A single crystal of an uncompensated metal ( overall) is placed in a fixed magnetic…

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

Solid State Physics, Ch The Boltzmann equation and electrical transport

Problem

A single crystal of an uncompensated metal (ne≠nhn_e\ne n_h overall) is placed in a fixed magnetic field of magnitude BB, and the transverse magnetoresistance ρxx(B)\rho_{xx}(B) is measured as the field direction is rotated in a plane through the crystal, at fixed BB. The measured pattern shows sharp, narrow features at field orientations 0∘,60∘,120∘,180∘,240∘,300∘0^\circ, 60^\circ, 120^\circ, 180^\circ, 240^\circ, 300^\circ, where ρxx\rho_{xx} continues to grow with increasing BB without levelling off, while at all other orientations ρxx\rho_{xx} approaches a constant value as BB is increased further. ((a)) Translate this rotation pattern into a statement about the Fermi surface: what feature must exist along the six marked field directions and not along the others? ((b)) State the functional dependence of ρxx\rho_{xx} on BB expected at one of the six marked orientations, and contrast it with the dependence expected elsewhere.

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