arXiv:cond-mat/9602104v2 29 Feb 1996 Low frequency shot noise in double-barrier resonant-tunneling GaAs/Al x Ga 1-x As structures in a strong magnetic field Ø. Lund Bø (1) and Yu. Galperin (1,2) (1) Department of Physics, University of Oslo, P. O. Box 1048 Blindern, N 0316 Oslo, Norway, (2) A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia, (May 6, 2019) Low frequency shot noise and dc current profiles for a double-barrier resonant-tunneling structure (DBRTS) under a strong magnetic field applied perpendicular to the interfaces have been studied. Both the structures with 3D and 2D emitter have been considered. The calculations, carried out with the Keldysh Green’s function technique, show strong dependencies of both the current and noise profiles on the bias voltage and magnetic field. The noise spectrum appears sensitive to charge accumulation due to barriere capaci- tances and both noise and dc-current are extremely sensitive to the Landau levels’ broadening in the emitter electrode and can be used as a powerful tool to investigate the latter. As an example, two specific shapes of the levels’ broadening have been considered - a semi-elliptic profile resulting from self- consistent Born approximation, and a Gaussian one resulting from the lowest order cumulant expansion. I. INTRODUCTION In recent years, there has been a great interest in resonant tunneling through double- barrier resonant tunneling structures (DBRTS) (Fig. 1). Such structures have been in focus of many experimental and theoretical investigations since its conception by Tsu and Esaki 1 and first realization of negative differential resistance by Sollner et al. 2 . Many important characteristics of DBRTS have been intensely studied, e.g. dc-properties , phonon assisted tunneling, time dependent processes and frequency response. Noise properties of DBRTS have also been studied both experimentally 3 and theoretically 4–8 . At low temperatures and in the presence of transport current, shot noise is the dominant source of electrical noise. This kind of noise is due to discreteness of the electron charge, and it is sensitive to the degree of correlation between tunneling processes. In general, a correlation leads to an additional frequency dependence of shot noise, as well as to its suppression below the so- called full noise, S(0) = 2e|I dc | (at T = 0) 9 . Here S(ω) is the noise spectrum (see the exact definition below), while I dc is the average dc current. In a mesoscopic conductor having several independent modes of transverse motion (channels), the noise is determined by the partial transmission probabilities T m as 10–12 S ∝ ∑ m T m (1 − T m ), while the conductance goes as G ∝ ∑ m T m . Suppression of the shot noise is thus expected in a phase coherent system when the tunneling probabilities are of the order unity for open quantum channels. Our concern is a DBRTS in a strong magnetic field perpendicular to the interfaces. Mag- netic field is an important tool for sample characterization because it leads to the formation of Landau levels, as well as to drastic modification of electron wave functions. We study the situation when the magnetic field B is applied parallel to the tunneling current I, as schematically illustrated in Fig. 1. In such a configuration, the magnetic field leads to an effectively one-dimensional tunneling problem. Consequently, both the dc current and the noise appear extremely sensitive to the details of the density-of-states behavior. We believe that such a sensitivity can provide a powerful tool to investigate details of the Landau levels’ broadening in resonant tunneling structures. The paper is organized as follows: Section II describes the model Hamiltonian as well as the basic expression from which the current and shot noise profiles will be derived in Section III. In Appendix A and Appendix B the Green’s functions used in our calculations are expanded. 1