Schematic illustration of a possible experimental scheme to harness transport through a semiconductor 2DEG quantum-dot system, where 2DEG is formed at the GaAs/Al0.3Ga0.7As hetero-interface. The heterostructure sits on a substrate (purple), covered by 300 nm SiO2 (blue) and contacted by Au/Cr (yellow). By applying a suitable gate voltage to generate a circular forbidden region (for classical orbits) at the center of the device, the resulting closed system is a Sinai billiard. Open quantum-dot system can be formed by attaching leads to the billiard system. In this paper we place the leads in the middle of the dot, as shown in the second row. Similar idea can be applied to graphene systems.
(a) Conductance versus Fermi energy for four semiconductor 2DEG quantum-dot systems (bottom to top): rectangular dot, rectangular dot with a rectangular forbidden region of area , and Sinai dots of radii and . The area of the original rectangular dot is and the lead width is . (b) Conductance fluctuation patterns for graphene quantum dots of the same geometry as in (a). 20 The curves in (a) and (b) have been shifted vertically by some arbitrary values to facilitate visualization. (c) Normalized number of sharp resonances, which is defined (see text) to quantify the degree of transmission fluctuations, corresponding to the four cases in (a), i.e., the top two rectangular symbols represent two rectangular quantum dots while the bottom two circles correspond to two Sinai quantum dots.
Normalized number of sharp resonances versus radius of the central circular forbidden region [Fig. 1 ]. The area for original rectangular quantum dot is .
Contour plot of escape rate in the parameter plane of W and R. For each parameter combination, 106 random particles, each of unit velocity, are used to calculate the escape rate. For each particle, its path length in the scattering region (the Sinai billiard region) is calculated. The distribution of the path length is observed to decay exponentially, and the escape rate is the exponential rate.
(a) Conductance versus energy for one small quantum dot of area , where the number of discrete points used in the simulation is 218; (b) the corresponding imaginary parts versus real parts of eigenenergy of (cross), calculated from Eq. (13) (square) and Eq. (16) (circle). The Fermi energy is , as indicated by the arrow.
Imaginary and real parts of the eigenenergies for (a) rectangular quantum dot, (b) rectangular dot with a rectangular forbidden region at the center, (c) Sinai quantum dot with , and (d) Sinai dot with , where for all cases. Each eigenenergy is represented by one blue circle. The red dashed lines indicate and they are just for eye guidance.
Typical quantum pointer states for (a) rectangular quantum dot, (b)rectangular quantum dot with a rectangular forbidden region, (c) and (d)Sinai quantum dots of radii and , respectively. Darker regions indicate higher values of LDS. The color scale has been normalized for each panel for better visualization. The mean value of LDS in the leads are 0.0154, 0.0351, 0.0491, 0.0669 for panels (a)-(d), respectively. We observe the presence of pronounced pointer states in the two integrable cases.
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