凝聚态体系中激发态载流子动力学研究

激发态动力学是凝聚态物理中至关重要且富有挑战的科学问题,不仅需要从时间、空间、能量和动量等多个维度来描述,同时还需要考虑各种准粒子的相互作用以及多体效应.本文聚焦凝聚态体系激发态动力学的理论和应用研究,结合含时密度泛函、GW-BSE与面跳跃方法,发展了激发态动力学第一性原理计算软件Hefei-NAMD,构建了可以同时从时间、空间、动量、能量、自旋等多个维度研究凝聚态体系激发态动力学的理论和程序框架,并实现了自旋分辨的GW+real-time BSE(GW+rtBSE)激子动力学.利用这套方法,研究了凝聚态体系激发态动力学的许多问题,包括界面电荷转移动力学、电子空穴复合动力学以及二维TMD材料的谷激子动力学等.这些研究从第一性原理计算的角度,模拟激发态载流子在实空间、能量空间和动量空间的含时演化,为凝聚态体系的激发态动力学及准粒子耦合过程提供了深刻细致的理解.     

密度泛函理论的若干进展

密度泛函理论 (DFT)作为处理非均匀相互作用多粒子体系的近似方法已经在计算凝聚态物理、计算材料科学和计算量子化学诸多领域取得巨大成功并获得广泛应用。然而它也存在一些被广泛关注的弱点或困难。例如关于激发态问题 ,强关联问题和处理大原子数复杂体系方面的困难。本文将针对DFT在以上三方面的问题 ,评述近年来的主要努力和进展。着重介绍最近发展的含时间密度泛函理论 (TDDFT) ,它有可能发展成为处理激发态问题的标准方法。关于强电子关联体系的处理 ,主要介绍LDA以外的新发展 ,包括LDA ++方法和计及动力学平均场理论的LDA +DMFT方法。最后 ,评述DFT框架内的线性标度Order N算法的物理基础和主要策略。该算法将在处理大原子数复杂体系问题上发挥重要作用。     

MgS和MgSe带隙的GW近似修正（英文）

应用基于密度泛函理论下的局域密度近似(DFT-LDA)方法研究了岩石矿结构的MgS和MgSe的晶体结构和能带结构.本文得到稳定结构的晶格常数与已知实验数据相吻合,MgS和MgSe都是间接带隙半导体且带隙值分别为2.74 eV和1.70 eV.尽管本文利用LDA计算的带隙值与之前的理论值很接近,但是局域密度近似常常低估带隙值.因此应用准粒子GW(G是格林函数,W是库伦屏蔽相互作用)近似对MgS和MgSe的带隙值进行了修正,其结果分别为4.15 eV和2.74 eV.GW近似的结果应该是合适的值.     

LSDA+U方法对富勒烯内掺稀土原子的结构和电子结构的理论研究

在密度泛函理论框架下的局域密度近似方法 (LDA)能够准确地给出广延态电子体系的基态电子结构 ,是研究复杂体系的电子结构的一种非常成功的方法。由于这种方法不含参数 ,被广泛地用于微观体系的研究。但是 ,在处理的体系中含有局域电子时 ,由于方法的局限 ,给出的结果与光电子谱等试验结果符合得并不好。LSDA U方法是在局域自旋密度近似的框架下 ,结合模型哈密顿方法 ,对局域电子采用哈伯德模型描述 ,用以改进局域密度近似计算的一种方法。本文利用局域密度近似下的离散变分团簇方法 (DVM )对于内嵌稀土原子的富勒烯Er2 @C82 、Tm @C82 的电子结构进行了第一性原理的计算。对于体系中所含的稀土原子存在强关联的 4f电子 ,在LDA方法计算的基础上 ,考虑 4f电子在位库仑作用 ,用LSDA U方法研究了上述体系 ,得到了可以和XPS和吸收谱相比较的结果。     

