Condensed Matter Physics Commons^™

Schrödinger Theory Of Electrons In Electromagnetic Fields: New Perspectives, Viraht Sahni, Xiao-Yin Pan

Publications and Research

The Schrödinger theory of electrons in an external electromagnetic field is described from the new perspective of the individual electron. The perspective is arrived at via the time-dependent "Quantal Newtonian" law (or differential virial theorem). (The time-independent law, a special case, provides a similar description of stationary-state theory). These laws are in terms of "classical" fields whose sources are quantal expectations of Hermitian operators taken with respect to the wave function. The laws reveal the following physics: (a) in addition to the external field, each electron experiences an internal field whose components are representative of a specific property of the …

Electron Correlations In An Excited State Of A Quantum Dot In A Uniform Magnetic Field, Marlina Slamet, Viraht Sahni

Publications and Research

Electron correlations in a two-electron two-dimensional ‘artificial atom’ or quantum dot (with harmonic confining potential) in the presence of a uniform magnetic field in an excited singlet state are studied via quantal density functional theory (QDFT). QDFT allows for the separation of the electron correlations due to the Pauli exclusion principle and Coulomb repulsion, as well as the determination of the contribution of these correlations to the kinetic energy. The QDFT mapping is from the excited state of the quantum dot to one of noninteracting fermions in their ground state possessing the same basic variables of the density and physical …

Generalization Of The Schrödinger Theory Of Electrons, Viraht Sahni

Publications and Research

The Schrödinger theory for a system of electrons in the presence of both a static and time-dependent electromagnetic field is generalized so as to exhibit the intrinsic self-consistent nature of the corresponding Schrödinger equations. This is accomplished by proving that the Hamiltonian in the stationary-state and time-dependent cases {\hat{H}; \hat{H}(t)} are exactly known functionals of the corresponding wave functions {\Psi; \Psi(t)}, i.e. \hat{H} = \hat{H}[\Psi] and \hat{H}(t) = \hat{H}[\Psi(t)]. Thus, the Schrödinger equations may be written as \hat{H}[\Psi]\Psi = E[\Psi]\Psi and \hat{H}[\Psi(t)]\Psi(t) = i\partial\Psi(t)/\partial t. As a consequence the eiegenfunctions and energy eigenvalues {\Psi; E} of the stationary-state equation, and …

Properties Of The Schrödinger Theory Of Electrons In Electromagnetic Fields, Viraht Sahni, Xiao-Yin Pan

Publications and Research

The Schrödinger theory of electrons in an external electromagnetic field can be described from the perspective of the individual electron via the ‘Quantal Newtonian’ laws (or differential virial theorems). These laws are in terms of ‘classical’ fields whose sources are quantal expectations of Hermitian operators taken with respect to the wave function. The laws reveal the following physics: (a) In addition to the external field, each electron experiences an internal field whose components are representative of a specific property of the system such as the correlations due to the Pauli exclusion principle and Coulomb repulsion, the electron density, kinetic effects, …

Tuning Topological Surface States By Charge Transfer, Zhiyi Chen

Dissertations, Theses, and Capstone Projects

Three-dimensional (3D) topological insulators (TIs), Bi₂Se₃, Bi₂Te₃, Sb₂Te₃, are a class of materials that has non-trivial bulk band structure and metallic surface states. Access to charge transport through Dirac surface states in TIs can be challenging due to their intermixing with bulk states or non-topological two-dimensional electron gas quantum well states caused by bending of electronic bands near the surface. The band bending arises via charge transfer from surface adatoms or interfaces and, therefore, the choice of layers abutting topological surfaces is critical. Surfaces of these 3D TIs …

Electron Correlations In Local Effective Potential Theory, Viraht Sahni, Xiao-Yin Pan, Tao Yang

Publications and Research

Local effective potential theory, both stationary-state and time-dependent, constitutes the mapping from a system of electrons in an external field to one of the noninteracting fermions possessing the same basic variable such as the density, thereby enabling the determination of the energy and other properties of the electronic system. This paper is a description via Quantal Density Functional Theory (QDFT) of the electron correlations that must be accounted for in such a mapping. It is proved through QDFT that independent of the form of external field, (a) it is possible to map to a model system possessing all the basic …

