Effective Mass Hamiltonian Research Articles

The cell-centered Finite-Volume self-consistent approach for heterostructures: 1D electron gas at the Si–SiO2 interface

Achieving self-consistent convergence with the conventional effective-mass approach at ultra-low temperatures (below 4.2 K) is a challenging task, which mostly lies in the discontinuities in material properties (e.g. effective-mass, electron affinity, dielectric constant). In this article, we develop a novel self-consistent approach based on cell-centered finite-volume discretization of the Sturm–Liouville form of the effective-mass Schrödinger equation and generalized Poisson’s equation (FV-SP). We apply this approach to simulate the one-dimensional electron gas formed at the Si–SiO2 interface via a top gate. We find excellent self-consistent convergence from high to extremely low (as low as 50 mK) temperatures. We further examine the solidity of FV-SP method by changing external variables such as the electrochemical potential and the accumulative top gate voltage. Our approach allows for counting electron–electron interactions. Our results demonstrate that FV-SP approach is a powerful tool to solve effective-mass Hamiltonians.

Texture-induced spin-orbit coupling and skyrmion-electron bound states in a Néel antiferromagnet

We derive effective-mass electron Hamiltonian for a N\'eel antiferromagnet in the presence of a smooth texture of the staggered magnetization. For certain locations of electron band extrema, the texture produces a peculiar and anomalously strong spin-orbit coupling of the scale $\hbar v / L$, with $v$ the Fermi velocity and $L$ the characteristic length scale of the texture. For a Skyrmion texture, this coupling generates electron bound states, whose energy scale is given by the gap $\Delta$ in the electron spectrum. With dopant carriers, such bound states turn the Skyrmion into a charged particle, that can be manipulated by electric field.

Biexcitons in CdSe nanoplatelets: geometry, binding energy and radiative rate.

Biexciton properties in semiconductor nanostructures are highly sensitive to quantum confinement, relative electron-hole masses, dielectric environment and Coulomb correlations. Here we present a variational Quantum Monte Carlo model which, coupled to effective mass Hamiltonians, takes into account all of the above effects. The model is used to provide theoretical assessment on the biexciton ground state properties in colloidal CdSe nanoplatelets. A number of characteristic features is observed: (i) the finite thickness of these systems makes the biexciton geometry depart from the planar square expected in the two-dimensional (2D) limit, and form a distorted tetrahedron instead; (ii) the strong dielectric confinement enhances not only Coulomb attractions but also repulsions, which lowers the ratio of the biexciton-to-exciton binding energy down to EXXb/EXb = 0.07. (iii) EXXb is less sensitive than EXb to lateral confinement, and yet it can reach values above 30 meV, thus granting room temperature stability; (iv) the ratio of biexciton-to-exciton radiative rates, kradXX/kradX, decreases from 3.5 to ∼1 as the platelet area increases. These results pave the way for the rational design of biexciton properties in metal chalcogenide nanoplatelets.

Pressure and Temperature Effects on the Magnetic Properties of Donor Impurities in a GaAs/AlGaAs Quantum Heterostructure Subjected to a Magnetic Field

Abstract: The exact diagonalization method has been used to solve the effective-mass Hamiltonian of a single electron confined parabolically in the GaAs/AlGaAs quantum heterostructure, in the presence of a donor impurity and under the effect of an applied uniform magnetic field. The donor impurity is located at distance (d) along the growth direction which is perpendicular to the motion of the electron in a two-dimensional heterostructure layer. We have investigated the dependence of the magnetization (M) and magnetic susceptibility (χ) of a GaAs/AlGaAs quantum heterostructure nanomaterial on the magnetic field strength (ω_c), confining frequency (ω_o), donor impurity position (d), pressure (P) and temperature (T). Keywords: Exact diagonalization, Donor impurity, Magnetic field, Magnetization, Magnetic susceptibility, Pressure and temperature.

