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 field B=3.0T is applied to a metal whose Fermi surface, cut by the plane perpendicular to B, shows two branches: a closed circle centred at Γ of radius k1=0.90A˚−1, and a separate wavy line that runs the full width of the Brillouin zone and reappears, displaced by a reciprocal lattice vector G, at the opposite zone face.
((a)) Classify each branch as a closed orbit or an open orbit, and compute the real-space orbit radius for the closed branch.
((b)) Explain, for the open branch, why it does not contribute a periodic real-space orbit or a quantum-oscillation frequency, and state the direction in which an electron on it moves in real space, relative to B and to the direction in which the wavy line runs across the zone.