The remote plasmon polaron

– The Coulomb correlation of a remote electron separated from a two-dimensional electron system (2DES) is studied in the presence of a magnetic field applied perpendicular to the 2DES. The polarization produced by the remote electron is described as the excitation of virtual plasmons in the 2DES. The resulting composite quasi-particle, electron + polarization, is therefore called a plasmon polaron. The ground state energy of this quasi-particle is calculated using second-order perturbation theory and the results are related to recent resonant tunneling experiments. Qualitative agreement of the shift in the resonant tunneling peak with magnetic field is obtained. The electronic Coulomb interaction in a doped semiconductor system leads to exchange and correlation contributions to the electron energy similar to those in metals [1, 2]. It has been recently shown that resonant tunneling can reveal this Coulomb interaction as a shift in the bias position of the tunneling peak. A quantum resonance device was used, consisting of a double barrier and quantum well containing a single two-dimensional electron gas (2DEG) as injector into an “empty” quantum well region [3]. The dependence of the peak position on magnetic field and temperature were studied. A tunneling electron can be regarded in such experiments as a remote electron which is separated from the two-dimensional electron system (2DES) and interacts via the Coulomb interaction with the 2DES left behind. This interaction energy is related to the Coulomb (quasi-) gap obtained in the resonant tunneling experiment of a single electron into a 2DES, and between interacting adjacent 2DESs [3-5]. This general problem has attracted significant theoretical interest, and is well described in high or low field ranges by fully quantum-mechanical or semiclassical descriptions, as appropriate [6-8]. Here () Permanent address: Hakodate National College of Technology, 14-1 Tokura-cho Hakodate, 042 Hokkaido, Japan. E-mail: [email protected] () E-mail: [email protected] () E-mail: [email protected] c © EDP Sciences 236 EUROPHYSICS LETTERS we present an alternative theoretical approach which covers the entire magnetic-field range, and provides an intuitive explanation of the observed tunneling peak voltage shifts in the experiments of Lok et al. [3]. In a previous study, we formulated the problem of a remote electron interacting with the 2DES as a polaron problem, where the 2DES was assumed to be in the (low-density) Wigner crystal state. The electron polarizes the 2DES, and in that density regime this is treated as the excitation of phonons in the 2DES within a discrete phonon model [9]. In that formulation we neglected magnetic fields and the corresponding Landau levels. Using a previous treatment of the electronic state in a metal [2] and the dielectric function of a 2DES [10,11], we extend here our polaron model to arbitrary magnetic fields and to the 2DES liquid state. When a Landau level is fully filled, electrons in that level cannot respond to an external perturbation. Thus, only electrons in partially filled Landau levels are responsible for any local polarization by an external potential. The dielectric function exhibits oscillations reflecting the occupation of Landau levels and the plasmon frequency is modified by this dielectric function. As a consequence, the strength of the Coulomb interaction between the remote electron and the 2DES will be an oscillating function of the magnetic field. This interaction is calculated here within second-order perturbation theory. A remote electron placed a distance d away from the 2DES, which lies on the xy-plane, induces a modulation of the election density n(~r ) of the 2DES. If we denote the position of the j-th electron in the 2DES by ~rj = (xj , yj), the electron density is expressed as