Ground state of granular metals

Abstract

We argue that for granular metals a sizable fraction of the grains becomes charged because the energy fluctuation of the highest-occupied level of each grain, as predicted by random matrix theory, is larger than the charging energy. We have computed the ground state density of states and the degree of ionization of granular metals. The density of states shows a Coulomb gap around the Fermi energy, produced by the long-range part of the Coulomb interactions, which should dominate transport properties at low temperatures.PACS numbers: 71.70. Ms, 71.25.Mg, 71.55.Jv The effects of intragrain and intergrain electronelectron Coulomb interactions are bound to be very important in granular metals (GM), mainly in the dielectric regime [1]. Intragrain Coulomb interactions are responsible for the charging energy of the grains and for the possible formation of a Hubbard-type gap. On the other hand, in the dielectric regime the long-range intergrain Coulomb interaction could produce a Coulomb gap, a decrease around the Fermi level in the single-particle density of states (DOS) [2].The T l/2 law of variable range hopping conductivity has been extensively found in GM and has been interpreted as a manifestation of the Coulomb gap [3]. Photoemission experiments and tunnel conductivity measurements of GM in the dielectric regime have also been interpreted in terms of the Coulomb gap [4][5][6]. Sheng [7] has given an alternative explanation of both this type of behavior for the dc conductivity and of the DOS in terms of the distribution of charging energies. Pollak and Adkins [8] have argued against this explanation and claimed that the Coulomb model rather than the Hubbard model best represents GM.For the Coulomb gap to exist in GM in the dielectric regime a significant portion of the grains must be charged in the ground state. Whether this is the case and, if so, what the ionization-producing mechanism is remains to be clarified, and it is this problem we wish to address in this Letter.The accepted belief, at least until recently, is that the only two relevant energies are the charging energy of the grains and the interlevel spacing 8 near the highestoccupied level, both due to the microscopic size of the grains. If this were so, the vast majority of the grains would be neutral, since the charging energy is much bigger than this interlevel spacing, and no Coulomb gap could exist.Shklovskii and Efros [1] and more recently Pollak and Adkins [8] have proposed that variations in the "work function" associated with the different crystallographic faces of the grains could be of the same order of magnitude as the charging energies and thus be responsible for their ionization. Chui [9] has claimed that a great variety in grains size is responsible for overcoming the charging energies.In this Letter, we argue that the large variation in energy of the highest-occupied level of neutral grains, due to their random surfaces and small sizes, is the most important disorder energy of the problem which ionizes a large portion of the grains. We...

Coexistence of anomalous field effect and mesoscopic conductance fluctuations in granular aluminium

“…When the grains are very small, surface effects (irregular shapes and sizes) contribute to random changes in the grains potential that are much larger than the mean energy level spacing ∆, and that could be even larger than the charging energy E C . For metallic grains of 5 nm in diameter, Cuevas et al [58] estimate that this effect could by itself ionize more than half of the grains. In our case, by taking the approximate formula ∆ = 1/n(E F )d 3 (d is the diameter of the grains) and the density of states of bulk Al, we get that ∆ is about 4 K.…”

“…[58,59]. When the grains are very small, surface effects (irregular shapes and sizes) contribute to random changes in the grains potential that are much larger than the mean energy level spacing ∆, and that could be even larger than the charging energy E C .…”

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“…For the Coulomb gap to exist in granular metals (in the dielectric regime), a substantial fraction of the grains must be charged in the ground state. We presented strong arguments (Cuevas et al 1993) that the large variation in energy of the highest occupied level of neutral grains ionizes a large portion of the grains. Such variations are due to their random shapes and small sizes.…”