Maximally Localized Wannier Functions Research Articles

Efficient exact exchange using Wannier functions and other related developments in planewave-pseudopotential implementation of RT-TDDFT.

The plane-wave pseudopotential (PW-PP) formalism is widely used for the first-principles electronic structure calculation of extended periodic systems. The PW-PP approach has also been adapted for real-time time-dependent density functional theory (RT-TDDFT) to investigate time-dependent electronic dynamical phenomena. In this work, we detail recent advances in the PW-PP formalism for RT-TDDFT, particularly how maximally localized Wannier functions (MLWFs) are used to accelerate simulations using the exact exchange. We also discuss several related developments, including an anti-Hermitian correction for the time-dependent MLWFs (TD-MLWFs) when a time-dependent electric field is applied, the refinement procedure for TD-MLWFs, comparison of the velocity and length gauge approaches for applying an electric field, and elimination of long-range electrostatic interaction, as well as usage of a complex absorbing potential for modeling isolated systems when using the PW-PP formalism.

Topological Corner Modes by Composite Wannier States in Glide‐Symmetric Photonic Crystal

AbstractSecond‐order topological insulators can be characterized by their bulk polarization, which is believed to be intrinsically connected to the center of the Wannier function. In this study, the existence of second‐order topological insulators is demonstrated that feature a pair of partially degenerate photonic bands. These arise from the nonsymmorphic glide symmetry in an all‐dielectric photonic crystal. The center of the maximally localized Wannier function (MLWF) is consistently located at the origin but is not equivalent with respect to the sum of constituent polarizations. As a result, topological corner modes can be identified by the distinctly hybridized MLWFs that truncate at the sample boundary. Through full‐wave numerical simulations paired with microwave experiments, the second‐order topology is clearly confirmed and characterized. These topological corner states exhibit notably unique modal symmetries, which are made possible by the inversion of the Wannier bands. These results provide an alternative approach to explore higher‐order topological physics with significant potential for applications in integrated and quantum photonics.

Ballistic Performance of Quasi-One-Dimensional Hafnium Disulfide Field-Effect Transistors

Hafnium disulfide (HfS2) monolayer is one of the most promising two-dimensional (2D) materials for future nanoscale electronic devices, and patterning it into quasi-one-dimensional HfS2 nanoribbons (HfS2NRs) enables multi-channel architectures for field-effect transistors (FETs). Electronic, transport and ballistic device characteristics are studied for sub-7 nm-wide and ~15 nm-long zigzag HfS2NR FETs using non-equilibrium Green’s functions (NEGF) formalism with density functional theory (DFT) and maximally localized Wannier functions (MLWFs). We provide an in-depth analysis of quantum confinement effects on ON-state performance. We show that bandgap and hole transport mass are immune to downscaling effects, while the ON-state performance is boosted by up to 53% but only in n-type devices. Finally, we demonstrate that HfS2NR FETs can fulfill the industry requirements for future technology nodes, which makes them a promising solution for FET architectures based on multiple nanosheets or nanowires.

Electronic correlations and intrinsic magnetism of interstitial quasi-atomic states in Li8Au electride.

We investigate the electronic sub-system of a recently designed Li8Au superconducting electride to reveal its many-body correlated nature and magnetic properties. Using maximally localized Wannier functions (MLWFs) to describe the interstitial anion electron (IAE) states, it was found that these states are partially occupied with a population of 1.5e- and have negligible hybridization with the almost completely filled p-Au states. The averaged interaction screened Hubbard parameter U for quasi-atomic IAE states evaluated by the constrained random-phase approximation (CRPA) method is 2 eV, comparable to the width of the electride band suggesting moderate electronic correlations. Using dynamical mean field theory (DMFT) approach we found that IAEs in Li8Au electride behave as magnetic centers and possess their own well localised magnetic moments of 0.5μB per quasi-atomic IAE. The obtained results deepen the understanding of the significance of many-body effects in the IAE subsystem of electronic states and reveal the mechanism for the formation of intrinsic magnetic moments on IAEs, which behave like ferromagnetic quasi-atoms in the Li8Au electride. Overall, the observed correlation effects in Li8Au emphasize their importance in materials with excess electrons confined in cavities.

