Wannier Functions Research Articles

Ensemble Monte Carlo transport studies of zinc-blende cuprous halides

We present a comprehensive theoretical analysis of intrinsic high-field transport in cuprous halides: CuCl, CuBr, and CuI. Ensemble Monte Carlo transport simulations were performed based on analytical approximations of the multi-valley and three-band electronic structure model. The deformation potentials, extracted from carrier–phonon interaction matrix elements calculated via the Wannier function approach, were employed to determine scattering rates. Our detailed analysis uncovers intriguing transport characteristics based on the complex valence band structures, resulting from spin–orbit coupling and band inversion. Remarkably, the hole mobility in CuI was exceptionally high, reaching up to 193 cm2/V s, while CuCl exhibited unusual temperature dependencies in hole transport. Additionally, the electron mobility in CuI was found to be 254 cm2/V s, indicating a minimal disparity between carrier mobilities, which is advantageous for optoelectronic applications.

The edge states of one-dimensional spin-$\frac{1}{2}$-like noninteracting periodic systems under the most compactly supported Wannier-type functions

Abstract A hallmark of topological insulators is topologically protected edge states, which are determined by topological invariants defined under Bloch functions. Of course, not all edge states are stable, and they are independent of topological invariants. And in a recent study, it was found that even stable protected gapless edge states cannot be explained by topological invariants in two-dimensional (2D) systems. Motivated by this idea, we carried out a thorough study in one-dimensional (1D) spin-$\frac{1}{2}$-like noninteracting periodic systems and found that all edge states can be explained by the most compactly supported Wannier-type functions (MCWTFs). All the answers are contained in the flat-band Hamiltonian defined by MCWTFs. Edge states can be obtained by solving special equations using the parameters of MCWTFs. Symmetries are the special solutions of these equations, and we have proved the relationship between zero-energy edge states and symmetry analytically in partial cases, which was only a well-known result in the past. By solving the equations, we also find that not all zero-energy edge states are determined by symmetry, which is beyond the current framework. Through numerical verification, we show that these zero-energy edge states, like those protected by symmetry, are not affected by the energy spectrum of the system, so they are only related to the Bloch functions. We also derive special properties of zero-energy edge states protected by chiral symmetry from the perspective of MCWTFs, which are consistent with the previous literature. Finally, we do a test in the 2D case and find the connection between the Chern number and the Wannier functions. Our results show that compared with topological invariants, the origin of the edge state can be understood more comprehensively from the perspective of Wannier functions.

Exploring topological phases in superconducting transition metal (Sc, Ti, V)-carbides

The combination of non trivial band topology and superconductivity, resulting in topological superconductivity, igniting a fervent pursuit in the realm of quantum materials. Through density functional theory and maximally localized Wannier functions, we delve into the electronic and topological properties of transition metal carbides ΛC (with Λ= Sc, Ti, V). Phonon dispersions guarantee the structural stability of these superconductors. Witness the presence of band inversion within the Brillouin Zone of TiC and VC, contrasting the absence of such band inversion in ScC. In addition, the nonzero Z2 topological invariant as well as the occurrence of Dirac cone in the surface spectrum of TiC and VC, unveil their topologically nontrivial character. These transition metal carbides emerge as promising candidates for probing the depths of topological superconductivity and unraveling the associated Majorana bound states.

Wannier Function Localization Using Bloch Intrinsic Atomic Orbitals.

We extend the intrinsic atomic orbital (IAO) method for the localization of molecular orbitals to calculate well-localized generalized Wannier functions in crystals in the spirit of the Pipek-Mezey method. We furthermore present a one-shot diabatic Wannierization procedure that aligns the phases of the Bloch functions, providing immediate Wannier localization, which serves as an excellent initial guess for optimization. We test our Wannier localization implementation on a number of solid-state systems, highlighting the effectiveness of the diabatic preparation, especially for localizing core bands. Partial charges of Wannier functions generated using Bloch IAOs align well with chemical intuition, which we demonstrate through the example of the adsorption of CO on a MgO surface.

