Size-dependent energy scales in the ideal fermi gas |
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Authors: | V Subrahmanyam M Barma |
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Institution: | Tata Institute of Fundamental Research , Homi Bhabha Road, Bombay, 400 005, India |
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Abstract: | Abstract The simplest model for the electronic properties of small metal particles is an ideal Fermi gas confined to a finite volume. When the confining region of size L has a regular shape such as a sphere or a cube, there are two distinct scales of energy which characterize the spectrum of eigenvalues near the Fermi energy EF ≡ ?2 k 2 f/2m. The inner scale δ ~ EF /(kFL)2 is the mean spacing between successive energy levels, while the outer energy scale Δ ~ EF /(kFL) describes clustering of several levels, or shell structure. Consequences for the behaviour of thermodynamic properties are investigated. There are three regimes of temperature T: normal metallic (T > Δ), shell-metallic (δ < T < Δ) and semiconductor-like (T < δ). Finally, if the shape of a hard-walled container is allowed to vary so as to minimize the energy, it is argued that the optimal shape fluctuates between spherical and distorted as L is changed. |
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Keywords: | Fermi gas finite size effects energy scales shell structure small metal particles |
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