Two-dimensional hopping conductivity in a delta-doped GaAs/AlxGa1-xAs heterostructure

We present zero magnetic-field resistivity measurements of the variable-ran ge hopping (VRH) in a two-dimensional electron gas created at a delta-doped GaAs/AlxGa1-xAs heterostructure. When either the temperature or carrier de nsity are reduced the longitudinal resistivity shows a crossover from two-d imensional Mott VRH, rho(T)= rho(M) exp (T-M/T)(1/3) to Efros-Shklovskii (E S) Coulomb-gap behavior rho(T) = rho(ES) exp (T-ES/T)(1/2). In both regimes , near the crossover, the data collapse onto universal curves with a temper ature independent prefactor rho(M)approximate to(1/2)(h/E-2) Or rho(ES)appr oximate to h/e(2). The latter result is in close agreement with measurement s of Si metal-oxide-semiconductor held-effect transistors. We discuss the p ossible implications of our data on the theory of phonon-assisted VRH. [S01 63-1829(99)01108-X].