Classical Transport In Disordered Systems, Antonios Papaioannou

Dissertations, Theses, and Capstone Projects

This thesis reports on the manifestation of structural disorder on molecular transport and it consists of two parts. Part I discusses the relations between classical transport and the underlying structural complexity of the system. Both types of molecular diffusion, namely Gaussian and non-Gaussian are presented and the relevant time regimes are discussed. In addition the concept of structural universality is introduced and connected with the diffusion metrics. One of the most robust techniques for measuring molecular mean square displacements is magnetic resonance. This method requires encoding and subsequently reading out after an experimentally controlled time, a phase ϕ to the …

Properties Of Type-Ii Znte/Znse Submonolayer Quantum Dots Studied Via Excitonic Aharonov-Bohm Effect And Polarized Optical Spectroscopy, Haojie Ji

Dissertations, Theses, and Capstone Projects

In this thesis I develop understanding of the fundamental physical and material properties of type-II ZnTe/ZnSe submonolayer quantum dots (QDs), grown via combination of molecular beam epitaxy (MBE) and migration enhanced epitaxy (MEE). I use magneto-photoluminescence, including excitonic Aharonov-Bohm (AB) effect and polarized optical spectroscopy as the primary tools in this work.

I present previous studies as well as the background of optical and magneto-optical processes in semiconductor nanostructures and introduce the experimental methods in Chapters 1 - 3.

In Chapter 4 I focus on the excitonic AB effect in the type-II QDs. I develop a lateral tightly-bound exciton model …

Ultrafast Spectroscopy And Energy Transfer In An Organic/Inorganic Composite Of Zinc Oxide And Graphite Oxide, Jeff A. Secor

Dissertations, Theses, and Capstone Projects

The energy transfers and nature of defect levels of an organic/inorganic composite of Zinc Oxide and Graphite are studied with multidimensional spectroscopy. The edge and surface states of each composite are uncovered using excitation emission experiments showing which defect states are mediating the energy transfer from the metal oxide to the graphite oxide. Multidimensional time resolved spectroscopy further describes the effect of the carbon phase on the energy transfer pathways in the material.

Hohenberg-Kohn Theorems In Electrostatic And Uniform Magnetostatic Fields, Xiao-Yin Pan, Viraht Sahni

Publications and Research

The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby, a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle …

Hohenberg-Kohn Theorems In Electrostatic And Uniform Magnetostatic Fields, Xiao-Yin Pan, Viraht Sahni

Publications and Research

The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary electrostatic field and the constraint of fixed electron number. The HK theorems are generalized for spinless electrons to the added presence of an external uniform magnetostatic field by introducing the new constraint of fixed canonical orbital angular momentum. Thereby a bijective relationship between the external scalar and vector potentials, and the gauge invariant nondegenerate ground state density and physical current density, is proved. A corresponding Euler variational principle …

Hybridized Criticality And Elementary Excitations In Lihof4, Haifu Ma

Dissertations, Theses, and Capstone Projects

In this dissertation, I study the magnetic properties of LiHoF₄. Quantum criticality in rare earth ferromagnet LiHoF₄ is complicated by the presence of strong crystal field and hyperfine interactions resulting, e.g., in incomplete mode softening reported by Rønnow et al. We construct a systematic framework for treating elementary excitations in this material across the phase diagram. These excitations interpolate between purely electronic, nuclear and lattice modes and exhibit two-types of quantum critical softening, both complete (as anticipated by elementary treatments, see e.g. Sachdev) but also incomplete, in close correspondence with nuclear scattering results.

