I present a method to calculate the ballistic transport properties of atomic-scale structures under bias. The electronic structure of the system is calculated using the Kohn-Sham scheme of density functionai theory （...I present a method to calculate the ballistic transport properties of atomic-scale structures under bias. The electronic structure of the system is calculated using the Kohn-Sham scheme of density functionai theory （DFT）. The DFT eigenvectors are then transformed into a set of maximaily localized Wannier functions （MLWFs） [N. Maxzari and D. Vanderbilt, Phys. Rev. B 56 （1997） 12847]. The MLWFs are used as a minimai basis set to obtain the Hamitonian matrices of the scattering region and the adjacent leads, which are needed for transport calculation using the nonequilibrium Green＇s function formalism. The coupling of the scattering region to the semi-infinite leads is described by the self-energies of the leads. Using the nonequilibrium Green＇s function method, one calculates self-consistently the charge distribution of the system under bias and evaluates the transmission and current through the system. To solve the Poisson equation within the scheme of MLWFs I introduce a computationally efficient method. The method is applied to a molecular hydrogen contact in two transition metal monatomic wires （Cu and Pt）. It is found that for Pt the I-V characteristics is approximately linear dependence, however, for Cu the I-V characteristics manifests a linear dependence at low bias voltages and exhibits apparent nonlinearity at higher bias voltages. I have also calculated the transmission in the zero bias voltage limit for a single CO molecule adsorbed on Cu and Pt monatomic wires. While a chemical scissor effect occurs for the Cu monatomic wire with an adsorbed CO molecule, it is absent for the Pt monatomie wire due to the contribution of d-orbitals at the Fermi energy,展开更多
The nonlinear Wannier functions in square Kronig-Penney potential are investigated with the help of a set of exact nonlinear Bloch solutions. The nonlinear interaction makes the Wannier functions fall off as non-expon...The nonlinear Wannier functions in square Kronig-Penney potential are investigated with the help of a set of exact nonlinear Bloch solutions. The nonlinear interaction makes the Wannier functions fall off as non-exponential law with distance and enhances the tunneling coupling between the neighbor sites.展开更多
We present a general method for constructing maximally localized Wannier functions. It consists of three steps： （i） picking a localized trial wave function, （ii） performing a full band projection, and （iii） ort...We present a general method for constructing maximally localized Wannier functions. It consists of three steps： （i） picking a localized trial wave function, （ii） performing a full band projection, and （iii） orthonormalizing with the LSwdin method. Our method is capable of producing maximally localized Wannier functions without further minimization, and it can be applied straightforwardly to random potentials without using supercells. The effectiveness of our method is demonstrated for both simple bands and composite bands.展开更多
Based on the first-principles density functional theory electronic structure calculation,we investigate the possible phonon-mediated superconductivity in arsenene,a two-dimensional buckled arsenic atomic sheet,under e...Based on the first-principles density functional theory electronic structure calculation,we investigate the possible phonon-mediated superconductivity in arsenene,a two-dimensional buckled arsenic atomic sheet,under electron doping.We find that the strong superconducting pairing interaction results mainly from the pz-like electrons of arsenic atoms and the A1 phonon mode around the K point,and the superconducting transition temperature can be as high as 30.8 K in the arsenene with 0.2 doped electrons per unit cell and 12%-applied biaxial tensile strain.This transition temperature is about ten times higher than that in the bulk arsenic under high pressure.It is also the highest transition temperature that is predicted for electron-doped two-dimensional elemental superconductors,including graphene,silicene,phosphorene,and borophene.展开更多
