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Crossover regimes in lower dimensional structures

Modern growth and fabrication techniques can produce lower dimensional structures in the crossover regime. Such structures in the crossover regime can provide tunability of various properties. For example, a zero-dimensional (0-D) structure evolving towards a 2-D structure shows electronic structure which is neither 0-D-like, nor 2-D-like. Within the crossover regime the electronic density of states (DOS) at Fermi level (Ef) keeps on changing as the size of the system changes. DOS at Ef determines many properties of materials, such as electronic specific heat, spin susceptibility etc. Keeping the importance of DOS at Ef in mind, we determine their values and other details of electronic structure of lower dimensional structures of metals, in the 0-D to 1-D, 1-D to 2-D, 2-D to 3-D, 0-D to 2-D, 0-D to 3-Dand 1-D to 3-Dcrossover regimes, in a simple free electron model. We compare our results with analytical theory and experimental results, wherever available. We also present some results obtained by scanning tunneling spectroscopy measurements on Ag islands on Si(111) evolving from a 0-D to a 2-D structure. This simple model is quite useful in understanding lower dimensional structures in the crossover regimes.