A. V. Lopatin

Granular electronic systems

Granular metals are arrays of metallic particles of a size ranging usually from a few to hundreds of nanometers embedded into an insulating matrix. Metallic granules are often viewed as artificial atoms. Accordingly, granular arrays can be treated as artificial solids with programmable electronic properties. The ease of adjusting electronic properties of granular metals assures them an important role for nanotechnological applications and makes them most suitable for fundamental studies of disordered solids. This review discusses recent theoretical advances in the study of granular metals, emphasizing the interplay of disorder, quantum effects, fluctuations, and effects of confinement. These key elements are quantified by the tunneling conductance between granules

Transport properties of granular metals at low temperatures.

g

Thermodynamics of the superfluid dilute Bose gas with disorder.

, the charging energy of a single granule

Universal description of granular metals at low temperatures: granular Fermi liquid

{E}_{c}

Delocalization in two-dimensional disordered Bose systems and depinning transition in the vortex state in superconductors.

, the mean level spacing within a granule

Thermal transport in granular metals

\ensuremath{\delta}

Microscopic analysis of the superconducting quantum critical point: Finite-temperature crossovers in transport near a pair-breaking quantum phase transition

, and the mean electronic lifetime within the granule

Structural glass on a lattice in the limit of infinite dimensions

\ensuremath{\hbar}∕g\ensuremath{\delta}

Tunneling density of states of granular metals

. By tuning the coupling between granules the system can be made either a good metal for

Insulating state of granular superconductors in a strong-coupling regime

gg{g}_{c}=(1∕2\ensuremath{\pi}d)\mathrm{ln}({E}_{c}∕\ensuremath{\delta})