Single particle spectrum of the two dimensional electron gas

Abstract

Accurate spectroscopy has driven advances in chemistry, materials science, and physics. However, despite their importance in the study of highly correlated systems, two-dimensional systems (2DES) have proven difficult to probe spectroscopically. Typical energy scales are on the order of a millielectron volt (meV), requiring high resolution, while correlated states of interest, such as those found in the integer and fractional quantum Hall effect, are destroyed by excessive electron heating. Approaches based on tunneling have been hampered by problems such as ohmic heating and low in-plane conductivity, while optical approaches probe long-wavelength excitations which can be difficult to interpret. Here we present a refined spectroscopic technique, time domain capacitance spectroscopy (TDCS), with which we measure the single particle density of states (DOS) of a 2DES with temperature-limited resolution. In TDCS, sharp voltage pulses disequilibrate a metallic contact from a nearby 2DES, inducing a tunnel current. We detect this current by monitoring the image charge of the tunneled electrons on a distant electrode. No ohmic contact to the 2DES is required. The technique works when the 2DES is empty or has vanishing in-plane conductivity, as frequently occurs in studying the quantum Hall effect. Using TDCS, we perform unprecedentedly high resolution measurements of the DOS of a cold 2DES in GaAs over a range from 15 meV above to 15 meV below the Fermi surface. We provide the first direct measurements of the width of the single-particle exchange gap and single particle lifetimes in the quantum Hall system. At higher energies, we observe the splitting of highly excited Landau levels by spin polarization at the Fermi surface, demonstrating that the high energy spectrum reflects the low temperature ground state in these highly correlated systems. These measurements bring to light the difficult to reach and beautiful structure present far from the Fermi surface.