Phononless hopping conduction in two-dimensional layers of quantum dots

Regularities are studied in charge transport due to the hopping conduction of holes along two-dimensional layers of Ge quantum dots in Si. It is shown that the temperature dependence of the conductivity obeys the Efros–Shklovskii law. It is found that the effective localization radius of charge carriers in quantum dots varies nonmonotonically upon filling quantum dots with holes, which is explained by the successive filling of electron shells. The preexponential factor of the hopping conductivity ceases to depend on temperature at low temperatures ($T<10\,$K) and oscillates as the degree of filling quantum dots with holes varies, assuming values divisible by the conductance quantum $e^2/h$. The results obtained indicate that a transition from phonon-assisted hopping conduction to phononless charge transfer occurs as the temperature decreases. The Coulomb interaction of localized charge carriers has a dominant role in these phononless processes.