By (auth.), B. Kramer (eds.)
This sequence of Landolt-Börnstein volumes is summarizing our present wisdom of the phenomena of mesoscopic quantum structures with spatial extensions among these of atoms and usual macroscopic solids. At low temperatures, they're acknowledged to turn into "quantum robotically coherent" with states that reach over the entire system.
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Extra resources for Electronic Transport. Part 1: Quantum Point Contacts and Quantum Wires
44) nm Here tnm are the transmission amplitudes between tranverse modes m and n far from the constriction. The essence of the problem lies in the mode conversion which takes place at the entrance and exit of the QPC. Even in the absence of adiabatic transport, as discussed above, the states with lateral-quantization energy well below the Fermi energy couple well to the reservoirs and are almost perfectly transmitted (Tn = |tnn |2 ≈ 1). Indeed, for the simpliﬁed problem of a semiinﬁnite channel the transmission approaches unity very quickly as a function of the dimensionless parameter ∆ = kF w /π as shown in Fig.
7 Impurities Although the conductance quantization is a manifestation of ‘perfect’ transmission, a QPC is an inherently mesoscopic device and it is therfore to be expected that disorder will play a role in the determination of the individual device characteristics. The na¨ıve expectation that the Landolt-B¨ ornstein New Series III/34B(1) Ref. p. 72] Quantized transport 39 impurity conﬁguration in the immediate vicinity of the QPC will produce a characteristic device ‘ﬁngerprint’ has indeed been theoretically conﬁrmed.
However, such ﬂuctuations are not seen in the conductance of a QPC due to the ﬁltering action of the channel modes [93M2]. Any ﬂuctuations of the surrounding diﬀusive region are suppressed by a factor of 2(n/N ) where n is the number of channel modes and N the number of modes in the reservoir within an inelastic scattering length of the constriction. The lack of good quantization in channels whose length is considerably shorter than the elastic mean free path in high quality heterostructures has led to investigations of the role of the random impurity potential generated by the donors in the dopant layer [91N, 91L1].
Electronic Transport. Part 1: Quantum Point Contacts and Quantum Wires by (auth.), B. Kramer (eds.)