Based on density functional first-principles calculations and anisotropic Eliashberg equations,we have investigated the electronic structure,lattice dynamics,and phonon-mediated superconductivity in newly synthesized ...Based on density functional first-principles calculations and anisotropic Eliashberg equations,we have investigated the electronic structure,lattice dynamics,and phonon-mediated superconductivity in newly synthesized layered compound Sr BC under pressure.Different from Li BC and Mg B2,our calculations surprisingly reveal that Sr BC is isotropic in compressibility,due to the accumulation of substantial electrons in the interstitial region.We find that the Sr phonons strongly couple with B-2 pz orbital and the interstitial states,giving rise to a two-gap superconductivity in Sr BC,whose transition temperature shows an inverted V-shaped dependence on pressure.The maximal transition temperature is about 22 K at50 GPa.On both sides of 50 GPa,the transition temperature exhibits quasi-linear variation with positive and negative slopes,respectively.Such a variation of transition temperature is infrequent among phonon-mediated superconductors.The competition between enhanced electron–phonon matrix element and hardened phonons plays an essential role in governing the behavior of the critical temperature.展开更多
Maximally-localized Wannier functions(MLWFs)are widely employed as an essential tool for calculating the physical properties of materials due to their localized nature and computational efficiency.Projectability-disen...Maximally-localized Wannier functions(MLWFs)are widely employed as an essential tool for calculating the physical properties of materials due to their localized nature and computational efficiency.Projectability-disentangled Wannier functions(PDWFs)have recently emerged as a reliable and efficient approach for automatically constructing MLWFs that span both occupied and lowest unoccupied bands.Here,we extend the applicability of PDWFs to magnetic systems and/or those including spin-orbit coupling,and implement such extensions in automated workflows.Furthermore,we enhance the robustness and reliability of constructing PDWFs by defining an extended protocol that automatically expands the projectors manifold,when required,by introducing additional appropriate hydrogenic atomic orbitals.We benchmark our extended protocol on a set of 200 chemically diverse materials,as well as on the 40 systems with the largest band distance obtained with the standard PDWF approach,showing that on our test set the present approach delivers a success rate of over 98%in obtaining accurate Wannier-function interpolations,defined as an average band distance below20 meV between the DFT and Wannier-interpolated bands,up to 2 eV above the Fermi level for metals or above the conduction band minimum for insulators(and a 100%success rate when including only bands up to 1 eV above these values).展开更多
Electron-phonon coupling(EPC) in bulk materials is an important effect in multifarious physical and chemical phenomena. It is the key to explaining the mechanisms for superconductivity, electronic transport, etc. The ...Electron-phonon coupling(EPC) in bulk materials is an important effect in multifarious physical and chemical phenomena. It is the key to explaining the mechanisms for superconductivity, electronic transport, etc. The EPC matrix describes the coupling of the electronic eigenstates of the studied system under the perturbation of phonons. Although the EPC matrix is closely relevant to many fundamental physicochemical properties, it remains a challenge to calculate the EPC matrix precisely due to the high computational cost. In recent years, Giustino et al. developed the EPW method on open-source ab-initio software Quantum Espresso, which uses Wannier functions(WFs) to calculate EPC matrix. However, due to the limitation of their implementation,it is not possible yet to calculate the EPC matrix under some important computational conditions, e.g., for DFT+U and HSE calculation. Given the importance of these computational conditions(e.g., for transition metal oxides), we have developed our own implementation of EPC matrix calculation based on the domestic ab-initio software PWmat. Our code allows the DFT+U and HSE correction, so we can get a more accurate EPC matrix in the related problems. In this article, we will first review the formulae and elucidate how to calculate the EPC matrix by constructing WFs. Then we will introduce our code along with its workflow on PWmat and present our test results of two classical semiconductor systems Al As and Si, showing consistency with EPW. Next, the EPC matrix of Li Co O_(2), a classical cathode material for lithium-ion batteries, is calculated using different exchange correlation(XC) functionals including LDA, PBE, DFT+U and HSE. A comparison is provided for the related EPC matrix. It shows there could be a significant difference for the EPC matrix elements due to the use of different XC functionals.Our implementation thus opens the way for fast calculation of EPC for the important class of materials, like the transition metal oxides.展开更多
Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewe...Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.展开更多
