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Register a new userExploring the magnetoroton excitations in quantum wires: Inverse dielectric functions
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Authors
Manvir S. Kushwaha
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A theoretical investigation has been made of the magnetoplasmon excitations in a quantum wire characterized by a confining harmonic potential and subjected to a perpendicular magnetic field. We study the (nonlocal, dynamic) inverse dielectric function to examine the charge-density excitations within a two-subband model in the framework of Bohm-Pines random-phase approximation. A particular stress is put on the (intersubband) magnetoroton excitation which changes the sign of its group velocity twice before merging with the respective single-particle continuum. It has already been suggested that the electronic device based on such magnetoroton excitations can act as an {it active} laser medium [see, e.g., Phys. Rev. B {bf 78}, 153306 (2008)]. Scrutinizing the real and imaginary parts of the inverse dielectric function provides us with an important information on the longitudinal and transverse (Hall) resistances of the system.
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Motivated by the recent experiment of Hochgraefe et al., we have investigated the magnetoplasmon excitations in a periodic array of quantum wires with a periodic modulation along the wire direction. The equilibrium and dynamic properties of the system are treated self-consistently within the Thomas-Fermi-Dirac-von Weizsaecker approximation. A calculation of the dynamical response of the system to a far-infrared radiation field reveals a resonant anticrossing between the Kohn mode and a finite-wavevector longitudinal excitation which is induced by the density modulation along the wires. Our theoretical calculations are found to be in excellent agreement with experiment.
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...
A theoretical investigation has been made of the magnetoplasmon excitations in a quasi-one-dimensional electron system comprised of vertically stacked, self-assembled InAs/GaAs quantum dots. The smaller length scales involved in the experiments impel us to consider a perfectly periodic system of two-dimensionally confined InAs quantum dot layers separated by GaAs spacers. Subsequent system is subjected to a two-dimensional confining (harmonic) potential in the x-y plane and an applied magnetic field (B) in the symmetric gauge. This scheme defines virtually a system of quantum wire comprised of vertically stacked quantum dots (VSQD). We derive and discuss the Dyson equation, the generalized (nonlocal and dynamic) dielectric function, and the inverse dielectric function for investigating the single-particle and collective (magnetoplasmon) excitations within the framework of (full) random-phase approximation (RPA). As an application, we study the influence of the confinement potential and the magnetic field on the component eigenfunctions, the density of states (DOS), the Fermi energy, the collective excitations, and the inverse dielectric functions. These findings demonstrate, for the very first time, the significance of investigating the system of VSQD subjected to a quantizing magnetic field. Given the edge over the planar quantum dots and the foreseen applications in the single-electron devices and quantum computation, investigating the system of VSQD is deemed vital. The results suggest exploiting magnetoplasmon qubits to be a potential option for implementing the solemn idea of quantum state transfer in devising quantum gates for the quantum computation and quantum communication networks.
We study the conductance threshold of clean nearly straight quantum wires in the magnetic field. As a quantitative example we solve exactly the scattering problem for two-electrons in a wire with planar geometry and a weak bulge. From the scattering matrix we determine conductance via the Landauer-Buettiker formalism. The conductance anomalies found near 0.25(2e^2/h) and 0.75(2e^2/h) are related to a singlet resonance and a triplet resonance, respectively, and survive to temperatures of a few degrees. With increasing in-plane magnetic field the conductance exhibits a plateau at e^2/h, consistent with recent experiments.
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