Theoretical Design Of Two-Dimensional Functional Materials And Development Of Low-Rank Decomposition Algorithms For Accelerating Hybrid Functional Calculations In Periodic Systems

With balanced accuracy and computational cost,density functional theory(DFT)has been widely used in the research area of physics,chemistry and materials.DFT could provide results agree well with experiments and help explain experimental data,thus it is often used to predict the properties of new materials.One main part of our work is the research of two-dimensional(2D)functional materials and their applica-tions in spintronics and optoelectronics by first-principles density functional theory cal-culations.We propose a series of 2D giant tunable Rashba semiconductors,design spin field-effect transistors and highly-efficient heterojunction solar cells based on novel 2D semiconductors.Moreover,the accuracy of DFT depends mainly on the applied exchange-correlation functional.Semilocal functionals underestimate band gaps of semiconduc-tors,while Heyd-Scuseria-Emzerhof(HSE06)functional could provide systematically better results of transition metals and their compounds by including nonlocal Hartree-Fock exchange energy.However,the calculation of Fock energy constitute more than 95%of all computational time by conventional methods,which limits the application of hybrid functionals in large systems.In recent years,Adaptively Compressed Exchange Operator-interpolative separable density fitting(ACE-ISDF)method is proposed and developed to significantly reduce the computational cost associated with the exchange operator,hybrid functionals with ACE-ISDF method have comparable computational cost with semilocal functionals(O(Ne3)).One of our main work is applying ACE-ISDF method to periodic systems,its computational cost scales cubically with respect to the number of electrons,and quasilinearly with respect to the number of k points.The first chapter is an introduction about our research area.We introduce several 2D semiconductors,talk about the structures and principles of some devices in spin-tronics and optoelectronics.The design of devices require proper materials,while we need accurate methods to study the properties of materials(such as bandgaps and the position of energy levels)theoretically.Thus we also refer to hybrid functionals and study related algorithms.The second chapter provides an introduction to basic theories.We start from the many-body quantum systems,discuss the Hartree-Fock method and its limitations,then introduce DFT.DFT is a computational method investigating electronic structure of many-body systems,it replace the 3N dimensional(N is the number of electrons)many-body wave function with 3 dimensional charge density as the fundamental quantity of a system,which reduces computational cost significantly.Within the Kohn-Sham DFT framework,the intractable many-body problem is reduced to a problem of noninteract-ing electrons moving in the effective potential,while the accurate form of exchange-correlation functional is unknown and needs approximation.We have also introduced some common functionals and DFT softwares.In the third chapter.we study the two-dimensional giant tunable Rashba semi-conductors with two-atom-thick buckled honeycomb structure(BHS).Spin field-effect transistors(SFETs)based on the Rashba spin splitting could efficiently manipulate the spin of electrons electrically,while seeking desirable Rashba semiconductors with large Rashba constant and strong electric-field response to preserve the electron spin coher-ence in SFETs remains a key challenge.Herein we propose a series of 2D Rashba semiconductors with two-atom-thick buckled honeycomb structure(BHS)according to high-throughput first-principles density functional theory calculations.We find that these BHS semiconductors show large Rashba constants and are favorable to be in-tegrated into nanodevices superior to conventional bulk materials,among which 2D AlBi monolayer has the largest Rashba constant(2.77 eVA)of all 2D Rashba materials reported so far.We also propose a Rashba descriptor to estimate Rashba constants of BHS semiconductors without electronic structure calculations.Furthermore,these BHS semiconductors are demonstrated to be fabricated by mechanical exfoliation or chemi-cal vapor deposition in experiments.In particular,2D BiSb monolayer is a promising candidate for SFETs due to its large Rashba constant(1.94 eVA),strong electric field response(0.92 eA2)and short spin channel length(158 nm without strain,42 nm with strain).In the fourth chapter,we design highly-efficient heterojunction solar cells based on 2D tellurene and transition metal dichalcogenides(TMDs).In this work,by using first-principles density functional theory calculations,we demonstrate that tellurene is a promising candidate for designing highly-efficient solar cells superior to existing 2D semiconductors,since it has desirable optoelectronic properties,including ideal band gap,high carrier mobility,strong visible light absorption and high stability in ambient conditions.Furthermore,tellurene and TMDs show desirable type ? band alignment,strong CBM and VBM charge separation and enhanced sunlight absorption for con-structing highly-efficient heterojunction solar cells.In particular,we find the calculated maximum power conversion efficiency of Te/WTe2 and Te/MoTe2 heterojunction solar cells reach 22.5%and 20.1%,respectively,which is superior to other contemporary 2D heterojunction solar cells.The fifth chapter is about low-rank decomposition algorithms of hybrid function-als in periodic systems.The product of Fock exchange operator and occupied orbitals is the most time consuming step in DFT calculations.The recently developed adaptively compressed exchange operator(ACE)and interpolative separable density fitting(ISDF)methods could reduce the computational cost associated with exchange operator.ACE method is a low-rank decomposition of the exchange operator in the space spanned by occupied orbitals.It converts Fock operator to ACE operator,and the use of ACE opera-tor instead of Fock operator in inner Hamiltonian diagonalization loops could reduce the number of products between Fock operator and wave function significantly,thus reduce the preconstant of time complexity of hybrid functional calculations.ISDF method is a low-rank decomposition of the product of orbitals,it reduces the number of Poisson equations to be solved from O(Ne2)to O(Ne)(Ne is the number of electrons),thus the time complexity of Fock energy is reduced to O(Ne3)from O(Ne4).ACD-ISDF method,the combination of ACE and ISDF methods,successfully reduces the time complexity of hybrid functional calculations to the semilocal functional level.We apply the ACE-ISDF method to periodic systems,derive the form of related formulas,and apply Fourier convolution to reduce the time complexity with respect to the number of k points(Nk)from quadratic to quasilinear(Nklog(Nk)),and the cost with respect to the number of electrons is still cubic.