Modification of the Bose-Hubbard model parameters in an optical lattice by two-particle Wannier functions

Modification of the Bose-Hubbard model parameters in an optical lattice by two-particle Wannier functions

Berry curvature induced anomalous Hall effect in Pt2MnGa

The intrinsic anomalous Hall effect in ferromagnetic materials depends on the spin–orbit-coupling-induced effect in the electronic structure. The presence of anomalous Hall effect can be realized from the existence of the finite Berry curvature. Since the Heusler material Pt2MnGa is ferromagnetic in its collinear state and no report on its transport properties has yet been made, the anomalous Hall effect in this system is investigated using a combined approach of the density functional theory and maximally localized Wannier function. Analysis of the Berry curvature reveals positive and negative peaks along the high symmetry k-points. These peaks together lead to a significant negative anomalous Hall conductivity, which makes the material a promising candidate for applications in spintronics.

Polarization textures in crystal supercells with topological bands

Two-dimensional materials are a highly tunable platform for studying the momentum space topology of the electronic wavefunctions and real space topology in terms of skyrmions, merons, and vortices of an order parameter. Such textures for electronic polarization can exist in moiré heterostructures. A quantum-mechanical definition of local polarization textures in insulating supercells was recently proposed. Here, we propose a definition for local polarization that is also valid for systems with topologically nontrivial bands. We introduce semilocal hybrid polarizations, which are valid even when the Wannier functions in a system cannot be made exponentially localized in all dimensions. We use this definition to explicitly show that nontrivial real-space polarization textures can exist in topologically nontrivial systems with nonzero Chern number under (1) an external superlattice potential, and (2) under a stacking-induced moiré potential. In the latter, we find that while the magnitude of the local polarization decreases discontinuously across a topological phase transition from trivial to topologically nontrivial, the polarization does not completely vanish. Our findings suggest that band topology and real-space polar topology may coexist in real materials. Published by the American Physical Society 2024

Dynamical and optical properties of rare phenakite mineral: A combined experimental and computational study

The electronic structure, optical and dynamical properties of the natural phenakite Be2SiO4, are studied using ab initio calculations completed by Raman spectroscopy experiments. The calculated structural properties are in excellent agreement with experimental data and are accompanied by chemical bonds analysis using Maximally Localized Wannier Functions method. The theoretical analysis of projected density of states reveals the nature of the valence band as composed by electronic states of oxygen atoms, while conducting band is composed by electronic states of Si-atoms. Using linear response method the optical properties are calculated and compared with optical properties of quartz. It was shown the similarity of rare phenakite crystal and quartz. The calculated phonon dispersion structure reveals mostly delocalized nature of phonon states with quasilocalized phonons in high-frequency range, where the most intense band in Raman spectrum is observed. The band is ambiguously assigned to the breathing mode in SiO4 tetrahedra. Basing on such peculiarity in the spectra the rapid nondestructive diagnostic method of the sample is purposed.

Non-Abelian Hopf-Euler insulators

We discuss a class of three-band non-Abelian topological insulators in three dimensions that carry a single bulk Hopf index protected by spatiotemporal (PT) inversion symmetry. These phases may also host subdimensional topological invariants given by the Euler characteristic class, resulting in real Hopf-Euler insulators. Such systems naturally realize helical nodal structures in the three-dimensional Brillouin zone, providing a physical manifestation of the linking number described by the Hopf invariant. We show that, by opening a gap between the valence bands of these systems, one finds a fully-gapped “flag” phase, which displays a three-band multigap Pontryagin invariant. Unlike the previously reported PT-symmetric four-band real Hopf insulator, which hosts a Z⊕Z invariant, these phases are not unitarily equivalent to two copies of a complex two-band Hopf insulator. We show that such uncharted phases can be obtained through dimensional extension of two-dimensional Euler insulators, and that they support (i) an optical bulk integrated circular shift effect quantized by the Hopf invariant, (ii) quantum-geometric breathing in the real-space Wannier functions, and (iii) surface Euler topology on boundaries. Consequently, our findings pave the way for novel experimental realizations of real-space quantum geometry, as these systems may be directly simulated by utilizing synthetic dimensions in metamaterials or ultracold atoms. Published by the American Physical Society 2024

