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The unusual behavior of the 2DEG exhibited in Fig. 7 is known as the quantum Hall effect. The quantization of the Hall conductivity σ xy = 1/ρ xy has the important property of being incredibly precise. Actual measurements of the Hall conductivity have been found to be either integral or fractional multiples of 1/R0 to nearly one part in a billion. 8 Ω. This magnitude is referred to as the von Klitzing constant RK (after von Klitzing, the discoverer of exact quantization); since 1990, a fixed conventional value RK−90 has been used worldwide to calibrate resistors.

10 shows the first energy level (n x , ny , nz = 1) for a 0D structure of dimensions L x , Ly , and Lz , with Ly = Lz . As with the 2D and 1D structures, smaller dimensions result in increased eigenenergies, which is a manifestation of the Heisenberg uncertainty principle. 10 and Lz . 5 Chapter Summary The reduction of spatial dimensions to nanoscale values leads to a transition from classical physics to quantum mechanics. In the latter framework, the properties of systems of particles are described in terms of wavefunctions of single particles.

In the ballistic transport regime l < λe , electrons can propagate without losing their initial momentum since scattering events can be neglected. The expression for ballistic conductance including two-spin orientation (spin degeneracy) in the ideal case becomes G= 2e2 . h This relationship is usually called the Landauer formula. 581 × 104 Ω. The Landauer formula for quantum transport can be generalized to a network in which several wires connect a barrier with reservoirs, leading to an expression that sums over the contribution of each channel.

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