Phase‐Coherent Transport

Abstract

Abstract In this chapter the essential phenomena of phase‐coherent transport in nanoelectronic structures are discussed. First, the relevant length scales – that is, the elastic mean free path, the inelastic mean free path, or the phase‐coherence length – are defined, and these are subsequently used to classify the ballistic and diffusive transport regimes. Quantized conductance in split‐gate point contacts is discussed as a transport phenomenon in the ballistic regime. The origin of quantized conductance is explained on the basis of the Landauer–Büttiker formalism. The weak localization effect – a transport phenomenon in the diffusive regime – is explained first on the basis of an intuitive picture, but later the exact expressions describing weak localization for different dimensions of the sample are presented and discussed. It will also be demonstrated that the presence of spin‐orbit coupling can result in an enhanced conductivity, opposite to the weak localization effect. Periodic resistance oscillations can be observed in ring‐shaped conductors, and the Al'tshuler–Aronov–Spivak oscillations found in interconnected ring structures are discussed first. For single‐ring structures, the Aharonov–Bohm effect is introduced, which originates from the interference of electron waves propagating along the upper and lower branches of the ring. In very small structures with only a few scattering centers, universal conductance fluctuations are observed; the origin of these fluctuations is explained and their suppression, for example by increasing the temperature, is discussed.