Magneto resistance with two carrier types, Problem 6.9 shows that in the drift velocity approximation the motion of charge carriers in electric and magnetic fields does not lead to transverse magneto resistance. The result is different with two carrier types. Consider a conductor with a concentration n of electrons of effective mass me and relaxation time ?e; and a concentration p of holes of effective mass mh and relaxation time ?A. Treat the limit of very strong magnetic fields w_c?>> 1.

(a) Show in this limit that ?xy = (n ? p)ec/B.

(b) Show that the Hall field is given by, with Q ? wc?, which vanishes if n = p.?

(c) Show that the effective conductivity on the x direction is if n = p, ? ? B^?2. If n ? p, ? saturates in strong fields; that is, it approaches a limit independent of B as B ? ?

(n-pl(+6) (n ec n *a - [( + ) + (-PP ( 2 + .) ] ?) Jeff B Ey = - E. E, -1