Quantum point contacts

H. van Houten, C. W. J. Beenakker, and B. J. van Wees, Quantum Point Contacts G. Timp, When Does a Wire Become an Electron Waveguide ... 

Now we show that the validity of the cascade Langevin approach extends beyond the limits of validity of Boltzmann equation. Consider a frequency-dependent noise in a chaotic cavity, i.e. in a metallic island of irregular shape connected to the electrodes L, R via two quantum point contacts of conductances Gl,r e1 /h and arbitrary transparencies / /. . As the dwell time of... 

This model is quite universal, describing a variety of correlated electron systems coupled to the leads the Anderson impurity model, the multilevel quantum dot with diagonal noninteracting Hamiltonian quantum dots, when the off-diagonal matrix elements of eap describe hopping between individual dots, and, finally, the ID and 2D quantum point contacts. 

An optical MZ interferometer is described schematically in Fig. 1 a. In the electronic counterpart, depicted in Fig. 1 b, a quantum point contact (QPC) functions as a beam splitter and an Ohmic contact serves as a detector. The QPC is formed in the 2DEG by depositing split metallic gates, separated by a small gap, on the surface of the semiconduuctor and biasing them negatively... 

A numerical analysis, based on a Green s function approach, has been carried out to explain the interference patterns of an electron beam injected and detected via quantum point contacts. The calculations show the profound influence of back-scattering from potential fluctuations located close to the injector or detector on the transmission probability of the propagated electron beam. The interference patterns are sensitive to even small changes of the scatter location. 

Zimmerman, J.E., Thiene, R, and Hardings, 1 1970. Design and operation of stable rf biased superconducting point-contact quantum devices. /. Appl. Phys. 41 1572. 

Figure 19b displays the 2D histogram of the experimentally obtained conductance of N4 plotted vs distance [63]. The distance scale z is normalized with respect to z = 0 at G = 0.7 G0, to a common point. The chosen procedure is justified, because of the steep decay of the tunneling current after breaking of the last atomic contact. The histogram counts the occurrence of [log(G/Go), z ] pairs in a 2D field. Figure 19b exhibits the features of gold quantum contacts at G > Go, and a second cloud-like pattern in [10 5 10 4 G0, 0 0.5 nm]. We attribute the latter to the formation of single-molecule junctions of only one type. The center of the cloud is located at G = 3.5 4.5 x 10 5 Go, close to the peak position in the ID histogram (Fig. 19a). The extension of the cloud along the distance scale is around 0.5 nm, close to the typical length of the plateaus (the inset of Fig. 19a).

A residual interaction that is also quite simple has been developed and applied with good results. Recall that the nucleon-nucleon force is attractive and very short ranged, so one might image that the nucleons must be in contact to interact. Thus, the simplest residual interaction is an attractive force that only acts when the nucleons touch or a 8 interaction (in the sense of a Kronecker 8 from quantum mechanics). This can be written as V(r, r%) = a where a is the strength of the interaction, and the 8 function only allows the force to be positive when the nucleons are at exactly the same point in space. In practice, the strength of the potential must be determined by comparison to experimental data. Notice,... 

If the voltage is high enough, the noise of isolated contacts can be considered as white at frequencies at which the distribution function / fluctuates. This allows us to consider the contacts as independent generators of white noise, whose intensity is determined by the instantaneous distribution function of electrons in the cavity. Based on this time-scale separation, we perform a recursive expansion of higher cumulants of current in terms of its lower cumulants. In the low-frequency limit, the expressions for the third and fourth cumulants coincide with those obtained by quantum-mechanical methods for arbitrary ratio of conductances Gl/Gr and transparencies Pl,r [9]. Very recently, the same recursive relations were obtained as a saddle-point expansion of a stochastic path integral [10]. 

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