MgS和MgSe带隙的GW近似修正

应用基于密度泛函理论下的局域密度近似（DFT-LDA）方法研究了岩石矿结构的 MgS和MgSe的晶体结构和能带结构。本文得到稳定结构的晶格常数与已知实验数据相吻合,MgS和MgSe都是间接带隙半导体且带隙值分别为2.74 eV和1.70 eV。尽管本文利用LDA计算的带隙值与之前的理论值很接近,但是局域密度近似常常低估带隙值。因此应用准粒子GW（G是格林函数,W是库伦屏蔽相互作用）近似 对MgS和MgSe的带隙值进行了修正,其结果分别为4.15eV和2.74 eV。GW近似的结果应该是合适的值。     

MgS和MgSe带隙的GW近似修正

应用基于密度泛函理论下的局域密度近似（DFT-LDA）方法研究了岩石矿结构的 MgS和MgSe的晶体结构和能带结构。本文得到稳定结构的晶格常数与已知实验数据相吻合,MgS和MgSe都是间接带隙半导体且带隙值分别为2.74 eV和1.70 eV。尽管本文利用LDA计算的带隙值与之前的理论值很接近,但是局域密度近似常常低估带隙值。因此应用准粒子GW（G是格林函数,W是库伦屏蔽相互作用）近似 对MgS和MgSe的带隙值进行了修正,其结果分别为4.15eV和2.74 eV。GW近似的结果应该是合适的值。     

LSDA+U方法对富勒烯内掺稀土原子的结构和电子结构的理论研究

在密度泛函理论框架下的局域密度近似方法 (LDA)能够准确地给出广延态电子体系的基态电子结构 ,是研究复杂体系的电子结构的一种非常成功的方法。由于这种方法不含参数 ,被广泛地用于微观体系的研究。但是 ,在处理的体系中含有局域电子时 ,由于方法的局限 ,给出的结果与光电子谱等试验结果符合得并不好。LSDA +U方法是在局域自旋密度近似的框架下 ,结合模型哈密顿方法 ,对局域电子采用哈伯德模型描述 ,用以改进局域密度近似计算的一种方法。本文利用局域密度近似下的离散变分团簇方法 (DVM )对于内嵌稀土原子的富勒烯Er2 @C82 、Tm @C82 的电子结构进行了第一性原理的计算。对于体系中所含的稀土原子存在强关联的 4f电子 ,在LDA方法计算的基础上 ,考虑 4f电子在位库仑作用 ,用LSDA +U方法研究了上述体系 ,得到了可以和XPS和吸收谱相比较的结果。     

旋转受限相互作用玻色系统的相变温度及基态粒子占据率

利用局域密度近似(LDA)导出了简谐势阱中存在弱相互作用的旋转玻色气体发生玻色-爱因斯坦凝聚时的粒子数、相变温度和基态粒子占据率的解析表达式,探讨了粒子间相互作用对相变温度和基态粒子占据率的影响.计算表明,当粒子间的相互作用消失时,所有解析结果均能够与无相互作用的旋转理想玻色气体获得很好的一致.     

II-VI族稀磁半导体微纳结构中的激子磁极化子及其发光

自旋是基本粒子（电子、光子）角动量的内在形式.固体中体现自旋特征的集体电子行为如拓扑绝缘体等是当前凝聚态物理领域关注的焦点,是基态行为.激子作为电子空穴对的激发态且寿命很短,可复合发光,它是否能体现自旋极化主导的行为?对此人们的认识远不如针对基态的电子.激子磁极化子（exciton magnetic polaron,EMP）是由磁性半导体微结构中铁磁自旋耦合态与自由激子相互作用形成的复合元激发,但其研究很有限.本文概述了我们在稀磁半导体微纳米结构中的EMP及其发光动态学光谱、自旋极化激子凝聚态的形成方面取得的一些进展,展望了未来可能在自旋光电子器件、磁控激光、光致磁性等量子技术方面的潜在应用.     