Dimensionality-Driven Evolution of Electronic Structure and Transport Properties in Pressure-Induced Phases of Ca<sub>2</sub>N Electride

We investigate how a change in dimensionality of interstitial electronic states in the Ca2N electride influences its electronic structure and transport properties. Employing the Maximally Localized Wannier Functions (MLWF) approach, we successfully describe the interstitial quasi-atomic states (ISQ) located in non-nuclear Wyckoff positions between Ca atoms. This allowed us to conclude that the electride subsystem is responsible for the formation of a band structure in the vicinity of the Fermi level in all Ca2N phases observed under pressure. Using the obtained MLWF basis, we calculate the electronic and thermal conductivity, along with the Seebeck coefficient, by solving the semi-classical Boltzmann transport equations. The results achieved permit the conclusion that the counterintuitive increase in resistance under pressure observed experimentally is attributed to enhanced localization of interstitial electronic states through electride subspace dimensionality transformations. We also established a substantial anisotropy in the transport properties within the 2D phase and found that the conductivity inside the plane of the electride layers is provided by electrons, while along the direction normal to the layers, holes become the majority carriers.

Projectability disentanglement for accurate and automated electronic-structure Hamiltonians

Maximally-localized Wannier functions (MLWFs) are broadly used to characterize the electronic structure of materials. Generally, one can construct MLWFs describing isolated bands (e.g. valence bands of insulators) or entangled bands (e.g. valence and conduction bands of insulators, or metals). Obtaining accurate and compact MLWFs often requires chemical intuition and trial and error, a challenging step even for experienced researchers and a roadblock for high-throughput calculations. Here, we present an automated approach, projectability-disentangled Wannier functions (PDWFs), that constructs MLWFs spanning the occupied bands and their complement for the empty states, providing a tight-binding picture of optimized atomic orbitals in crystals. Key to the algorithm is a projectability measure for each Bloch state onto atomic orbitals, determining if that state should be kept identically, discarded, or mixed into the disentanglement. We showcase the accuracy on a test set of 200 materials, and the reliability by constructing 21,737 Wannier Hamiltonians.

Automated mixing of maximally localized Wannier functions into target manifolds

Maximally localized Wannier functions (MLWFs) are widely used in electronic-structure calculations. We have recently developed automated approaches to generate MLWFs that represent natural tight-binding sets of atomic-like orbitals; these describe accurately both the occupied states and the complementary unoccupied ones. For many applications, it is required to use MLWFs that describe instead certain target groups of bands: the valence or the conduction bands, or correlated manifolds. Here, we start from these tight-binding sets of MLWFs, and mix them using a combination of parallel transport and maximal localization to construct manifold-remixed Wannier functions (MRWFs): these are orthogonal sets of MLWFs that fully and only span desired target submanifolds. The algorithm is simple and robust, and is showcased here in reference applications (silicon, MoS2, and SrVO3) and in a mid-throughput study of 77 insulators.

Ultrahigh hydrogen storage using metal-decorated defected biphenylene

Hydrogen (H2) energy has emerged as a principal contender for renewable green energy applications because of the ultra-high energy density and natural abundance. The implementation of this prospective technology necessitates the ultra-high capacity of H2 storage mediums. This work reports the exceptional H2 storage capacities of two-dimensional (2D) carbon allotrope biphenylene (BPL) functionalized by Li, Na, K, and Ca. The combined theoretical approaches including the density functional theory (DFT), ab-initio molecular dynamics (AIMD), maximally localized Wannier functions (MLWFs), and thermodynamic analysis were employed to elucidate the storage efficiencies at operationally practical conditions. The findings reveal that pristine BPL decorated by the selected metals are all inefficient for H2 storage because of the sensitive crystal instability caused by the energetic aggregation of the metallic dopants. On the other hand, point-defected BPL resolves this issue because it adequately magnifies the binding energies with all the decorated metals via the highly ionic bonds. Crucially, these binding energies exceed the cohesive counterparts of the parental metal bulks, consequently stabilizing the crystal integrity. Intriguingly, the Li- and Na-decorated divacancy BPL retain the ultimate H2 storage capacities of 6.76 wt% and 6.66 wt% at the practical temperature and pressure, respectively, surpassing the goal value of 5.50 wt% to be achieved by 2025. Hence, metal-functionalized BPL are conclusively the promising carbon materials for the H2 storage functionality.

PyGWBSE: a high throughput workflow package for GW-BSE calculations

We develop an open-source python workflow package, pyGWBSE to perform automated first-principles calculations within the GW-BSE (Bethe-Salpeter) framework. GW-BSE is a many body perturbation theory based approach to explore the quasiparticle (QP) and excitonic properties of materials. GW approximation accurately predicts bandgaps of materials by overcoming the bandgap underestimation issue of the more widely used density functional theory (DFT). BSE formalism produces absorption spectra directly comparable with experimental observations. pyGWBSE package achieves complete automation of the entire multi-step GW-BSE computation, including the convergence tests of several parameters that are crucial for the accuracy of these calculations. pyGWBSE is integrated with Wannier90, to generate QP bandstructures, interpolated using the maximally-localized wannier functions. pyGWBSE also enables the automated creation of databases of metadata and data, including QP and excitonic properties, which can be extremely useful for future material discovery studies in the field of ultra-wide bandgap semiconductors, electronics, photovoltaics, and photocatalysis.

