Transport properties of granular systems are governed by Coulomb blockade effects caused by the discreteness of the electron charge. We show that, in the limit of vanishing mean level spacing on the grains, the low-temperature behavior of 1d and 2d arrays is insulating at any inter-grain coupling (characterized by a dimensionless conductance g). In 2d and g ≫ 1, there is a sharp Berezinskii-Kosterlitz-Thouless crossover to the conducting phase at a certain temperature, TBKT. These results are obtained by applying an instanton analysis to map the conventional 'phase' description of granular arrays onto the dual 'charge' representation.
Bibliographical noteFunding Information:
We are grateful to K.B. Efetov, M. Fogler, and A.I. Larkin for valuable discussions. Work at the University of Minnesota was supported by the A.P. Sloan foundation and the NSF Grant DMR04-05212 (AK) and by NSF Grants DMR02-37296, and EIA02-10736 (LG). J.S.M. was partially supported by a Feodor Lynen fellowship of the Humboldt Foundation as well as by the US Department of Energy, Office of Science, under Contract No. W-31-109-ENG-38. Work at the University of Cologne was supported by Sonderforschungsbereich SFB/TR 12 of the Deutsche Forschungsgemeinschaft.
- Coulomb blockade
- Granular arrays
- Metal-insulator transition
- Quantum transport