This work presents a physics-informed neural network approach bridging deep-learning force field and electronic structure simulations,illustrated through twisted two-dimensional large-scale material systems.The deep p...This work presents a physics-informed neural network approach bridging deep-learning force field and electronic structure simulations,illustrated through twisted two-dimensional large-scale material systems.The deep potential molecular dynamics model is adopted as the backbone,and the electronic structure simulation is integrated.Using Wannier functions as the basis,we categorize Wannier Hamiltonian elements based on physical principles to incorporate diverse information from a deep-learning force field model.This information-sharing mechanism streamlines the architecture of our dual-functional model,enhancing its efficiency and effectiveness.This Wannier-based dualfunctional model for simulating electronic band and structural relaxation(WANDER)serves as a powerful tool to explore large-scale systems.By endowing a well-developed machine-learning force field with electronic structure simulation capabilities,the study marks a significant advancement in developing multimodal machine-learning-based computational methods that can achieve multiple functionalities traditionally exclusive to first-principles calculations.Moreover,utilizing Wannier functions as the basis lays the groundwork for predicting more physical quantities.展开更多
基金Support from Ningbo Science Foundation under Grant No.2010A610179also from the Start-Up Fund and K.C.Wong Magna Fund in Ningbo University
文摘I present a method to calculate the ballistic transport properties of atomic-scale structures under bias. The electronic structure of the system is calculated using the Kohn-Sham scheme of density functionai theory （DFT）. The DFT eigenvectors are then transformed into a set of maximaily localized Wannier functions （MLWFs） [N. Maxzari and D. Vanderbilt, Phys. Rev. B 56 （1997） 12847]. The MLWFs are used as a minimai basis set to obtain the Hamitonian matrices of the scattering region and the adjacent leads, which are needed for transport calculation using the nonequilibrium Green＇s function formalism. The coupling of the scattering region to the semi-infinite leads is described by the self-energies of the leads. Using the nonequilibrium Green＇s function method, one calculates self-consistently the charge distribution of the system under bias and evaluates the transmission and current through the system. To solve the Poisson equation within the scheme of MLWFs I introduce a computationally efficient method. The method is applied to a molecular hydrogen contact in two transition metal monatomic wires （Cu and Pt）. It is found that for Pt the I-V characteristics is approximately linear dependence, however, for Cu the I-V characteristics manifests a linear dependence at low bias voltages and exhibits apparent nonlinearity at higher bias voltages. I have also calculated the transmission in the zero bias voltage limit for a single CO molecule adsorbed on Cu and Pt monatomic wires. While a chemical scissor effect occurs for the Cu monatomic wire with an adsorbed CO molecule, it is absent for the Pt monatomie wire due to the contribution of d-orbitals at the Fermi energy,
基金Project supported by the National Natural Science Foundation of China (Grant No 10674087)973 Program (Grant Nos 2006CB921603 and 2008CB317103)+2 种基金the Natural Science Foundation of Shanxi Province of China (Grant No 200611004)NCET(NCET-06-0259)IMR SYNL-T.S. Kê Research Fellowship
文摘The nonlinear Wannier functions in square Kronig-Penney potential are investigated with the help of a set of exact nonlinear Bloch solutions. The nonlinear interaction makes the Wannier functions fall off as non-exponential law with distance and enhances the tunneling coupling between the neighbor sites.
基金Acknowledgements We thank Ji Feng and Xianqing Lin for helpful discussion. This work was supported by the National Basic Research Program of China （Grants No. 2013CB921903 and No. 2012CB921300） and the National Natural Science Foundation of China （Grants Nos. 11274024, 11334001, and 11429402）.
文摘We present a general method for constructing maximally localized Wannier functions. It consists of three steps： （i） picking a localized trial wave function, （ii） performing a full band projection, and （iii） orthonormalizing with the LSwdin method. Our method is capable of producing maximally localized Wannier functions without further minimization, and it can be applied straightforwardly to random potentials without using supercells. The effectiveness of our method is demonstrated for both simple bands and composite bands.