Construction of maximally-localized Wannier functions using crystal symmetry

In this study, we show two methods concerning constructions of Maximally localized Wannier functions (MLWFs) using crystal symmetry. The first one is to compute input matrices for generating MLWFs only using wavefunctions in the irreducible Brillouin zone (IBZ). This approach reduces the computational costs and the size of intermediate files in proportion to the number of k points in the IBZ. The second method is to calculate the symmetry-adapted Wannier functions that are compatible with so-called frozen window technique, that is, the procedure to disentangle band structures by forcing Bloch states in a certain energy range to be included. We demonstrate how these work in the case of Fe, Co3Sn2S2, Cu, and Nb. These methods are implemented in PW2WANNIER90 code, which interfaces Quantum-ESPRESSO with the Wannier90, and the open-source python library, SymWannier. The code supports both unitary and anti-unitary symmetry operations as well as nonsymmorphic group operations, spin-orbit couplings, and ultrasoft/PAW pseudopotentials. All of these codes are available on GitHub (https://github.com/wannier-utils-dev/symWannier).

WanTiBEXOS: A Wannier based Tight Binding code for electronic band structure, excitonic and optoelectronic properties of solids

The Bethe–Salpeter equation (BSE) approach becomes a methodology commonly used for simulating excitonic and optical properties in computer materials sciences. However, BSE approach based directly on first principles demands a high computational cost, being prohibitive for larger systems. In order to overcome this challenge, we have developed WanTiBEXOS, a parallel computational FORTRAN code, constituted of a maximally localized Wannier functions based tight-binding (MLWF-TB) model in conjunction with BSE framework. The MLWF-TB Hamiltonian used in WanTiBEXOS package can be obtained via any density functional theory package interfaced with Wannier90 code. It's expected, due MLWF-TB formalism, a computational time reduction around one or more orders of magnitude in comparison with BSE ab initio implementations. In order to demonstrate its reliability, flexibility, efficiency and versatility of WanTiBEXOS, we simulate electronic and optical property calculations for the representative materials, including conventional bulk semiconductors, perovskites, nano-monolayer materials and van der Waals heterostructures. Program summaryProgram Title: WanTiBEXOSCPC Library link to program files:https://doi.org/10.17632/4vh76mnkv5.1Developer's repository link:https://github.com/ac-dias/wantibexosLicensing provisions: GNU General Public Licence 3.0Programming language: Fortran90 (Intel compiler)External routines: OpenMP and Intel Math Kernel Library (MKL)Nature of problem: Calculate electronic, optical, and excitonic properties of solids.Solution method: Tight-binding approach under maximally localized Wannier functions (MLWF) parametrization to describe standard electronic properties and the Bethe–Salpeter formalism for excitonic properties.

Time evolution of energies and populations in germanium perturbed by a near-infrared pulse on the atto-second scale

Implementing time-resolved spectroscopy is one of the challenging topics in solid-state physics: indeed, it can be a crucial step to unveil the early time dynamics of fundamental processes in systems such as semiconductors, metals, superconductors and topological materials. Then, it is essential to build theoretical tools in order to understand the experimental results and what actually happens in solid-state systems on a new and finer timescale: the atto-second one. Accordingly, we have developed a theoretical–numerical tool in order to study the time evolution of the electronic populations on the atto-second scale in materials perturbed by a laser pulse. After finding the ab-initio band structure of the material, we compute the maximally-localized Wannier functions and obtain the hopping terms. Then, we study the effect of the laser pulse using the Peierls substitution method and obtain the equation of motion for the electronic populations. Finally, we obtain a dynamical DOS of the system and the corresponding dynamical electronic populations. In this work, as a relevant case study, we report our results for germanium. We identify oscillations in the eigenenergies and in the populations which roughly follow either the field or its square, with some phase shifts with respect to the field.

Robust Pipek-Mezey Orbital Localization in Periodic Solids.

