular finding is further illustrated through the calculation of electronic bandgap and localization of wavefunctions, optical emission characteristics, and the internal quantum efficiency of the device.

Theory of Exciton Energy Transfer in Carbon Nanotube Composites

We compute the exciton transfer (ET) rate between semiconducting single-wall carbon nanotubes (SWNTs). We show that the main reasons for the wide range of measured ET rates reported in the literature are 1) exciton confinement in local quantum wells stemming from disorder in the environment and 2) exciton thermalization between dark and bright states due to intratube scattering. The SWNT excitonic states are calculated by solving the Bethe-Salpeter equation using tight-binding basis functions. The ET rates due to intertube Coulomb interaction are computed via Fermi's golden rule. In pristine samples, the ET rate between parallel (bundled) SWNTs of similar chirality is very high ($\sim 10^{14}\;\text{s}^{-1}$) while the ET rate for dissimilar or nonparallel tubes is considerably lower ($\sim 10^{12}\;\text{s}^{-1}$). Exciton confinement reduces the ET rate between same-chirality parallel SWNTs by two orders of magnitude, but has little effect otherwise. Consequently, the ET rate in most measurements will be on the order of $ 10^{12}\;\text{s}^{-1}$, regardless of the tube relative orientation or chirality. Exciton thermalization between bright and dark states further reduces the ET rate to about $10^{11}\;\text{s}^{-1}$. The ET rate also increases with increasing temperature and decreases with increasing dielectric constant of the surrounding medium.

Extension of the basis set of linearized augmented plane wave (LAPW) method by using supplemented tight binding basis functions.

In order to increase the accuracy of the linearized augmented plane wave (LAPW) method, we present a new approach where the plane wave basis function is augmented by two different atomic radial components constructed at two different linearization energies corresponding to two different electron bands (or energy windows). We demonstrate that this case can be reduced to the standard treatment within the LAPW paradigm where the usual basis set is enriched by the basis functions of the tight binding type, which go to zero with zero derivative at the sphere boundary. We show that the task is closely related with the problem of extended core states which is currently solved by applying the LAPW method with local orbitals (LAPW+LO). In comparison with LAPW+LO, the number of supplemented basis functions in our approach is doubled, which opens up a new channel for the extension of the LAPW and LAPW+LO basis sets. The appearance of new supplemented basis functions absent in the LAPW+LO treatment is closely related with the existence of the u̇l-component in the canonical LAPW method. We discuss properties of additional tight binding basis functions and apply the extended basis set for computation of electron energy bands of lanthanum (face and body centered structures) and hexagonal close packed lattice of cadmium. We demonstrate that the new treatment gives lower total energies in comparison with both canonical LAPW and LAPW+LO, with the energy difference more pronounced for intermediate and poor LAPW basis sets.

Quantum Transport in AlGaSb/InAs TFETs With Gate Field In-Line With Tunneling Direction

Quantum transport simulations are performed in tunneling FETs (TFETs) with the gate electric field in-line with the tunneling junction direction (in-line TFETs). Charge self-consistency and thermalization effects are included in a semiclassical Poisson solution to compute the electrostatic potential. The obtained potential is then used for current calculation with the ballistic nonequilibrium Green’s function method (NEGF) in the tight binding basis. It is shown that the NEGF method predicts a higher subthreshold swing than the often-used dynamic nonlocal (DNL) path band-to-band method. The NEGF method accounts for the direct source–drain tunneling, which is underestimated in the DNL path approach in the studied geometries. Undercut is shown to be essential to obtain switching slope below 60 mV/decade in the in-line TFETs.

Atomistic modeling of coupled electron-phonon transport in nanowire transistors

Self-heating effects are investigated in ultrascaled gate-all-around silicon nanowire field-effect transistors (NWFETs) using a full-band and atomistic quantum transport simulator where electron and phonon transport are fully coupled. The nonequilibrium Green's function formalism is used for that purpose, within a nearest-neighbor $s{p}^{3}{d}^{5}{s}^{*}$ tight-binding basis for electrons and a modified valence-force-field model for phonons. Electron-phonon and phonon-electron interactions are taken into account through specific scattering self-energies treated in the self-consistent Born approximation. The electron and phonon systems are driven out of equilibrium; energy is exchanged between them while the total energy current remains conserved. This gives rise to local variations of the lattice temperature and the formation of hot spots. The resulting self-heating effects strongly increase the electron-phonon scattering strength and lead to a significant reduction of the ON-current in the considered ultrascaled Si NWFET with a diameter of 3 nm and a length of 45 nm. At the same time, the lattice temperature exhibits a maximum close to the drain contact of the transistor.

Investigation of ripple-limited low-field mobility in large-scale graphene nanoribbons

Combining molecular dynamics and quantum transport simulations, we study the degradation of mobility in graphene nanoribbons caused by substrate-induced ripples. First, the atom coordinates of large-scale structures are relaxed such that surface properties are consistent with those of graphene on a substrate. Then, the electron current and low-field mobility of the resulting non-flat nanoribbons are calculated within the Non-equilibrium Green's Function formalism in the coherent transport limit. An accurate tight-binding basis coupling the σ- and π-bands of graphene is used for this purpose. It is found that the presence of ripples decreases the mobility of graphene nanoribbons on SiO2 below 3000 cm2/Vs, which is comparable to experimentally reported values.