Comparison between Trion and Exciton Electronic Properties in CdSe and PbS Nanoplatelets

The optoelectronic properties of metal chalcogenide colloidal nanoplatelets are often interpreted in terms of excitonic states. However, recent spectroscopic experiments evidence the presence of trion states, enabled by the slow Auger recombination in these structures. We analyze how the presence of an additional charge in trions modifies the emission energy and oscillator strength as compared to neutral excitons. These properties are very sensitive to dielectric confinement and electronic correlations, which we describe accurately using image-charge and variational Quantum Monte Carlo methods in effective mass Hamiltonians. We observe that the giant oscillator strength of neutral excitons is largely suppressedin trions. Both negative and positive trions are redshifted with respect to the exciton, and their emission energy increases with increasing dielectric mismatch between the platelet and its surroundings, which is a consequence of the self-energy potential. Our results are consistent with experiments in the literature, and assess on the validity of previous theoretical approximations.

A simple variational quantum Monte Carlo-effective mass approach for excitons and trions in quantum dots

A computational model is presented to calculate the ground state energy of neutral and charged excitons confined in semiconductor quantum dots. The model is based on the variational Quantum Monte Carlo method and effective mass Hamiltonians. Through an iterative Newton–Raphson process, minimizing the local energy, and (optional) parallelization of random walkers, fast and accurate estimates of both confinement and Coulomb binding energies can be obtained in standard desktop computers. To illustrate the reach of the model, we provide Fortran programs and illustrative calculations for colloidal CdSe nanoplatelets with large lateral dimensions and dielectric confinement, where electronic correlations are strong. The results compare well with exact variational calculations and largely outperform configuration interaction calculations in computational efficiency. Program summaryProgram title: vqmc-emaCPC Library link to program files:https://doi.org/10.17632/dtpyc2pffg.1Licensing provisions: GPLv3Programming language: Fortran 90Nature of problem: Calculation of either exciton or trion ground state energy and wave function in a cuboidal semiconductor nanoplatelet. Hard wall quantum confinement coexists with dielectric confinement (self-energy and Coulomb polarization terms).Solution method: Variational quantum Monte Carlo with effective mass Hamiltonians, integrated into a Newton–Raphson solver. OMP parallelization library can be (optionally) linked.

Electronic States in Nanowires with Hexagonal Cross-Section

The electron spectrum in a uniform nanowire with a hexagonal cross-section is calculated by means of a numerical diagonalization of the effective-mass Hamiltonian. Two basis sets are utilized. The wave-functions of low-lying states are calculated and visualized. The approach has an advantage over mesh methods based on finite-differences (or finite-elements) schemes: non-physical solutions do not arise. Our scheme can be easily generalized to the case of multi-band (Luttinger or Kane) ${\bf k}\cdot{\bf p}$ Hamiltonians. The external fields (electrical, magnetic or strain) can be consistently introduced into the problem as well.

Quantum-Mechanical Explicit Solution for the Confined Harmonic Oscillator Model with the Von Roos Kinetic Energy Operator

Exactly-solvable confined model of the nonrelativistic quantum harmonic oscillator is proposed. Its position-dependent effective mass Hamiltonian is defined via the von Roos kinetic energy operator. The confinement effect to harmonic oscillator potential is included as a result of certain behaviour of the position-dependent effective mass. The corresponding Schrodinger equation in the canonical approach is exactly solved and it is shown that the discrete energy spectrum of the system under consideration depends on the confinement parameter a, von Roos parameters α, β, γ and has a non-equidistant form. Wave functions of the stationary states of the model are expressed through the Gegenbauer polynomials. The limit a → ∞ recovers both equidistant energy spectrum and wave functions of the stationary nonrelativistic harmonic oscillator expressed by Hermite polynomials.

Mapping between conical space and non-relativistic position-dependent effective mass systems

The purpose of this work is to reproduce the dynamic of a neutral quantum particle bounded in a conical surface utilizing a position-dependent effective mass background in the non-relativistic regime. We start this task with the construction of the position-dependent effective mass Hamiltonian, containing the effective potential in the Zhou–Kroemer parametrization. We obtain a differential equation for the mass distribution which could reproduce the exact wavefunctions of a scalar quantum particle constrained to a conical space.