We describe a robust method for determining Pipek-Mezey (PM) Wannier functions (WF), recently introduced by Jónsson et al. (J. Chem. Theor. Chem. 2017, 13, 460), which provide some formal advantages over the more common Boys (also known as maximally-localized) Wannier functions. The Broyden-Fletcher-Goldfarb-Shanno-based PMWF solver is demonstrated to yield dramatically faster convergence compared to the alternatives (steepest ascent and conjugate gradient) in a variety of one-, two-, and three-dimensional solids (including some with vanishing gaps) and can be used to obtain Wannier functions robustly in supercells with thousands of atoms. Evaluation of the PM functional and its gradient in periodic linear combination of atomic orbital representation used a particularly simple definition of atomic charges obtained by Moore-Penrose pseudoinverse projection onto the minimal atomic orbital basis. An automated "canonicalize phase then randomize" method for generating the initial guess for WFs contributes significantly to the robustness of the solver.

Local approaches for electric dipole moments in periodic systems and their application to real-time time-dependent density functional theory.

Within periodic boundary conditions, the traditional quantum mechanical position operator is ill-defined, necessitating the use of alternative methods, most commonly the Berry phase formulation in the modern theory of polarization. Since any information about local properties is lost in this change of framework, the Berry phase formulation can only determine the total electric polarization of a system. Previous approaches toward recovering local electric dipole moments have been based on applying the conventional dipole moment operator to the centers of maximally localized Wannier functions (MLWFs). Recently, another approach to local electric dipole moments has been demonstrated in the field of subsystem density functional theory (DFT) embedding. We demonstrate in this work that this approach, aside from its use in ground state DFT-based molecular dynamics, can also be applied to obtain electric dipole moments during real-time propagated time-dependent DFT (RT-TDDFT). Moreover, we present an analogous approach to obtain local electric dipole moments from MLWFs, which enables subsystem analysis in cases where DFT embedding is not applicable. The techniques were implemented in the quantum chemistry software CP2K for the mixed Gaussian and plane wave method and applied to cis-diimide and water in the gas phase, cis-diimide in aqueous solution, and a liquid mixture of dimethyl carbonate and ethylene carbonate to obtain absorption and infrared spectra decomposed into localized subsystem contributions.

Dielectric Constant of Liquid Water Determined with Neural Network Quantum Molecular Dynamics.

The static dielectric constant ϵ_{0} and its temperature dependence for liquid water is investigated using neural network quantum molecular dynamics (NNQMD). We compute the exact dielectric constant in canonical ensemble from NNQMD trajectories using fluctuations in macroscopic polarization computed from maximally localized Wannier functions (MLWF). Two deep neural networks are constructed. The first, NNQMD, is trained on QMD configurations for liquid water under a variety of temperature and density conditions to learn potential energy surface and forces and then perform molecular dynamics simulations. The second network, NNMLWF, is trained to predict locations of MLWF of individual molecules using the atomic configurations from NNQMD. Training data for both the neural networks is produced using a highly accurate quantum-mechanical method, DFT-SCAN that yields an excellent description of liquid water. We produce 280×10^{6} configurations of water at 7 temperatures using NNQMD and predict MLWF centers using NNMLWF to compute the polarization fluctuations. The length of trajectories needed for a converged value of the dielectric constant at 0°C is found to be 20ns (40×10^{6} configurations with 0.5fs time step). The computed dielectric constants for 0, 15, 30, 45, 60, 75, and 90°C are in good agreement with experiments. Our scalable scheme to compute dielectric constants with quantum accuracy is also applicable to other polar molecular liquids.

Maximally localized Wannier functions for describing a topological phase transition in stanene

Starting from first-principles calculations on pristine stanene and using maximally localized Wannier functions (MLWFs), we analyze the different phases of the system when it is driven to a topological phase transition. The transition is achieved by a continuous parameter represented by an external electric field ${\mathcal{E}}_{z}$ as a generic inversion-symmetry-breaking term. We also compare the results with those of a multiorbital tight-binding (TB) model for stanene, whose hopping integrals are determined by Slater-Koster parameters. The system is in a topological (trivial) phase for ${\mathcal{E}}_{z}<{\mathcal{E}}_{c}$ (${\mathcal{E}}_{z}>{\mathcal{E}}_{c}$). We obtain that the critical field is ${\mathcal{E}}_{c}\ensuremath{\simeq}0.69\phantom{\rule{4pt}{0ex}}\mathrm{eV}/\AA{}$ for the more realistic MLWF compared to ${\mathcal{E}}_{c}\ensuremath{\simeq}0.15\phantom{\rule{4pt}{0ex}}\mathrm{eV}/\AA{}$ in the TB model. This suggests a larger stability of the topological phase of stanene when deposited on inert substrates.

