A crystal with lattice period along the field direction is placed in a uniform…

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

A crystal with lattice period a=4.0 A˚a=4.0\,\mathrm{\AA} along the field direction is placed in a uniform electric field E=5.0×104 V m−1E=5.0\times10^{4}\,\mathrm{V\,m^{-1}}, with no magnetic field and no scattering assumed in the derivation of the Bloch period. ((a)) Compute the Bloch oscillation period TB=h/eEaT_B=h/eEa. ((b)) An electron in this crystal has a collision time τ=3.0×10−14 s\tau=3.0\times10^{-14}\,\mathrm{s} at the temperature of the experiment. Express TBT_B as a multiple of τ\tau and state whether the oscillation could be observed.

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