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Register a new userInelastic electron and light scattering from the elementary electronic excitations in quantum wells: Zero magnetic field
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Authors
Manvir S. Kushwaha
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The most fundamental approach to an understanding of electronic, optical, and transport phenomena which the condensed matter physics (of conventional as well as nonconventional systems) offers is generally founded on two experiments: the inelastic electron scattering and the inelastic light scattering. This work embarks on providing a systematic framework for the theory of inelastic electron scattering and of inelastic light scattering from the electronic excitations in GaAs/Ga$_{1-x}$Al$_{x}$As quantum wells. To this end, we start with the Kubos correlation function to derive the generalized nonlocal, dynamic dielectric function, and the inverse dielectric function within the framework of Bohm-Pines random-phase approximation. This is followed by a thorough development of the theory of inelastic electron scattering and of inelastic light scattering. The methodological part is then subjected to the analytical diagnoses which allow us to sense the subtlety of the analytical results and the importance of their applications. The general analytical results, which know no bounds regarding, e.g., the subband occupancy, are then specified so as to make them applicable to practicality. After trying and testing the eigenfunctions, we compute the density of states, the Fermi energy, the full excitation spectrum made up of intrasubband and intersubband -- single-particle and collective (plasmon) -- excitations, the loss functions for all the principal geometries envisioned for the inelastic electron scattering, and the Raman intensity, which provides a measure of the real transitions induced by the (laser) probe, for the inelastic light scattering...
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The nanofabrication technology has taught us that an $m$-dimensional confining potential imposed upon an $n$-dimensional electron gas paves the way to a quasi-($n-m$)-dimensional electron gas, with $m le n$ and $1le n, m le 3$. This is the road to the (semiconducting) quasi-$n$ dimensional electron gas systems we have been happily traversing on now for almost three decades. Achieving quasi-one dimensional electron gas (Q-1DEG) [or quantum wire(s) for more practical purposes] led us to some mixed moments in this journey: while the reduced phase space for the scattering led us believe in the route to the faster electron devices, the proximity to the 1D systems left us in the dilemma of describing it as a Fermi liquid or as a Luttinger liquid. No one had ever suspected the potential of the former, but it took quite a while for some to convince the others on the latter. A realistic Q-1DEG system at the low temperatures is best describable as a Fermi liquid rather than as a Luttinger liquid. In the language of condensed matter physics, a critical scrutiny of Q-1DEG systems has provided us with a host of exotic (electronic, optical, and transport) phenomena revealing their unparallel behavior characteristics unseen in their higher or lower dimensional counterparts. Here, we embark on the systematic investigation of the inelastic electron scattering (IES) and of inelastic light scattering (ILS) from the elementary electronic excitations in quantum wires in the absence of an applied magnetic field. To that end, we begin with the Kubos correlation functions to derive the generalized nonlocal, dynamic dielectric function, the inverse dielectric function, and the Dyson equation for the dynamic screened potential in the framework of Bohm-Pines full and famous random-phase approximation...
We predict inelastic light scattering spectra from electron collective excitations in a coaxial quantum well embedded in a core-multishell GaAs/AlGaAs nanowire. The complex composition, the hexagonal cross section and the remote doping of typical samples are explicitly included, and the free electron gas is obtained by a DFT approach. Inelastic light scattering cross sections due to charge and spin collective excitations belonging to quasi-1D and quasi-2D states, which coexist in such radial heterostructures, are predicted in the non-resonant approximation from a fully three-dimensional multi-subband TDDFT formalism. We show that collective excitations can be classified in azimuthal, radial and longitudinal excitations, according to the associated density fluctuations, and we suggest that their character can be exposed by specific spectral dispersion of inelastic light scattering along different planes of the heterostructure.
We study the electron spin relaxation in both symmetric and asymmetric GaAs/AlGaAs quantum wells (QWs) grown on (110) substrates in an external magnetic field B applied along the QW normal. The spin polarization is induced by circularly polarized light and detected by time-resolved Kerr rotation technique. In the asymmetric structure, where a {delta}-doped layer on one side of the QW produces the Rashba contribution to the conduction-band spin-orbit splitting, the lifetime of electron spins aligned along the growth axis exhibits an anomalous dependence on B in the range 0<B<0.5 T; this results from the interplay between the Dresselhaus and Rashba effective fields which are perpendicular to each other. For larger magnetic fields, the spin lifetime increases, which is the consequence of the cyclotron motion of the electrons and is also observed in (001)-grown quantum wells. The experimental results are in agreement with the calculation of the spin lifetimes in (110)- grown asymmetric quantum wells described by the point group Cs where the growth direction is not the principal axis of the spin-relaxation-rate tensor.
Oscillations of the real component of AC conductivity $sigma_1$ in a magnetic field were measured in the n-AlGaAs/GaAs structure with a wide (75 nm) quantum well by contactless acoustic methods at $T$=(20-500)~mK. In a wide quantum well, the electronic band structure is associated with the two-subband electron spectrum, namely the symmetric (S) and antisymmetric (AS) subbands formed due to electrostatic repulsion of electrons. A change of the oscillations amplitude in tilted magnetic field observed in the experiments occurs due to crossings of Landau levels of different subbands (S and AS) at the Fermi level. The theory developed in this work shows that these crossings are caused by the difference in the cyclotron energies in the S and AS subbands induced by the in-plane magnetic field.
The influence of a longitudinal magnetic field on the Coulomb drag current created in the ballistic transport regime in a quantum well by a ballistic current in a nearby parallel quantum well is investigated. We consider the case where the magnetic field is so strong that the Larmour radius is smaller than the width of the well. Both in Ohmic and non-Ohmic case, sharp oscillations of the drag current as a function of the gate voltage or chemical potential are predicted. We also study dependence of the drag current on the voltage $V$ across the driving wire, as well as on the magnetic field $B$. Studying the Coulomb drag one can make conclusions about the electron spectrum and and electron-electron interaction in quantum wells.
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