Dominant role of the shear strain induced admixture in spin-flip processes in self-assembled quantum dots

We study theoretically the spin-flip relaxation processes for a single electron in a self-assembled InAs/GaAs quantum dot, using an 8-band kp theory in the envelope function approximation. We show that the dominating channel of spin relaxation is spin admixture induced by symmetry-breaking shear strain, which can be mapped onto two effective spin-phonon terms in a conduction band (effective mass) Hamiltonian that have a similar structure and interfere constructively. Unlike the Dresselhaus coupling that dominates spin relaxation in larger, unstrained dots, the shear strain contribution cannot be modeled by a unique standard term in the Hamiltonian but rather relies on the actual strain distribution in the quantum dot.

Tuning quantum cascade laser wavelength by the injector doping

Tuning the wavelength of emitted radiation is a tremendous feature of quantum cascade lasers which enables their use in various applications. Usually, this tuning is executed by the change of the bias current or the temperature. In this paper, it is demonstrated, both experimentally and theoretically, that yet another possibility of tuning laser wavelength offers the change of doping density. For the experimental demonstration, a set of GaAs/AlGaAs devices emitting in the range 9.3–9.7 µ{rm {m}} was MBE grown and processed. For the theoretical analysis, the simulations that employ nonequilibrium Green’s function formalism, applied to the single-band effective mass Hamiltonian, are used. The analysis shows that the physical mechanism responsible for wavelength-doping correlation is a linear Stark effect. The range of tuning is limited on both low and high doping side. Both these limits are established and discussed.

Cross-section geometry effects in the subband structure and spin-related properties of a HgTe/CdTe nanowire

By means of a multiband effective mass Hamiltonian, a theoretical characterization of the effect of the geometrical features of the confinement profile --in particular, a longitudinal groove-- on the subbands dispersion and spin-related properties of a rectangular HgTe/CdTe nanowire is presented. Through an external electric field applied perpendicular to the wire, the interplay of the induced Rashba spin splitting and these geometrical features is investigated. It is found that by exploiting this interplay a rich complexity of the subband structure arises, permitting the generation and modulation of spin-polarized currents without magnetic fields.

Numerical investigation of triexciton stabilization in diamond with multiple valleys and bands

The existence of polyexcitons, the $N$-body complexes of excitons for $N > 2$ in 3D bulk systems, has been controversial for more than 40 years since its first theoretical suggestion. We investigated the stability of fundamental excitonic complexes in diamond numerically with the stochastic variational method (SVM) and an explicitly correlated Gaussian (ECG) basis. The electron-hole many-body system is described by an effective mass Hamiltonian. Our model includes the effective mass anisotropy and multiple valley and band degrees of freedom. We show that the excitons, trions, biexcitons, charged biexcitons, and triexcitons are stable in diamond. Numerical calculations reproduce from 81% to 86% of the experimentally reported binding energies for neutral bound states.

Persistent spin helices in 2D electron systems

We present a theoretical investigation of persistent spin helices in two-dimensional electron systems with spin-orbit coupling. For this purpose, we consider a single-particle effective mass Hamiltonian with a generalized linear-in-k spin-orbit coupling term corresponding to a quantum well grown in an arbitrary crystallographic direction, and derive the general condition for the formation of the persistent spin helix. This condition applied for the Hamiltonians describing quantum wells with different growth directions indicates the possibility of existence of the persistent spin helix in a wide class of 2D systems apart from the [001] model with equal Rashba and Dresselhaus spin-orbit coupling strengths and the [110] Dresselhaus model.