A Static And Dynamic Investigation Of Quantum Nonlinear Transport In Highly Dense And Mobile 2d Electron Systems, Scott A. Dietrich

Dissertations, Theses, and Capstone Projects

Heterostructures made of semiconductor materials may be one of most versatile environments for the study of the physics of electron transport in two dimensions. These systems are highly customizable and demonstrate a wide range of interesting physical phenomena. In response to both microwave radiation and DC excitations, strongly nonlinear transport that gives rise to non-equilibrium electron states has been reported and investigated. We have studied GaAs quantum wells with a high density of high mobility two-dimensional electrons placed in a quantizing magnetic field. This study presents the observation of several nonlinear transport mechanisms produced by the quantum nature of these …

C-Metrics In Gauged Stu Supergravity And Beyond, H. Lu, Justin F. Vázquez-Poritz

Publications and Research

We construct charged generalizations of the dilaton C-metric in various fourdimensional theories, including STU gauged supergravity as well as a one-parameter family of Einstein-Maxwell-dilaton theories whose scalar potential can be expressed in terms of a superpotential. In addition, we present time-dependent generalizations of the dilaton C-metric and dilaton Ernst solutions, for which the time evolution is driven by the dilaton. These C-metric solutions provide holographic descriptions of a strongly-coupled three-dimensional field theory on the background of a black hole, a gravitational soliton, and a black hole undergoing time evolution.

Spontaneous Time-Reversal Symmetry Breaking In Two Dimensional Electronic Systems, Wei Liu

Dissertations, Theses, and Capstone Projects

The discovery of high temperature superconductivity inspired a number of novel proposals, one of which, put forward by C.M.Varma, involves the breaking of time-reversal symmetry to explain the physics of the underdoped pseudogap phase. It was proposed that time-reversal symmetry is spontaneously broken as a result of strong repulsion between the Cu-O electrons to form loop-currents in the system.

In this work, we developed a general theory to study the quantum phase transitions in the 2 dimensional strongly interacting electronic systems in which time-reversal symmetry is spontaneously broken in the ground state. We first applied the theory of magnetic groups …

Transport And Optical Properties Of Low-Dimensional Complex Systems, Andrii Iurov

Dissertations, Theses, and Capstone Projects

Over the last five years of my research work, I, my research was mainly concerned with certain crucial tunneling, transport and optical properties of novel low-dimensional graphitic and carbon-based materials as well as topological insulators. Both single-electron and many-body problems were addressed. We investigated the Dirac electrons transmission through a potential barrier in the presence of circularly polarized light. An anomalous photon-assisted enhanced transmission is predicted and explained in a comparison with the well-known Klein paradox. It is demonstrated that the perfect transmission for nearly-head-on collision in an infinite graphene is suppressed in gapped dressed states of electrons, which is …

Wigner High-Electron-Correlation Regime Of Nonuniform Density Systems: A Quantal-Density-Functional-Theory Study, Douglas Achan, Lou Massa, Viraht Sahni

Publications and Research

The Wigner regime of a system of electrons in an external field is characterized by a low electron density and a high electron-interaction energy relative to the kinetic energy. The low-correlation regime is in turn described by a high electron density and an electron-interaction energy smaller than the kinetic energy. The Wigner regime of a nonuniform-electron-density system is investigated via quantal density functional theory (QDFT). Within QDFT, the contributions of electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects are separately delineated and explicitly defined. The nonuniform-electron-density system studied is that of the Hooke's atom in …

Dynamics And Manipulation Of Nanomagnets, Liufei Cai

Dissertations, Theses, and Capstone Projects

This thesis presents my work on the spin dynamics of nanomagnets and investigates the possibility of manipulating nanomagnets by various means. Most of the work has been published\cite{LC-PRB2010, LC-PRB2012, LC-PRB2013, LC-EPL2014}. Some has been submitted for publication\cite{LC-arxiv2014}. The structure of this thesis is as follows.

