Inelastic electron and Raman scattering from the collective excitations in quantum wires: Zero magnetic field

Abstract

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 ⩽ n and 1 ⩽ n, m ⩽ 3. This is the road to the (semiconducting) quasi-n dimensional electron gas systems we have been happily traversing on now for almost two 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 unseen in their higher- or lower-dimensional counterparts. This has motivated us to undertake a systematic investigation of the inelastic electron scattering (IES) and the inelastic light scattering (ILS) from the elementary electronic excitations in quantum wires. We begin with the Kubo's correlation functions to derive the generalized dielectric function, the inverse dielectric function, and the Dyson equation for the dynamic screened potential in the framework of Bohm-Pines’ random-phase approximation. These fundamental tools then lead us to develop methodically the theory of IES and ILS for the Q-1DEG systems. As an application of the general formal results, which know no bounds regarding the subband occupancy, we compute the density of states, the Fermi energy, the full excitation spectrum [comprised of intrasubband and intersubband single-particle as well as collective excitations], the loss functions for the IES and the Raman intensity for the ILS. We observe that it is the collective (plasmon) excitations that largely contribute to the predominant peaks in the energy-loss and the Raman spectra. The inductive reasoning is that the IES can be a potential alternative of the overused ILS for investigating collective excitations in quantum wires. We trust that this research work shall be useful to all – from novice to expert and from theorist to experimentalist – who believe in the power of traditional science

Plasmons in spatially separated rolled-up electron-hole double-layer systems

“…18,19 More important, the expression for V l ll 0 nm ðqÞ is nonzero when l þ n ¼ l 0 þ m which yields only the Fourier-transformed toroidal functionQ l À1=2 has to be exploited in calculations(see Fig. 2).…”

“…Two very recent studies have provided us with a thorough and systematic way of the plasmon modes and the inelastic electron/light scattering from the electron excitations in low-dimensional quantum wells and wires. 17,18 Additionally, both spatially separated and unseparated multi-subband Q1D quantum wires with a square-well, cylindrical, or parabolic confinement provide us with designing and creating multi-component SSQP with more than one subband populated. [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] As is well known, any two-component plasma has two branches of collective excitations, high energy optical plasmons (OP), and low energy acoustic plasmons (AP).…”

“…0 appropriate to the long wavelength limit calculations. Now, within the framework of RPA, the generalized frequency dependent dielectric function in our model could then be expressed as a 2 Â 2 matrix given by [17][18][19]21,43,[48][49][50] …”

“…The radius of the hole gas is q h and the electron-hole charge separation in the radial direction is shown by d ¼ jq e À q h j. generalized dielectric matrix is N 2 Â N 2 , where N is the number of subbands in the model. [17][18][19] So as to reduce the complexity we restrict ourselves to a two-subband model in the zero temperature limit where the occupied lowest subband and the empty first excited one are labeled with subindices 0 and 1, respectively. Thus, the dynamic dielectric function can be simplified to an 8 Â 8 matrix to be easily treated in the numeric.…”

Prediction of inelastic light scattering spectra from electronic collective excitations in GaAs/AlGaAs core-multishell nanowires

“…The scattering cross section due to CDEs is obtained from the imaginary part of the momentum-dependent density-density response function (DDRF) [12,28],…”