基金Project supported by the National Key Research and Development Program of China(Grant No.2017YFA0302901)the National Natural Science Foundation of China(Grant Nos.11474331,11404383,and 11474004)+1 种基金the Natural Science Foundation of Zhejiang Province,China(Grant No.LY17A040005)the K.C.Wong Magna Fund in Ningbo University
文摘Based on the first-principles density functional theory electronic structure calculation,we investigate the possible phonon-mediated superconductivity in arsenene,a two-dimensional buckled arsenic atomic sheet,under electron doping.We find that the strong superconducting pairing interaction results mainly from the pz-like electrons of arsenic atoms and the A1 phonon mode around the K point,and the superconducting transition temperature can be as high as 30.8 K in the arsenene with 0.2 doped electrons per unit cell and 12%-applied biaxial tensile strain.This transition temperature is about ten times higher than that in the bulk arsenic under high pressure.It is also the highest transition temperature that is predicted for electron-doped two-dimensional elemental superconductors,including graphene,silicene,phosphorene,and borophene.
基金the National Natural Science Foundation of China(Grant Nos.11974194 and 11974207)K.C.Wong Magna Fund in Ningbo University。
文摘Based on density functional first-principles calculations and anisotropic Eliashberg equations,we have investigated the electronic structure,lattice dynamics,and phonon-mediated superconductivity in newly synthesized layered compound Sr BC under pressure.Different from Li BC and Mg B2,our calculations surprisingly reveal that Sr BC is isotropic in compressibility,due to the accumulation of substantial electrons in the interstitial region.We find that the Sr phonons strongly couple with B-2 pz orbital and the interstitial states,giving rise to a two-gap superconductivity in Sr BC,whose transition temperature shows an inverted V-shaped dependence on pressure.The maximal transition temperature is about 22 K at50 GPa.On both sides of 50 GPa,the transition temperature exhibits quasi-linear variation with positive and negative slopes,respectively.Such a variation of transition temperature is infrequent among phonon-mediated superconductors.The competition between enhanced electron–phonon matrix element and hardened phonons plays an essential role in governing the behavior of the critical temperature.
基金supported by the NCCR MARVEL,a National Center of Competence in Research,funded by the Swiss National Science Foundation(grant number 205602)YJ acknowledge support by the China Scholarship Council program+5 种基金JQ acknowledges support by the HORIZON-RIA 2D-PRINTABLE(proposal number:101135196)this work has received funding from the Swiss State Secretariat for Education,Research and Innovation(SERI)NP and GP acknowledge support by the Swiss National Science Foundation(SNSF)Project Funding(grant 200021E_206190 FISH4DIET)WZ acknowledge support by the National Key Research and Development Program of China(Grant No.2022YFB4400200)National Natural Science Foundation of China(Grant Nos.T2394474,T2394470)the Beijing Outstanding Young Scientist Program and Tencent Foundation through the XPLORER PRIZE.We acknowledge access to Piz Daint or Alps at the Swiss National Supercomputing Center,Switzerland under MARVEL's share with the project ID mr32.We acknowledge fruitful discussions with Edward Baxter Linscott and Miki Bonacci.
文摘Maximally-localized Wannier functions(MLWFs)are widely employed as an essential tool for calculating the physical properties of materials due to their localized nature and computational efficiency.Projectability-disentangled Wannier functions(PDWFs)have recently emerged as a reliable and efficient approach for automatically constructing MLWFs that span both occupied and lowest unoccupied bands.Here,we extend the applicability of PDWFs to magnetic systems and/or those including spin-orbit coupling,and implement such extensions in automated workflows.Furthermore,we enhance the robustness and reliability of constructing PDWFs by defining an extended protocol that automatically expands the projectors manifold,when required,by introducing additional appropriate hydrogenic atomic orbitals.We benchmark our extended protocol on a set of 200 chemically diverse materials,as well as on the 40 systems with the largest band distance obtained with the standard PDWF approach,showing that on our test set the present approach delivers a success rate of over 98%in obtaining accurate Wannier-function interpolations,defined as an average band distance below20 meV between the DFT and Wannier-interpolated bands,up to 2 eV above the Fermi level for metals or above the conduction band minimum for insulators(and a 100%success rate when including only bands up to 1 eV above these values).