In Chapter 1, I present the theory of manipulation of a nanomagnet by rotating ac fields whose frequency is time dependent. Theory has been developed that maps the problem onto Landau-Zener problem. For the linear frequency sweep the switching phase diagrams are obtained on the amplitude of the ac field and the frequency sweep rate. …

Wave Function For Harmonically Confined Electrons In Time-Dependent Electric And Magnetostatic Fields, Hong-Ming Zhu, Jin-Wang Chen, Xiao-Yin Pan, Viraht Sahni

Publications and Research

We derive via the interaction “representation” the many-body wave function for harmonically confined electrons in the presence of a magnetostatic field and perturbed by a spatially homogeneous time-dependent electric field—the Generalized Kohn Theorem (GKT) wave function. In the absence of the harmonic confinement – the uniform electron gas – the GKT wave function reduces to the Kohn Theorem wave function. Without the magnetostatic field, the GKTwave function is the Harmonic Potential Theorem wave function. We further prove the validity of the connection between the GKT wave function derived and the system in an accelerated frame of reference. Finally, we provide …

Wave Function For Time-Dependent Harmonically Confined Electrons In A Time-Dependent Electric Field, Yu-Qi Li, Xiao-Yin Pan, Viraht Sahni

Publications and Research

The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the Harmonic Potential Theorem wave function for the case of the time-independent harmonic confining potential.

Comment On "Density And Physical Current Density Functional Theory", Xiao-Yin Pan, Viraht Sahni

Publications and Research

In this letter to the editor, the authors comment on an earlier article they had published, "Density and Physical Current Density Functional Theory" (Pan, X.-Y. and Sahni, V. (2010), Density and physical current density functional theory. Int. J. Quantum Chem., 110: 2833–2843. doi: 10.1002/qua.22862).

Hohenberg-Kohn Theorem Including Electron Spin, Xiao-Yin Pan, Viraht Sahni

Publications and Research

The Hohenberg-Kohn theorem is generalized to the case of a finite system of N electrons in external electrostatic epsilon(r) = -del nu(r) and magnetostatic B(r) = del x A(r) fields in which the interaction of the latter with both the orbital and spin angular momentum is considered. For a nondegenerate ground state a bijective relationship is proved between the gauge invariant density rho(r) and physical current density j(r) and the potentials {nu(r), A(r)}. The possible many-to-one relationship between the potentials {v(r), A(r)} and the wave function is explicitly accounted for in the proof. With the knowledge that the basic variables …

Hohenberg-Kohn And Percus-Levy-Lieb Proofs Of Density-Functional Theory, Viraht Sahni, Xiao-Yin Pan

Publications and Research

The premise of density-functional theory is that knowledge of the ground-state density uniquely determines the Hamiltonian, and thereby, via solution of the corresponding time-independent Schrodinger equation, all the properties of the system. The density therefore constitutes a basic variable of quantum mechanics. There are at present two paths from the density to the Hamiltonian: the Hohenberg and Kohn proof of the bijectivity between the external potential and the basic variable, and the Percus, Levy, and Lieb constrained-search proof. We argue the Hohenberg- and Kohn-type proof to be the more fundamental, and that this is the case in general when both …

Demonstration Of The Gunnarsson-Lundqvist Theorem And The Multiplicity Of Potentials For Excited States, Yu-Qi Li, Xiao-Yin Pan, Biao Li, Viraht Sahni

Publications and Research

The Gunnarsson-Lundqvist (GL) theorem of density functional theory states that there is a one-to-one relationship between the density of the lowest nondegenerate excited state of a given symmetry and the external potential. As a consequence, knowledge of this excited state density determines the external potential uniquely. [The GL theorem is the equivalent for such excited states of theHohenberg-Kohn (HK) theorem for nondegenerate ground states.] For other excited states, there is no equivalent of the GL or HK theorem. For these states, there thus exist multiple potentials that generate the excited-state density. We show, by example, the satisfaction that the GL …

Wave-Function Functionals For The Density, Marlina Slamet, Xiao-Yin Pan, Viraht Sahni

Publications and Research

We extend the idea of the constrained-search variational method for the construction of wave-function functionals psi[chi] of functions chi. The search is constrained to those functions chi such that psi[chi] reproduces the density rho(r) while simultaneously leading to an upper bound to the energy. The functionals are thereby normalized and automatically satisfy the electron-nucleus coalescence condition. The functionals psi[chi] are also constructed to satisfy the electron-electron coalescence condition. The method is applied to the ground state of the helium atom to construct functionals psi[chi] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle …