Enhancement of Tunneling from a Correlated 2D Electron System by a Many-Electron Mössbauer-Type Recoil in a Magnetic Field

Abstract

We consider the effect of electron correlations on tunneling from a 2D electron layer in a magnetic field parallel to the layer. A tunneling electron can exchange its momentum with other electrons, which leads to an exponential increase of the tunneling rate compared to the single-electron approximation. The effect depends on the interrelation between the dynamics of tunneling and momentum exchange. The results explain and provide a no parameter fit to the data on electrons on helium. We also discuss tunneling in semiconductor heterostructures.PACS numbers: 73.40. Gk, 73.50.Jt Low density two-dimensional electron systems (2DES) in semiconductor heterostructures and on liquid helium are among the most ideal many-electron systems. Such systems display strong effects of the electron-electron interaction, including those specifically related to electron correlations [1,2]. They show up dramatically in various unusual transport properties. One of the most broadly used techniques for investigating many-electron effects is tunneling [3], a recent example being the observation [4] of the giant increase of interlayer tunneling in doublelayer heterostructures, apparently related to the onset of interlayer correlations.For electrons on helium, an exponentially strong deviation from the single-electron rate of tunneling transverse to a magnetic field has been known experimentally since 1993 [5], but remained unexplained. Such a field couples the tunneling motion away from the 2DES to the in-plane degrees of freedom. The effect of the field and the role of electron correlations cannot be described by a simple phenomenological tunneling Hamiltonian.In this paper we provide a theory of tunneling from a correlated 2DES in a magnetic field B parallel to the electron layer. We show, using the model of a Wigner crystal (WC), that the tunneling is affected by the interelectron momentum exchange and its dynamics, which is largely determined by short-range order. We discuss tunneling from 2DES on helium and in single quantum well heterostructures. The results explain and give a no parameter fit to the experimental data [5], see Fig. 1. They suggest new types of experiments which involve tunneling through broad barriers and will be sensitive to short-range order in a 2DES.Electron correlations change the tunneling rate by effectively decreasing the single-electron magnetic barrier. This barrier emerges because, when an electron tunnels from the layer (in the z-direction), it acquires an in-plane Hall velocity v H = ω c z in the B ×ẑ direction and the corresponding in-plane kinetic energy mω 2 c z 2 /2, where ω c = eB/mc is the cyclotron frequency. Respectively, the energy for motion along the z-axis is decreased, or the tunneling barrier is increased by mω 2 c z 2 /2. In a correlated 2DES, the tunneling electron exchanges its Hall momentum with other electrons, thus decreasing the energy loss [6]. This is somewhat similar to the Mössbauer effect where the momentum of a gamma quantum is given to the crystal as a whole [7]. In our ca...

Tunneling decay in a magnetic field

“…Here we will made a further simplification and think of an electron as tunneling in a static potential created by all other electrons. As we showed earlier, this is a good approximation for the tunneling problem 11 . The static potential from surrounding electrons can be assumed to be parabolic with respect to the in-plane coordinates x, y.…”

“…This system was experimentally investigated in Ref. 10 , and showed an unexpected dependence of the tunneling rate on B and electron density that we recently addressed 11,23 .…”

“…The major effect on tunneling comes from highfrequency in-plane vibrations, which have large density of states 11 . Therefore it is not unreasonable to use the Einstein model of the Wigner crystal, in which all vibrations have same frequency ω 0 .…”

“…This change, in turn, strongly depends on properties of the system, as in the well-known effect of giant hopping magnetoresistance in solids 1 . Therefore tunneling in a magnetic field has been broadly used as a sensitive and revealing probe of electron systems in solids, including quantum Hall systems 2-5 , two-layer heterostructures away from the quantum Hall region [6][7][8][9] , and correlated electron layers on the surface of liquid helium 10,11 . Correlated two-dimensional (2D) electron systems are currently attracting much interest 12 .…”

Tunneling from a correlated two-dimensional electron system transverse to a magnetic field

“…A theoretical framework for analysis of the problem at zero temperature was outlined in our recent communications. 6,7 The physics of the effects we discuss relies on the fact that a magnetic field B parallel to a 2DES couples the outof-plane tunneling motion of an electron to the in-plane motion. For an isolated electron, which is separated from the continuum by a 1D potential barrier U(z), see Fig.…”