基金supported by the starting fund of Peking University Shenzhen Graduate SchoolFujian Science&Technology Innovation Laboratory for Energy Devices of China (Grant No. 1C-LAB)+2 种基金the Chemistry and Chemical Engineering Guangdong Laboratory (Grant No. 1922018)the Soft Science Research Project of Guangdong Province (Grant No. 2017B030301013)the Major Science and Technology Infrastructure Project of Material Genome Big-Science Facilities Platform supported by Municipal Development and Reform Commission of Shenzhen。
文摘Electron-phonon coupling(EPC) in bulk materials is an important effect in multifarious physical and chemical phenomena. It is the key to explaining the mechanisms for superconductivity, electronic transport, etc. The EPC matrix describes the coupling of the electronic eigenstates of the studied system under the perturbation of phonons. Although the EPC matrix is closely relevant to many fundamental physicochemical properties, it remains a challenge to calculate the EPC matrix precisely due to the high computational cost. In recent years, Giustino et al. developed the EPW method on open-source ab-initio software Quantum Espresso, which uses Wannier functions(WFs) to calculate EPC matrix. However, due to the limitation of their implementation,it is not possible yet to calculate the EPC matrix under some important computational conditions, e.g., for DFT+U and HSE calculation. Given the importance of these computational conditions(e.g., for transition metal oxides), we have developed our own implementation of EPC matrix calculation based on the domestic ab-initio software PWmat. Our code allows the DFT+U and HSE correction, so we can get a more accurate EPC matrix in the related problems. In this article, we will first review the formulae and elucidate how to calculate the EPC matrix by constructing WFs. Then we will introduce our code along with its workflow on PWmat and present our test results of two classical semiconductor systems Al As and Si, showing consistency with EPW. Next, the EPC matrix of Li Co O_(2), a classical cathode material for lithium-ion batteries, is calculated using different exchange correlation(XC) functionals including LDA, PBE, DFT+U and HSE. A comparison is provided for the related EPC matrix. It shows there could be a significant difference for the EPC matrix elements due to the use of different XC functionals.Our implementation thus opens the way for fast calculation of EPC for the important class of materials, like the transition metal oxides.
基金supported by the Universidad del Pais Vasco/Euskal Herriko Unibertsitatea (Grant No. UFI 11/55)the Ministerio de Economia y Competitividad (Grant No. FIS2012-36673-C03-03)+2 种基金the Basque Government (Grant No. IT472-10)the Helmholtz Gemeinschaft Deutscher-Young Investigators Group (Grant No. VH-NG-717, Functional Nanoscale Structure and Probe Simulation Laboratory)the Impuls und Vernetzungsfonds der HelmholtzGemeinschaft Postdoc Programme
文摘Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients—one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum—are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented.
基金supported by the U.S.Department of Energy,Office of Science,Basic Energy Sciences,under Award No.DE-SC0023664W.G.was supported by the U.S.National Science Foundation under grant No.DMR-2323469The research used resources of the National Energy Research Scientific Computing Center(NERSC),a U.S.Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory,operated under Contract No.DE-AC02-05CH11231 using NERSC award BES-ERCAP0029544.We thank Fei Xue for the valuable discussions.
文摘This work presents a physics-informed neural network approach bridging deep-learning force field and electronic structure simulations,illustrated through twisted two-dimensional large-scale material systems.The deep potential molecular dynamics model is adopted as the backbone,and the electronic structure simulation is integrated.Using Wannier functions as the basis,we categorize Wannier Hamiltonian elements based on physical principles to incorporate diverse information from a deep-learning force field model.This information-sharing mechanism streamlines the architecture of our dual-functional model,enhancing its efficiency and effectiveness.This Wannier-based dualfunctional model for simulating electronic band and structural relaxation(WANDER)serves as a powerful tool to explore large-scale systems.By endowing a well-developed machine-learning force field with electronic structure simulation capabilities,the study marks a significant advancement in developing multimodal machine-learning-based computational methods that can achieve multiple functionalities traditionally exclusive to first-principles calculations.Moreover,utilizing Wannier functions as the basis lays the groundwork for predicting more physical quantities.
