We provide a semiclassical theory of tunneling decay in a magnetic field and a three-dimensional potential of a general form. Because of broken time-reversal symmetry, the standard WKB technique has to be modified. The decay rate is found from the analysis of the set of the particle Hamiltonian trajectories in complex phase space and time. In a magnetic field, the tunneling particle comes out from the barrier with a finite velocity and behind the boundary of the classically allowed region. The exit location is obtained by matching the decaying and outgoing WKB waves at a caustic in complex configuration space. Different branches of the WKB wave function match on the switching surface in real space, where the slope of the wave function sharply changes. The theory is not limited to tunneling from potential wells which are parabolic near the minimum. For parabolic wells, we provide a bounce-type formulation in a magnetic field. The theory is applied to specific models which are relevant to tunneling from correlated two-dimensional electron systems in a magnetic field parallel to the electron layer.

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...

We show that in a magnetic field parallel to a two-dimensional ͑2D͒ electron layer, strong electron correlations can change the rate of tunneling from the layer to the 3D continuum exponentially. It leads to a specific density dependence of the escape rate. The mechanism is a dynamical Mössbauer-type recoil, in which the Hall momentum of the tunneling electron is partly transferred to the whole electron system, depending on the interrelation between the rate of interelectron momentum exchange and the tunneling duration. We show that, in a certain temperature range, the parallel magnetic field can enhance rather than suppress the tunneling rate. The effect is due to the field induced energy exchange between the in-plane and out-of-plane motion. A parallel magnetic field can also lead to switchings between tunneling from different intra-well states, and between tunneling and thermal activation. Explicit results are obtained for a Wigner crystal. They are in qualitative and quantitative agreement with the relevant experimental data for electrons on helium, with no adjustable parameters. The theoretical results also suggest new experiments in semiconductor systems which will reveal electron correlations and their dynamical aspects.