双原子分子激发态势能的自旋相关局域Hartree-Fock密度泛函理论方法

基于自旋相关局域Hartree-Fock (SLHF)势函数，本文提出了一种计算双原子分子激发态势能的密度泛函理论(DFT)方法，并将该方法应用于和的激发态势能曲线的计算。在只考虑交换能的情况下，本文的DFT计算结果与文献中精确方法和Hartree-Fock (HF)方法的结果符合的非常好，说明采用SLHF势函数作为交换势的DFT方法是一个很好的计算激发态势能的方法。本文还计算和探讨了电子的关联势函数和关联能，发现传统的近似方法在较大核间距的情况下大大低估了电子的关联能.     

Microscopic theory of optical excitations,photoluminescence, and terahertz response in semiconductors

This article presents a comprehensive many-body theory for optically excited semiconductors. The coupled equations of motion for the correlation functions of the Coulomb-interacting electron-hole system are derived and solved for different excitation conditions. The generation of a coherent excitonic polarization and its conversion into incoherent populations is analyzed. The spontaneous emission properties of the excited system are evaluated using a fully quantized theory. Luminescence from excitonic and electron-hole plasma populations is computed, and significant hole burning in the exciton center of mass distributions is predicted. It is shown how different excitations states of the many-body system can be identified by their characteristic signatures in the absorption spectra of a terahertz probe field.     

Valence electron photoemission spectrum of semiconductors: ab initio description of multiple satellites

The experimental valence band photoemission spectrum of semiconductors exhibits multiple satellites that cannot be described by the GW approximation for the self-energy in the framework of many-body perturbation theory. Taking silicon as a prototypical example, we compare experimental high energy photoemission spectra with GW calculations and analyze the origin of the GW failure. We then propose an approximation to the functional differential equation that determines the exact one-body Green's function, whose solution has an exponential form. This yields a calculated spectrum, including cross sections, secondary electrons, and an estimate for extrinsic and interference effects, in excellent agreement with experiment. Our result can be recast as a dynamical vertex correction beyond GW, giving hints for further developments.     

All-electron exact exchange treatment of semiconductors: effect of core-valence interaction on band-gap and d-band position

We present the first all-electron full-potential exact exchange (EXX) Kohn-Sham density functional calculations on a range of semiconductors and insulators (Ge, GaAs, CdS, Si, ZnS, C, BN, Ne, Ar, Kr, and Xe). We remove one of the main computational obstacles of such calculations by the use of a highly efficient basis for inversion of the response function. We find that the band gaps are not as close to experiment as those obtained from previous pseudopotential EXX calculations. The locations of d bands, determined using the full-potential EXX method, are in excellent agreement with experiment, irrespective of whether these are core, semicore, or valence states. We conclude that the inclusion of the core-valence interaction is necessary for accurate determination of EXX Kohn-Sham band structures and that EXX alone is not a complete answer to the band-gap problem in semiconductors.     

半导体中光的相干传播理论(Ⅱ)

本文是关于半导体中光的相干传播理论的第二部分。考虑到电子空穴间的相互作用,我们讨论了光波与半导体的相互作用,得到了描述光激发电子空穴极化波的方程。我们指出只有在激发比较弱时,这组方程才可近似为一组线性方程,电子空穴极化波才可以看作玻色场。本文还着重讨论了分立的激子谱线的相干激发,证明了它可以近似等效于一个二能级系统的激发,等效的二能级系统的能级差和激发的程度有关,等效的二能级“原子”的“浓度”由激子波函数的性质决定。 关键词：     

锐钛矿二氧化钛体相缺陷的准粒子能带结构

Quasiparticle band structures of the defective anatase TiO₂ bulk with O vacancy, Ti interstitial and H interstitial are investigated by the GW method within many-body Green''s function theory. The computed direct band gap of the perfect anatase bulk is 4.3 eV, far larger than the experimental optical absorption edge (3.2 eV). We found that this can be ascribed to the inherent defects in anatase which drag the conduction band (CB) edge down. The occupied band-gap states induced by these defects locate close to the CB edge, excluding the possible contribution of these bulk defects to the deep band-gap state below CB as observed in experiments.     