Anticipation of Large Intrinsic Spin Hall Conductivity in Mercury Chalcogenides: A First‐Principles Study

AbstractThe report carried out detailed first‐principle calculations of Mercury chalcogenides (HgX; X = Te, Se and S) using density functional theory, verifying the bulk band inversion property with different exchange‐correlation functionals. The Wannier function method is used to study the non‐trivial topology of HgX systems, spin Berry curvature, and intrinsic spin Hall conductivity. Quantized intrinsic spin Hall conductivity is observed in the HgX systems. Large intrinsic spin Hall conductivity is found in the systems due to a strong spin Berry curvature accumulation near the triply degenerate points in the Brillouin zone. Calculation shows that the intrinsic spin Hall conductivity for all three HgX systems has stable plateaus, with Mercury Telluride having a maximum width of up to 1.05 eV. The maximum intrinsic spin Hall conductivity of –931/e () is obtained in mercury sulfide, higher than the reported values for spin Hall conductivity and the plateau width in typical topological insulators such as , , and as well as in transition metal pnictides (TaX, X = As, P and N) and transition metal iridates.

Detecting the spread of valence-band Wannier functions by optical sum rules

Detecting the spread of valence-band Wannier functions by optical sum rules

Nonempirical Prediction of the Length-Dependent Ionization Potential in Molecular Chains.

The ionization potential of molecular chains is well-known to be a tunable nanoscale property that exhibits clear quantum confinement effects. State-of-the-art methods can accurately predict the ionization potential in the small molecule limit and in the solid-state limit, but for intermediate, nanosized systems prediction of the evolution of the electronic structure between the two limits is more difficult. Recently, optimal tuning of range-separated hybrid functionals has emerged as a highly accurate method for predicting ionization potentials. This was first achieved for molecules using the ionization potential theorem (IPT) and more recently extended to solid-state systems, based on an ansatz that generalizes the IPT to the removal of charge from a localized Wannier function. Here, we study one-dimensional molecular chains of increasing size, from the monomer limit to the infinite polymer limit using this approach. By comparing our results with other localization-based methods and where available with experiment, we demonstrate that Wannier-localization-based optimal tuning is highly accurate in predicting ionization potentials for any chain length, including the nanoscale regime.

Two-dimensional flat-band solitons in superhoneycomb lattices

Abstract Flat-band periodic materials are characterized by a linear spectrum containing at least one band where the propagation constant remains nearly constant irrespective of the Bloch momentum across the Brillouin zone. These materials provide a unique platform for investigating phenomena related to light localization. Meantime, the interaction between flat-band physics and nonlinearity in continuous systems remains largely unexplored, particularly in continuous systems where the band flatness deviates slightly from zero, in contrast to simplified discrete systems with exactly flat bands. Here, we use a continuous superhoneycomb lattice featuring a flat band in its spectrum to theoretically and numerically introduce a range of stable flat-band solitons. These solutions encompass fundamental, dipole, multi-peak, and even vortex solitons. Numerical analysis demonstrates that these solitons are stable in a broad range of powers. They do not bifurcate from the flat band and can be analyzed using Wannier function expansion leading to their designation as Wannier solitons. These solitons showcase novel possibilities for light localization and transmission within nonlinear flat-band systems.

Tuning Excitonic Properties of Monochalcogenides via Design of Janus Structures.

