Two‐dimensional phononless VRH conduction in arrays of Ge/Si quantum dots

Abstract

We report measurements of a two-dimensional variable-range hopping conductance in delta-doped Ge/Si heterostructures with a layer of Ge nanometer-scale quantum dots. We found that the conductance σ vs. temperature T follows the Efros-Shklovskii behavior σ = σ0 exp[−(T0/T ) 1/2 ] with the temperatureindependent prefactor σ 0 ∼ e 2 /h. A strong reduction of the measured value of T 0 from that calculated for single-particle hopping was observed. All these results provide a manifestation of interaction-driven many-electron correlated hopping in dense arrays of quantum dots. IntroductionIn general, the temperature dependence of the conductivity for variable-rangle hopping (VRH) is given by. VRH conductivity in the presence of long-range Hartree interaction between localized single-particle excitations obeys the Efros-Shklovskii (ES) law/κξ is the characteristic interaction energy scale, C is a numerical coefficient that depends on dimensionality, k B is the Boltzmann constant, κ is the relative permittivity of the host lattice, ξ is the localization length of electrons. Within the mechanism of phonon-assisted VRH, the prefactor σ 0 takes the form σ 0 = γ/T m , where γ is a temperature-independent parameter and m ∼ 1 [2]. The theoretical value of the constant C for single-particle hopping in two dimensions (2D) is C 6 [2, 3].Several authors have argued that under certain conditions dc VRH conduction can be dominated by many-particle Coulomb correlations between electronic transitions [4,5]. Sequential correlations appear when the hops of an electron facilitates the hopping probability of another electron due to rearrangement of the local potentials and/or site occupations in the vicinity of the initial and final states for tunneling process. There can be also interaction-driven simultaneous hopping of several electrons resulting in a lowering of the energy configuration of the system. Because formation of such dressed polaron state provides partial screening of Coulomb interaction at large distances, the characteristic interaction energy in correlated hopping is reduced relative to its single-particle value [6,7]. Pérez-Garrido et al. [4] showed that in a regime of many-particle excitations, σ(T ) dependence has the ES form with numerical constant C = 0.6 ± 0.2, i.e., the parameter T 0 turns out to be about one order of magnitude smaller than Efros and Shklovskii's prediction for single-electron hoping. A reduction of hopping constants from the singleparticle value in gated GaAs/AlGaAs heterostructures has been observed in [8]. Kozub, Baranovskii and Shlimak, assuming that interaction-assisted fluctuations of energies of hopping sites have spectral density