2 research outputs found
Order Parameter Description of the Anderson-Mott Transition
An order parameter description of the Anderson-Mott transition (AMT) is
given. We first derive an order parameter field theory for the AMT, and then
present a mean-field solution. It is shown that the mean-field critical
exponents are exact above the upper critical dimension. Renormalization group
methods are then used to show that a random-field like term is generated under
renormalization. This leads to similarities between the AMT and random-field
magnets, and to an upper critical dimension for the AMT. For
, an expansion is used to calculate the critical
exponents. To first order in they are found to coincide with the
exponents for the random-field Ising model. We then discuss a general scaling
theory for the AMT. Some well established scaling relations, such as Wegner's
scaling law, are found to be modified due to random-field effects. New
experiments are proposed to test for random-field aspects of the AMT.Comment: 28pp., REVTeX, no figure
Electronic excitations and the tunneling spectra of metallic nanograins
Tunneling-induced electronic excitations in a metallic nanograin are
classified in terms of {\em generations}: subspaces of excitations containing a
specific number of electron-hole pairs. This yields a hierarchy of populated
excited states of the nanograin that strongly depends on (a) the available
electronic energy levels; and (b) the ratio between the electronic relaxation
rate within the nano-grain and the bottleneck rate for tunneling transitions.
To study the response of the electronic energy level structure of the nanograin
to the excitations, and its signature in the tunneling spectrum, we propose a
microscopic mean-field theory. Two main features emerge when considering an Al
nanograin coated with Al oxide: (i) The electronic energy response fluctuates
strongly in the presence of disorder, from level to level and excitation to
excitation. Such fluctuations produce a dramatic sample dependence of the
tunneling spectra. On the other hand, for excitations that are energetically
accessible at low applied bias voltages, the magnitude of the response,
reflected in the renormalization of the single-electron energy levels, is
smaller than the average spacing between energy levels. (ii) If the tunneling
and electronic relaxation time scales are such as to admit a significant
non-equilibrium population of the excited nanoparticle states, it should be
possible to realize much higher spectral densities of resonances than have been
observed to date in such devices. These resonances arise from tunneling into
ground-state and excited electronic energy levels, as well as from charge
fluctuations present during tunneling.Comment: Submitted to the Physical Review