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Wigner-Seitz cell & Brillouin zone of a body centered cubic (bcc)

Wigner-Seitz cell & Brillouin zone of a body centered cubic (bcc)

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<strong>Wigner</strong>-<strong>Seitz</strong> <strong>cell</strong> & <strong>Brillouin</strong> <strong>zone</strong> <strong>of</strong> a <strong>body</strong> <strong>centered</strong> <strong>cubic</strong> (<strong>bcc</strong>)<br />

crystal, e.g., Fe, Na, Mo, Ta, W …<br />

[110]<br />

[111]<br />

<strong>Wigner</strong> <strong>Seitz</strong> Cell <strong>Brillouin</strong> Zone<br />

[100]<br />

(Ashcr<strong>of</strong>t & Mermin, Kittel)


<strong>Wigner</strong>-<strong>Seitz</strong> <strong>cell</strong> & <strong>Brillouin</strong> <strong>zone</strong> <strong>of</strong> a face <strong>centered</strong> <strong>cubic</strong> (fcc)<br />

crystal, e.g., Ag, Al, Au, Cu …<br />

<strong>Wigner</strong> <strong>Seitz</strong> Cell <strong>Brillouin</strong> Zone<br />

(Ashcr<strong>of</strong>t & Mermin, Kittel)


Band structure <strong>of</strong> Aluminum<br />

Segal, Physical Review, vol. 125, pp.109-122, (1962)


Band structure <strong>of</strong> Copper<br />

Segal, Physical Review, vol. 125, pp.109-122, (1962)


Band structure <strong>of</strong> a semiconductor (e.g., Si, Ge)


Band structure <strong>of</strong> an insulator (e.g., Diamond)<br />

http://www.i<strong>of</strong>fe.rssi.ru/SVA/NSM/Semicond/index.html


Carbon Nanotubes – Metallic/Non-metallic<br />

Straight Nanotubes<br />

Twisted Nanotubes<br />

Collins & Avouris, Scientific American, December 2000, p. 62


<strong>Brillouin</strong> <strong>zone</strong> and Energy dispersion<br />

<strong>of</strong> a Carbon nanotube<br />

Hamada et al, "New One-dimensional Conductors: Graphitic Microtubules",<br />

Physical Review Letters, vol. 68, No. 10, pp.1579-1581., (1992).


Sodium<br />

Fermi Surfaces<br />

Iron<br />

Copper<br />

Fermi surface database: http://www.phys.ufl.edu/fermisurface/

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