Electronic structure of Mn-doped InAs nanowires in the magnetic field

An eight-band k→·p→ effective-mass Hamiltonian for narrow-gap zinc-blende semiconductor nanowires in the magnetic field is derived, and then the electronic structures of Mn-doped InAs nanowires are calculated via the derived Hamiltonian. Through the calculation, it is found that the valence band structures of Mn-doped InAs nanowires can be changed greatly when R increases from 3 nm to 10 nm, and the energy interval between two neighbouring valence subbands will become narrower as the increase of the radius R. Meanwhile, we find the ground hole state of Mn-doped InAs nanowires is h0−1/2 in the magnetic field, and the valence band structures will present strong band-crossings because of the behaviors of two special hole states h0−3/2 and h03/2. Additionally, the split energies of the degenerate hole states will saturate at a certain temperature when the temperature T increases to 300 K, while the split energies can up to dozens of meV linearly when the concentration of manganese ions x increases to 0.02. However, the variations of T and x has little influences on the split energies of the degenerate electron states. Finally, we also study the radial probability densities of the electron states and the hole states in Mn-doped InAs nanowires. Surprisingly, a few of peaks will arise in the radial probability densities of the electron states, while there are only one or two peaks in the radial probability densities of the hole states.

Resonant tunneling diodes as energy-selective contacts used in hot-carrier solar cells

Among the four features unique to hot-carrier solar cells (HC-SCs): (i) carrier thermalization time and (ii) carrier equilibration time in the absorber, (iii) energy-selection width and (iv) conductance of the energy-selective contacts (ESCs), requisites of (i)-(iii) for high conversion efficiency have been clarified. We have tackled the remaining issues related to (iv) in the present study. The detailed balance model of HC-SC operation has been improved to involve a finite value of the ESC conductance to find the required values, which in turn has been revealed to be feasible using resonant tunneling diodes (RTDs) consisting of semiconductor quantum dots (QDs) and quantum wells (QWs) by means of a formulation to calculate the conductance of the QD- and QW-RTDs derived using the rigorous solutions of the effective-mass Hamiltonians. Thus, all of the four requisites unique to HC-SCs to achieve high conversion efficiency have been elucidated, and the two requisites related to the ESCs can be fulfilled using the QD- and QW-RTDs.

Physical model for high indium content InGaN/GaN self-assembled quantum dot ridge-waveguide lasers emitting at red wavelengths (λ ~ 630 nm).

We present a physical model for recently demonstrated high indium content self-assembled In0.4Ga0.6N/GaN quantum dot (QD)-based ridge-waveguide lasers emitting at red wavelengths. The strain distribution in the QD is calculated using linear elastic theory with the application of shrink-fit boundary condition at the InGaN/GaN material interface, and the electronic states are evaluated using a single-band effective mass Hamiltonian. A Schrödinger-Poisson self-consistent solver is used to describe the effect of charge screening under current injection. Our theoretical result shows a good match to the measured Hakki-Paoli gain spectrum. Combining the calculated gain spectrum and cavity properties, we have developed a device-level simulation to successfully explain the electrical and optical characteristics of this specific laser. Possible solutions to improving the device performance have been explored.

Nonequilibrium Green's function formulation of intersubband absorption for nonparabolic single-band effective mass Hamiltonian

The formulas are derived that enable calculations of intersubband absorption coefficient within nonequilibrium Green's function method applied to a single-band effective-mass Hamiltonian with the energy dependent effective mass. The derivation provides also the formulas for the virtual valence band components of the two-band Green's functions which can be used for more exact estimation of the density of states and electrons and more reliable treatment of electronic transport in unipolar n-type heterostructure semiconductor devices.

Anisotropic exciton Stark shift in black phosphorus

We calculate the excitonic spectrum of few-layer black phosphorus by direct diagonalization of the effective mass Hamiltonian in the presence of an applied in-plane electric field. The strong attractive interaction between electrons and holes in this system allows one to investigate the Stark effect up to very high ionizing fields, including also the excited states. Our results show that the band anisotropy in black phosphorus becomes evident in the direction dependent field induced polarizability of the exciton.

Supersymmetry and coherent states for the displacement-operator-derived effective mass system

Applying the supersymmetric quantum mechanics approach, we derive shape-invariant trigonometric potentials for the displacement-operator-derived effective mass Hamiltonian. By linearizing the algebra resulting from SUSY-QM factorization of the constructed systems, their coherent states are defined and shown to be exponentially dependent on a function of the quantum numbers.