Tunneling spectroscopy of the two-dimensional electron gas

Abstract

We measure the single particle density of states (DOS) of a two-dimensional electron system (2DES) in a GaAs/AlGaAs heterostructure. Using a technique that we call "Time Domain Capacitance Spectroscopy" (TDCS), we measure the complete current-voltage characteristics for tunneling into the 2DES without making ohmic contacts to it. TDCS detects the tunneling current in regimes difficult to access by conventional methods, such as when the in-plane conductance is low. For the first time we detect the contributions of localized states to the tunneling current. The DOS of an interacting 2DES in the diffusive limit displays logarithmic energy dependence near the Fermi level. Using TDCS, we measure the voltage dependence of the tunneling conductance of a semiconductor 2DES and observe the logarithmic Coulomb anomaly for the first time in 2D systems other than thin metal films. As we increase the density, this suppression in tunneling conductance narrows and recedes. Nevertheless suppression reappears when we apply a magnetic field perpendicular to the 2D plane. We find that the tunneling conductance depends linearly on voltage near zero bias for all magnetic field strengths and electron densities. Moreover, the slopes of this linear gap are strongly field dependent. The data are suggestive of a new model of the tunneling gap in the presence of disorder and screening. We also use TDCS to study the interactions among electronic spins. By applying excitations less than kT, we observe that equilibrium tunneling into spin-polarized quantum Hall states (v=l, 3, 1/3) occurs at two distinct tunneling rates for samples of very high mobility. Some electrons tunnel into the 2DES at a fast rate while the rest tunnel at a rate up to 2 orders of magnitude slower. Such novel double-rate tunneling is not observed at even-integer filling fractions where the 2DES is not spin-polarized. The dependence of the two rates on magnetic field, temperature and tunnel barrier thickness suggests that slow in-plane spin relaxation, possibly related to formation of Skyrmions, leads to a bottleneck for tunneling of electrons.