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Inmaculada Murillo Leo , Manuel Lopez Granados , Jose Luis Garcia Fierro , Rafael Mariscal
催化学报 doi:10.1016/S1872-2067(14)60086-3
关键词:
Journal of Mathematical Chemistry
Semiclassical theory has been used, with some success, to discuss Anderson localization due to disorder. Our attention is focused on the quantum-chemical network model via a Boltzmann-like equation, and Garcia-Garcia's semiclassical approach, contacted with early work of Care and March on compensated semiconductor. This work is related with the recent semiclassical treatment on the effect of disorder on the nature of electron states in the quantum-chemical network model.
关键词: Anderson localization;Semiclassical theory;Critical exponent;Disorder;Dimensionality;Scaling;metal-insulator-transition;ising lattices;systems;models;semiconductors;dimensions;conduction;electrons;solids;states
Journal of Physics and Chemistry of Solids
Using Wegner's result relating critical exponents s and v for conductivity and localization length, respectively, via dimensionality d and that for v given by Garcia-Garcia, we derive what we term a semiclassical (Sc) relation for v in terms of s, which is independent of dimensionality. Forming the ratio s/v versus d from the above relations, s/v = 0 at d = 2 is due to a singularity in the sc relation for v. We argue that, in reality, s/v = 0 results from s being zero at d = 2. Finally we conjecture that (i) Wegner's prediction s/v = 1 when d = 3 and (ii) v tends to 1/2 at large s, are both insensitive to interactions. (C) 2011 Elsevier Ltd. All rights reserved.
关键词: Electronic materials;Semiconductors;Critical phenomena;Electrical;conductivity;Phase transitions;disordered-systems;magnetic-field;2 dimensions