On calculation of multicomponent system composition in lightly doped semiconductors

We propose the model of the multicomponent exciton gas in lightly doped semiconductors. The conditions of the equilibrium approximation are discussed. The complete system of equations for the determination of the gas composition is established. The contribution of the excited states of the particles and the influence of the different interparticle interactions is discussed.     

Electronic structure and absorption spectrum of biexciton obtained by using exciton basis

We approach the biexciton Schrödinger equation not through the free-carrier basis as usually done, but through the free-exciton basis, exciton–exciton interactions being treated according to the recently developed composite boson many-body formalism which allows an exact handling of carrier exchange between excitons, as induced by the Pauli exclusion principle. We numerically solve the resulting biexciton Schrödinger equation with the exciton levels restricted to the ground state and we derive the biexciton ground state as well as the bound and unbound excited states as a function of hole-to-electron mass ratio. The biexciton ground-state energy we find, agrees reasonably well with variational results. Next, we use the obtained biexciton wave functions to calculate optical absorption in the presence of a dilute exciton gas in quantum well. We find an asymmetric peak with a characteristic low-energy tail, identified with the biexciton ground state, and a set of Lorentzian-like peaks associated with biexciton unbound states, i.e., exciton–exciton scattering states. Last, we propose a pump–probe experiment to probe the momentum distribution of the exciton condensate.     

Self-consistent green function approach for calculation of electronic structure in transition metals

We present an approach for self-consistent calculations of the many-body Green function in transition metals. The distinguishing feature of our approach is the use of one-site approximation and the self-consistent quasiparticle wave function basis set obtained from the solution of the Schr?dinger equation with a nonlocal potential. We analyze several sets of skeleton diagrams as generating functionals for the Green function self-energy, including GW and fluctuating exchange sets. Calculations for Fe and Ni revealed stronger energy dependence of the effective interaction and self-energy of the d electrons near the Fermi level compared to s and p electron states.     

X-ray edge spectra — a sea-boson perspective

The well-studied X-ray-edge problem is revisited using the sea-boson method. This approach is contrasted with the well-known theories of Mahan, Nozières and De Dominicis (MND). The present approach does not use the sudden approximation and the holes carry a momentum label unlike in the MND theory. We focus on the case of doped semiconductors rather than metals. The problem of electrons in a partially filled conduction band and holes in the initially hole-depleted valence band is recast in the sea-boson language. The resulting hamiltonian is shown to be equivalent to the electron-phonon hamiltonian with the excitons taking on the role of electrons and intra-conduction band particle-hole excitations known as ‘conductrons’ taking on the role of phonons. It is shown that the excitonic pole in the computed absorption spectra is replaced by a branch cut with a simple radical leading to a broadening of the exicton line due to these many-body effects. A critical comparison is made with the MND theory as well as with relevant experiments.     

Calculation of the coupling constants of many-electron atoms with external fields using expansions in a discrete basis of sturmian-type virtual orbitals

Based on a generalization of the method of Sturmian expansions to the case of many-electron systems, a fundamentally new approach was developed for the construction of a complete set of intermediate states in many-body perturbation theory thereby avoiding integration over states of the continuous spectrum. A complete system of eigenfunctions of the generalized eigenvalue problem for the one-electron Hartree-Fock equation with a factor before the energy operator and fixed values of the Lagrange multipliers is used as a basis of single-particle virtual orbitals for an initial approximation to the eigenfunctions of the Hartree-Fock self-consistent field method. In the case of bound states, the spectrum of the effective operator is purely discrete, thus permitting one to completely eliminate integration over continuum virtual orbitals in applying methods of many-body perturbation theory to atomic and molecular calculations for a number of cases. As a consequence, one manages to avoid a number of the technical difficulties associated with inclusion of such states. The possibilities of the developed approach are illustrated in application to the investigation of the interaction of many-electron atoms with external fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 73–85, August, 1990.