Two-dimensional (2D) Janus structures offer a unique range of properties as a result of their symmetry breaking, resulting from the distinct chemical composition on each side of the monolayers. Here, we report a theoretical investigation of 2D Janus Q'A'AQ P3m1 monochalcogenides from group IV (A and A' = Ge and Sn; Q, Q' = S and Se) and 2D non-Janus QAAQ P3̅m1 counterparts. Our theoretical framework is based on density functional theory calculations combined with maximally localized Wannier functions and tight-binding parametrization to evaluate the excitonic properties. The phonon band structures exhibit exclusively real (nonimaginary) branches for all materials. Particularly, SeGeSnS has greater energetic stability than its non-Janus counterparts, representing an outstanding energetic stability among the investigated materials. However, SGeSnS and SGeSnSe have higher formation energies than the already synthesized MoSSe, making them more challenging to grow than the other investigated structures. The electronic structure analysis demonstrates that materials with Janus structures exhibit band gaps wider than those of their non-Janus counterparts, with the absolute value of the band gap predominantly determined by the core rather than the surface composition. Moreover, exciton binding energies range from 0.20 to 0.37 eV, reducing band gap values in the range of 21% to 32%. Thus, excitonic effects influence the optoelectronic properties more than the point-inversion symmetry breaking inherent in the Janus structures; however, both features are necessary to enhance the interaction between the materials and sunlight. We also found anisotropic behavior of the absorption coefficient, which was attributed to the inherent structural asymmetry of the Janus materials.

Enhancing shift current response via virtual multiband transitions

Materials exhibiting a significant shift current response could potentially outperform conventional solar cell materials. The myriad of factors governing shift-current response, however, poses significant challenges in finding such strong shift-current materials. Here we propose a general design principle that exploits inter-orbital mixing to excite virtual multiband transitions in materials with multiple flat bands to achieve an enhanced shift current response. We further relate this design principle to maximizing Wannier function spread as expressed through the formalism of quantum geometry. We demonstrate the viability of our design using a 1D stacked Rice-Mele model. Furthermore, we consider a concrete material realization - alternating angle twisted multilayer graphene (TMG) - a natural platform to experimentally realize such an effect. We identify a set of twist angles at which the shift current response is maximized via virtual transitions for each multilayer graphene and highlight the importance of TMG as a promising material to achieve an enhanced shift current response at terahertz frequencies. Our proposed mechanism also applies to other 2D systems and can serve as a guiding principle for designing multiband systems that exhibit an enhanced shift current response.

Vibrational Spectra Simulations in Amino Acid-Based Imidazolium Ionic Liquids.

We present maximally localized Wannier functions and Voronoi tessellation to obtain dipole moment distributions for vibrational spectra in several important ionic liquids calculated by using ab initio molecular dynamics simulations. IR and Raman spectra of various imidazolium-based ionic liquids (ILs) paired with six amino acid anions are shown herein. For IR spectra, two approaches (Wannier and Voronoi) are in agreement with respect to the relative intensities and the overall shapes for the main peaks. Under Raman spectra, the polarizability of the covalent bonds is shown to affect the strength of the Raman scattering signal. The advantage of the Voronoi tessellation method, being that it does not have strong spikes in its time development, is demonstrated by the comparison of two theoretical methods (Wannier and Voronoi) with experimental data. We analyze the errors between theoretical and experimental spectroscopic data, with the Voronoi method shown to accurately reproduce experimental values. In addition, theoretical spectroscopy shows the ability to accurately separate components of a mixture. The combination of theoretical and experimental methods is utilized to understand the spectroscopic properties of amino acid-based imidazolium ILs.

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.

