Open orbit and magneto resistance. We considered the transverse magneto resistance of free electrons in Problem 6.9 and of electrons and holes in Problem 8.5. In some crystals the magneto resistance saturates except in special crystal orientations. An open orbit carries current only in a single direction in the plane normal to the magnetic field; such carriers are not deflected by the field. In the arrangement of Fig. 6.14, let the open orbits be parallel to k in real space these orbits carry current parallel to the y as. Let ?_yy = s?₀ be the conductivity of the open orbits; this defines the constant s. The magneto conductivity tensor in the high field limit w₀? >> 1 is with Q = w_c?.?

(a) Show that the Hall field is Ey = ? Ex/sQ.?

(b) Show that the effective resistivity in the x direction is p (Q²/?₀) (s/s + 1), so that the resistivity does not saturate, hut increases as B².

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