Hopping Transport in Granular Metals

Andrei Lopatin

Argonne National Laboratory

Granular metals are artificially designed structures that can be viewed as arrays of metallic nanoparticles separated by the insulating substance. In my talk I will review the resent progress achieved in our theoretical understanding of the low temperature transport in the weak coupling

insulating phase.

I will begin with consideration of a strictly periodic system and show that it predicts activation conductivity behavior with the Mott gap entering the activation exponent. The Mott gap is reduced due to the intergranular coupling and vanishes at the certain critical value of the tunneling conductance. Experimentally measured conductivity temperature dependence,

however, is not activation but resembles the Mott-Efros-Shklovskii variable range hopping law. I will explain such behavior in terms of a granular model that takes into account the presence of electrostatic disorder that gives rise to the finite bare density of states in the vicinity of the Fermi

level. The tunneling between the grains is described via multiple cotunneling mechanism. Both elastic and inelastic cotunneling processes are possible; the former dominates at low temperatures/applied electric fields, while the later controls tunneling at high temperatures/fields.

In granular superconductors in the weak coupling regime the transport is governed by the hopping of either electrons or Cooper pairs depending on the relation between the superconducting gap and the charging energy of a single granule: If the local charging energy exceeds the superconducting gap the transport is mediated by single electron hopping, while in the opposite case the transport is dominated by hopping of Cooper pairs. In the former case

at temperatures lower than the superconducting gap the inelastic cotunneling processes are suppressed and this leads to the giant negative magnetoresistance. I will present the transport phase diagram that, in particular, includes a new regime dominated by inelastic cotunneling but

having an activation conductivity temperature behavior.