PART B: Topological insulators
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چکیده
9.4.1. Hall effect † Consider electrons moving in a 2D plane (the system is known as a 2D electron gas or 2DEG). If we apply an in-plane electric field E, we will get some electric current j. Typically, E J . Let’s assume they are in the x direction Ex and jx. The resistivity is rxx = Ex jx † Apply a B field perpendicular to the 2D plane. Lorentz force leads to charge accumulation for the top and bottom edge. This gives a E field perpendicular to the current (Ey). Hall resistivity: rxy = Ey jx † The rotational symmetry tells us that rxx = ryy and rxy = ryx † Classical mechanics: rxy ∂ B (9.32) e Ey = e v B (9.33) jx = e v n
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