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...

We present studies of the quantum-mechanical transport and the classical billiard transport through ballistic semiconductor quantum dots, where the transport is nonergodic or ''regular.'' These are shown to have quite similar behavior if the classical motion is limited to a collimated set of trajectories. These results are shown to agree substantially with experiments performed on actual semiconductor quantum dots. The results suggest that transport in regular semiconductor quantum dots is clearly distinguished from the equivalent transport in ergodic dots. In particular, the fluctuation spectrum is not random, but highly oscillatory and correlated. The correlation functions for these fluctuations show regular and periodic oscillations that contain only a few, often harmonically related, frequencies. This is fully in keeping with the expectations of semiclassical descriptions of the fluctuations in the density of states of such structures. ͓S0163-1829͑96͒03348-6͔

Akis, Ferry, and Bird Reply: In the preceding Comment [1], Zozoulenko and Lundberg (ZL) seem to have misinterpreted our Letter [2]. In reply, we make the following comments.We presented simulations of stadium-shaped quantum dots, and found that the magnetoconductance fluctuations showed a periodicity that could be decomposed into relatively few frequencies, indicating that only a few periodic orbits were responsible. This is the behavior we claimed as being universal. We did not claim that there was a single universal frequency in this structure. However, the implication by ZL that there is no periodicity at all in the stadium flies in the face of experiment, which has demonstrated a highly periodic nature to the fluctuations in such dots [3][4][5]. In curve 1 of Fig. 1(a) we show the power spectrum obtained from a more careful processing of the fluctuation curve [ Fig. 1(a) of [1] ]. Periodicities are clearly apparent in the latter figure, and our curve illustrates this. While the peaks are different from our Fig. 2(a) in [2], this is no surprise since minor differences are to be expected. We also find that the "scar" peak in our own data is quite prominent regardless of how we subtract the background. In Fig. 1(b), we plot a portion of the conductance G͑E, B͒, in the Fermi energy-magnetic field plane. Curves such as this would be unobtainable were ZL correct about the sensitivity, and this figure clearly illustrates the periodicity.

We argue that many major features in electronic transport in realistic quantum dots are not explainable by the usual semiclassical approach, due to the contributions of the quantum-mechanical tunneling of the electrons through the Kolmogorov-Arnol'd-Moser islands. We show that dynamical tunneling gives rise to a set of resonances characterized by two quantum numbers, which leads to conductance oscillations and concentration of wave functions near stable and unstable periodic orbits. Experimental results agree very well with our theoretical predictions, indicating that tunneling has to be taken into account to understand the physics of transport in generic nanostructures.

The concentrations of wave functions about classical periodic orbits, or quantum scars, are a fundamental phenomenon in physics. An open question is whether scarring can occur in relativistic quantum systems. To address this question, we investigate confinements made of graphene whose classical dynamics are chaotic and find unequivocal evidence of relativistic quantum scars. The scarred states can lead to strong conductance fluctuations in the corresponding open quantum dots via the mechanism of resonant transmission.