Lifetime of Two-Dimensional Electrons Measured by Tunneling Spectroscopy

For electrons tunneling between parallel two-dimensional electron systems, conservation of in-plane momentum produces sharply resonant current-voltage characteristics and provides a uniquely sensitive probe of the underlying electronic spectral functions. We report here the application of this technique to accurate measurements of the temperature dependence of the electron-electron scattering rate in clean two-dimensional systems. Our results are in qualitative agreement with existing calculations.Comment: file in REVTEX format produces 11 pages, 3 figures available from [email protected]

Tunneling Between a Pair of Parallel Hall Droplets

In this paper, we examine interwell tunneling between a pair of fractional quantum Hall liquids in a double quantum well system in a tilted magnetic field. Using a variational Monte Carlo method, we calculate moments of the intra-Landau level tunneling spectrum as a function of in-plane field component $B_{\parallel}$ and interwell spacing $d$. This is done for variety of incompressible states including a pair of $\nu=1/3$ layers ([330]), pair of $\nu=1/5$ layers ([550]), and Halperin's [331] state. The results suggest a technique to extract interwell correlations from the tunneling spectral data.Comment: 21 pages and 8 figures (included), RevTeX, preprint no. UCSDCU

Electron-electron interactions and two-dimensional - two-dimensional tunneling

We derive and evaluate expressions for the dc tunneling conductance between interacting two-dimensional electron systems at non-zero temperature. The possibility of using the dependence of the tunneling conductance on voltage and temperature to determine the temperature-dependent electron-electron scattering rate at the Fermi energy is discussed. The finite electronic lifetime produced by electron-electron interactions is calculated as a function of temperature for quasiparticles near the Fermi circle. Vertex corrections to the random phase approximation substantially increase the electronic scattering rate. Our results are in an excellent quantitative agreement with experiment.Comment: Revtex style, 21 pages and 8 postscript figures in a separate file; Phys. Rev. B (in press

Tunneling transverse to a magnetic field, and how it occurs in correlated 2D electron systems

We investigate tunneling decay in a magnetic field. Because of broken time-reversal symmetry, the standard WKB technique does not apply. The decay rate and the outcoming wave packet are found from the analysis of the set of the particle Hamiltonian trajectories and its singularities in complex space. The results are applied to tunneling from a strongly correlated 2D electron system in a magnetic field parallel to the layer. We show in a simple model that electron correlations exponentially strongly affect the tunneling rate.Comment: 4 pages, 3 figure

Tunneling Between Parallel Two-Dimensional Electron Gases

The tunneling between two parallel two-dimensional electron gases has been investigated as a function of temperature $T$, carrier density $n$, and the applied perpendicular magnetic field $B$. In zero magnetic field the equilibrium resonant lineshape is Lorentzian, reflecting the Lorentzian form of the spectral functions within each layer. From the width of the tunneling resonance the lifetime of the electrons within a 2DEG has been measured as a function of $n$ and $T$, giving information about the density dependence of the electron-impurity scattering and the temperature dependence of the electron-electron scattering. In a magnetic field there is a general suppression of equilibrium tunneling for fields above $B=0.6$ T. A gap in the tunneling density of states has been measured over a wide range of magnetic fields and filling factors, and various theoretical predictions have been examined. In a strong magnetic field, when there is only one partially filled Landau level in each layer, the temperature dependence of the conductance characteristics has been modeled with a double-Gaussian spectral density.Comment: LaTeX requires REVTeX macros. Eighteen pages. Fourteen postscript figures are included. (All figures have been bitmapped to save space. The original can be requested by email from [email protected]). Accepted for publication in Phys. Rev.

Electronic Spectral Functions for Quantum Hall Edge States

We have evaluated wavevector-dependent electronic spectral functions for integer and fractional quantum Hall edge states using a chiral Luttinger liquid model. The spectral functions have a finite width and a complicated line shape because of the long-range of the Coulomb interaction. We discuss the possibility of probing these line shapes in vertical tunneling experiments.Comment: 4 pages, RevTex, two figures included, to appear as a Rapid Communication in PRB; we updated references which have recently appeared in print and were cited as preprints in our ealier submissio

Itinerant Electron Ferromagnetism in the Quantum Hall Regime

We report on a study of the temperature and Zeeman-coupling-strength dependence of the one-particle Green's function of a two-dimensional (2D) electron gas at Landau level filling factor $\nu =1$ where the ground state is a strong ferromagnet. Our work places emphasis on the role played by the itinerancy of the electrons, which carry the spin magnetization and on analogies between this system and conventional itinerant electron ferromagnets. We discuss the application to this system of the self-consistent Hartree-Fock approximation, which is analogous to the band theory description of metallic ferromagnetism and fails badly at finite temperatures because it does not account for spin-wave excitations. We go beyond this level by evaluating the one-particle Green's function using a self-energy, which accounts for quasiparticle spin-wave interactions. We report results for the temperature dependence of the spin magnetization, the nuclear spin relaxation rate, and 2D-2D tunneling conductances. Our calculations predict a sharp peak in the tunneling conductance at large bias voltages with strength proportional to temperature. We compare with experiment, where available, and with predictions based on numerical exact diagonalization and other theoretical approaches.Comment: 29 pages, 20 figure

Signatures of phonon and defect-assisted tunneling in planar metal-hexagonal boron nitride-graphene junctions

Electron tunneling spectroscopy measurements on van der Waals heterostructures consisting of metal and graphene (or graphite) electrodes separated by atomically thin hexagonal boron nitride tunnel barriers are reported. The tunneling conductance, dI/dV, at low voltages is relatively weak, with a strong enhancement reproducibly observed to occur at around |V| ≈ 50 mV. While the weak tunneling at low energies is attributed to the absence of substantial overlap, in momentum space, of the metal and graphene Fermi surfaces, the enhancement at higher energies signals the onset of inelastic processes in which phonons in the heterostructure provide the momentum necessary to link the Fermi surfaces. Pronounced peaks in the second derivative of the tunnel current, d2I/dV2, are observed at voltages where known phonon modes in the tunnel junction have a high density of states. In addition, features in the tunneling conductance attributed to single electron charging of nanometer-scale defects in the boron nitride are also observed in these devices. The small electronic density of states of graphene allows the charging spectra of these defect states to be electrostatically tuned, leading to “Coulomb diamonds” in the tunneling conductance

Tunneling decay in a magnetic field

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.Comment: 16 pages, 11 figure

Spontaneous Coherence and Collective Modes in Double-Layer Quantum Dot Systems

We study the ground state and the collective excitations of parabolically-confined double-layer quantum dot systems in a strong magnetic field. We identify parameter regimes where electrons form maximum density droplet states, quantum-dot analogs of the incompressible states of the bulk integer quantum Hall effect. In these regimes the Hartree-Fock approximation and the time-dependent Hartree-Fock approximations can be used to describe the ground state and collective excitations respectively. We comment on the relationship between edge excitations of dots and edge magneto-plasmon excitations of bulk double-layer systems.Comment: 20 pages (figures included) and also available at http://fangio.magnet.fsu.edu/~jhu/Paper/qdot_cond.ps, replaced to fix figure