Atomic Structure of Glassy GeTe4 as a Playground to Assess the Performances of Density Functional Schemes Accounting for Dispersion Forces.

The atomic structure of glassy GeTe4 is obtained in the framework of first-principles molecular dynamics (FPMD) by considering five different approaches for the description of the electronic structure within density functional theory (DFT). Among these schemes, one is not corrected by accounting for the dispersion forces and it is based on the BLYP exchange-correlation (XC) functional, while all of the others consider the dispersion forces according to different theoretical strategies. In particular, by maintaining the BLYP expression for the XC functional, two of them (BLYP-D2 and BLYP-D3) exploit the Grimme expressions for the dispersion forces, while the fourth scheme is based on the maximally localized Wannier functions (MLWFs). Finally, we also considered the rVV10 functional constructed to include seamlessly the dispersion part. Our results point out the better performances of BLYP-D3 and MLWF in terms of comparison with experimental data for the total pair correlation functions, with BLYP-D2 and rVV10 being closer to the uncorrected BLYP data. The implications of such findings are discussed by considering the overall limited impact of dispersion forces on the atomic structure of glassy GeTe4.

Intermediate band induced by p-block metalloid antimony in SnS2 for higher solar energy utilization

Semiconductors with intermediate bands have attracted tremendous attention due to their superior solar energy utilization. Herein, we propose a simple approach to introduce the intermediate band through substituting tin by p-block metalloid antimony in SnS2. Experimentally, Sn1-xSbxS2 (x up to 0.06) semiconductors possessing an intermediate band were successfully synthesized through solid state reactions. After antimony doping, two absorption edges appear at 2.31 eV and 1.63 eV in the visible light region, and one absorption shoulder starting at 0.68 eV emerges in the infrared region, as observed from the UV–vis-NIR absorption spectra. These typical intermediate band absorption features are consistent with our first principles calculations. The state of the intermediate band of Sn1-xSbxS2 is mainly composed of the Sb-5s orbital from maximally-localized Wannier function analysis. Owing to the antimony intermediate band extending the solar absorption range, Sn1-xSbxS2 semiconductors exhibit a higher utilization of solar energy compared with pristine SnS2.

Emergent dual topology in the three-dimensional Kane-Mele Pt2HgSe3

Recently, the very first large-gap Kane-Mele quantum spin Hall insulator was predicted to be monolayer jacutingaite (Pt$_2$HgSe$_3$), a naturally-occurring exfoliable mineral discovered in Brazil in 2008. The stacking of quantum spin Hall monolayers into a van-der-Waals layered crystal typically leads to a (0;001) weak topological phase, which does not protect the existence of surface states on the (001) surface. Unexpectedly, recent angle-resolved photoemission spectroscopy experiments revealed the presence of surface states dispersing over large areas of the 001-surface Brillouin zone of jacutingaite single crystals. The 001-surface states have been shown to be topologically protected by a mirror Chern number $C_M=-2$, associated with a nodal line gapped by spin-orbit interactions. Here, we extend the two-dimensional Kane-Mele model to bulk jacutingaite and unveil the microscopic origin of the gapped nodal line and the emerging crystalline topological order. By using maximally-localized Wannier functions, we identify a large non-trivial second nearest-layer hopping term that breaks the standard paradigm of weak topological insulators. Complemented by this term, the predictions of the Kane-Mele model are in remarkable agreement with recent experiments and first-principles simulations, providing an appealing conceptual framework also relevant for other layered materials made of stacked honeycomb lattices.

Efficient Ab Initio Multiplet Calculations for Magnetic Adatoms on MgO.

Scanning probe microscopy and spectroscopy, and more recently, single-atom electron spin resonance, have allowed the direct observation of electron dynamics at the atomic limit. The interpretation of data is strongly dependent on model Hamiltonians. However, fitting effective spin Hamiltonians to experimental data lacks the ability to explore a vast number of potential systems of interest. By using plane-wave density functional theory as starting point, we build a multiplet Hamiltonian making use of maximally localized Wannier functions. The Hamiltonian contains spin-orbit and electron-electron interactions needed to obtain the relevant spin dynamics. The resulting reduced Hamiltonian is solved by exact diagonalization. We compare three prototypical cases of 3d transition metals Mn (total spin S = 5/2), Fe (S = 2), and Co (S = 3/2) on MgO with experimental data and find that our calculations can accurately predict the spin orientation and anisotropy of the magnetic adatom. Our method does not rely on experimental input and allows us to explore and predict the fundamental magnetic properties of adatoms on surfaces.