Lead-Orientation-Dependent Wave Function Scarring in Open Quantum Dots

Abstract

Experimental studies of the conductance of open quantum dots show a series of highly regular oscillations at low temperatures as the voltage applied to their defining gates is varied. Simulations of quantum transport through these dots reveal the oscillations to be correlated to the recurrence of specific groups of wave function scars. We furthermore find that nominally identical dots, differing only in the orientation of their input and output contacts, may be used to excite different families of scars, giving rise in turn to measurable transport results. [S0031-9007(99)09319-9] PACS numbers: 73.23. Ad, 85.30.Vw Semiconductor quantum dots, consisting of a submicron sized cavity and quantum point contact leads, are ideally suited for studying the influence of environmental coupling on the discrete level spectrum of quantum systems. Of particular interest here is the nature of electron transport in open dots, whose leads are configured to support a small number of propagating modes. While it is often argued that the level spectrum is continuous in such dots, recent studies have instead emphasized the role that the leads play in selectively exciting discrete dot states during transport [1][2][3][4][5]. In this Letter, we consider the sensitivity of this selection process to the nature of the coupling that is provided between the dot and its external environment. Splitgate dots with different lead orientations are fabricated and their transport properties are measured at low temperatures. When the voltage applied to their defining gates is varied, a series of regular oscillations is observed in the conductance, providing a unique signature of the couplinginduced modifications that arise in the level spectra of the dots. The details of the oscillations are found to be related to the recurrence with gate voltage of strongly scarred wave function states, whose features are sensitive to the lead configuration in the dots. We discuss these results in terms of the influence of the lead openings on electron transport in open dots.Here we summarize the results of studies of more than ten different split-gate dots, whose fabrication has been described elsewhere [6]. We focus, in particular, on the behavior exhibited by two dots with different lead configurations (see Fig. 1). The transport properties of these GaAs͞AlGaAs dots were measured in a dilution refrigerator, at a fridge temperature of 10 mK and using small constant currents with lockin detection [6]. From measurements at this temperature, the wafer mobility and carrier density were determined and were found to be 4 3 10 15 m 22 and 70 m 2 ͞V s, respectively. The effective size of the dots was estimated from the period of AharonovBohm oscillations in the edge state regime [6] and varied from 0.2 0.3 mm, depending on the value of the applied gate voltage. An upper-bound estimate of the number of electrons in the dots is therefore of the order of 100-400, for the same range of gate voltage. Another parameter inferred from magnetotransport studies was the electron ph...

Local density of states in mesoscopic samples from scanning gate microscopy

“…36,37 They correspond to quasi-classical states that scar the In Fig. 7 we plot the conductance of the AB ring with impurities as a function of the Fermi energy as well as its Fourier transform (inset).…”

Stochastic Carrier Dynamics in Semiconductor Superlattices

“…In semiconductor physics, chaotic electron transport has been explored using a variety of two-dimensional billiard and antidot barrier structures [1][2][3][4][5][6][7][8][9][10][11][12], in superlattices (SLs) [13][14][15], and in resonant tunnelling diodes containing a wide quantum well with a tilted magnetic field [1,[16][17][18]. Despite the diversity of these experiments, they all involve systems in which the transition to chaos occurs by the gradual and progressive destruction of stable orbits in response to an increasing perturbation.…”

Phase-Space Correlations of Chaotic Eigenstates

“…For example, in optical resonators [8] the power emitted at a certain point of the boundary depends strongly on the angle of incidence of the wave (total internal reflection). Also in quantum dots effects of eigenfunction directionality have been measured using tilted leads [12].In this paper we analyze for the first time dynamical correlations between points in phase space. Our results are surprising in view of the fact that spatial two-point correlators of eigenfunction amplitudes or densities vanish in the semiclassical limith → 0 for any x = x ′ [14].…”

“…For example, in optical resonators [8] the power emitted at a certain point of the boundary depends strongly on the angle of incidence of the wave (total internal reflection). Also in quantum dots effects of eigenfunction directionality have been measured using tilted leads [12].…”

“…Sq, 05.45.Mt Chaotic eigenfunctions and in particular their localization and correlation statistics are a topic of continuing interest [1,2,3,4,5,6,7]. Applications include classical, mesoscopic and pure quantum systems such as optical, mechanical and microwave resonators [8,9,10], electron transmission and interaction in chaotic quantum dots [11,12], and decay and fluctuations of heavy nuclei [13]. One foundation of eigenfunction statistics is the randomwave model of Berry [1] which is essentially equivalent to random-matrix theory (RMT) [2].…”