Search for an antiferromagnetic Weyl semimetal in (MnTe) m (Sb2Te3) n and (MnTe) m (Bi2Te3) n superlattices

The interaction between topology and magnetism can lead to novel topological materials including Chern insulators, axion insulators, and Dirac and Weyl semimetals. In this work, a family of van der Waals layered materials using MnTe and Sb2Te3 or Bi2Te3 superlattices as building blocks are systematically examined in a search for antiferromagnetic Weyl semimetals, preferably with a simple node structure. The approach is based on controlling the strength of the exchange interaction as a function of layer composition to induce the phase transition between the topological and the normal insulators. Our calculations, utilizing a combination of first-principles density functional theory and tight-binding analyses based on maximally localized Wannier functions, clearly indicate a promising candidate for a type-I magnetic Weyl semimetal. This centrosymmetric material, Mn10Sb8Te22 (or (MnTe) m (Sb2Te3) n with m = 10 and n = 4), shows ferromagnetic intralayer and antiferromagnetic interlayer interactions in the antiferromagnetic ground state. The obtained electronic bandstructure also exhibits a single pair of Weyl points in the spin-split bands consistent with a Weyl semimetal. The presence of Weyl nodes is further verified with Berry curvature, Wannier charge center, and surface state (i.e. Fermi arc) calculations. Other combinations of the MnSbTe-family materials are found to be antiferromagnetic topological or normal insulators on either side of the Mn:Sb ratio, respectively, illustrating the topological phase transition as anticipated. A similar investigation in the homologous (MnTe) m (Bi2Te3) n system produces mostly nontrivial antiferromagnetic insulators due to the strong spin–orbit coupling. When realized, the antiferromagnetic Weyl semimetals in the simplest form (i.e. a single pair of Weyl nodes) are expected to provide a promising candidate for low-power spintronic applications.

Large valley splitting induced by spin-orbit coupling effects in monolayer Hf3N2O2

Valleytronics is an emerging field of electronics that aims to utilize valley degrees of freedom in materials for information processing and storage. Nowadays, the valley splitting of 2D materials is not particularly large, therefore, the search for large valley splitting materials is very important for the development of valleytronics. This work theoretically predicts that MXene Hf3N2O2 is a 2D material with large valley splitting. It is an indirect bandgap semiconductor with a bandgap of 0.32 eV at the PBE level and increases to 0.55 eV at the HSE06 level. Since Hf3N2O2 breaks the symmetry of spatial inversion, when we consider spin–orbit coupling (SOC), there is a valley splitting at K/K′ of the valence band with a valley splitting value of 98.76 meV. The valley splitting value slightly decreases to 88.96 meV at the HSE06 level. In addition, The phonon spectrum and elastic constants indicate that it is both dynamically and mechanically stable. According to the maximum localization of the Wannier function, it is obtained that the Berry curvature is not zero at K/K′. When a biaxial strain is applied, Hf3N2O2 transitions from metal to semiconductor. With increasing biaxial strain, the valley splitting value increased from 70.13 meV to 109.11 meV. Our research shows that Hf3N2O2 is a promising material for valleytronics.

Fermionic and Bosonic Partition Functions at Imaginary Chemical Potential as Bloch Functions

In this work it is pointed out that the phase transitions of the <i>d</i>+1 Gross-Neveu (fermionic) and <I>CP<SUP>N</SUP></I><sup>−1</sup> (bosonic) models at finite temperature and imaginary chemical potential can be mapped to transformations of Hubbard-like regular hexagonal to square lattice with the intermediate steps to be specific surfaces (irregular hexagonal kind) with an ordered construction based on the even indexed Bloch-Wigner-Ramakrishnan polylogarithm function. The zeros and extrema of the Clausen <i>Cl<sub>d</sub></i>(<i>θ</i>) function play an important role to the analysis since they allow us not only to study the fermionic and bosonic theories and their phase transitions but also the possibility to explore the existence of conductors arising from the correspondence between the partition functions of the two models and the Bloch and Wannier functions that play a crucial role in the tight-binding approximation in solid state physics. The main aim of this work is not only to unveil the relevance of the canonical partition functions of a fermionic and a bosonic model to Bloch states by using an imaginary chemical potential but also to examine the overlap between two Bloch wave-functions that differ by a lattice momentum that calculates the momentum transfer of a Bloch wave during the interaction with a lattice point of a hexagonal construction.