Potassium is a body-centred cubic metal; take the lattice period along the field…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Free electrons, energy bands and electronic structure

Solid State Physics, Ch The Fermi surface: semiclassical dynamics and its measurement

Problem

Potassium is a body-centred cubic metal; take the lattice period along the field direction as a=5.23×10−10 ma = 5.23\times10^{-10}\,\mathrm{m}. Its resistivity at 300 K300\,\mathrm{K} corresponds to a collision time τ300K=2.4×10−14 s\tau_{300\mathrm{K}} = 2.4\times10^{-14}\,\mathrm{s}. ((a)) Estimate the static electric field EE that would be needed to make the Bloch oscillation period TBT_B equal to this collision time, so that an electron could complete roughly one full traversal of the Brillouin zone before scattering. ((b)) Dielectric breakdown fields of ordinary solids lie in the range 10710^7 to 109 V m−110^9\,\mathrm{V\,m^{-1}}. Using the field found in part (a), say what this implies about ever observing Bloch oscillations in a bulk crystal of potassium held at room temperature, and what kind of structure has actually shown them, with a much shorter artificial period.

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