Physica E 7 (2000) 745–749 www.elsevier.nl/locate/physe Nonuniform energy level broadening in open quantum dots: the inuence of the closed dot eigenstates on transport R. Akis, J.P. Bird * , D.K. Ferry, D. Vasileska Center for Solid State Electronics Research, Department of Electrical Engineering, Arizona State University, Tempe AZ 85287-5706, USA Abstract We present simulations of a realistically modeled quantum dot with soft boundaries and open leads supporting several modes. The wavefunctions of this open dot can be decomposed in terms of the eigenstates of a corresponding closed dot my means of projection. At particular resonances, this decomposition reveals that transport in the open dot can be mediated through a single eigenstate. Thus, the quantization of closed-dot energy levels can be preserved even as the dot is opened, but we nd that there is a selection of particular eigenstates that depends strongly on the positions and nature of the contacts. ? 2000 Elsevier Science B.V. All rights reserved. PACS: 73.23.-b; 73.23.Ad; 85.30.Vw; 72.20.-i Keywords: Quantum dots; Scarring; Transport; Chaos A very important issue with regard to transport in open quantum dots is the level broadening of the dot states. Recently, studies of magnetotransport uctua- tions in circular quantum dots connected to leads have used simple tunneling models in order to explain the results [1,2]. The conclusion drawn was that the pe- riodic nature of the uctuations could be understood almost exclusively in terms of the density of states of a closed dot, even when several modes passed through the quantum point contacts (QPCs). On the other hand, much of the semi-classical theory of open quantum dots begins with the assumption that the openness of * Corresponding author. Tel.: +1-602-965-7421; fax: +1-602-965-8058. E-mail address: bird@asu.edu (J.P. Bird) the dot broadens the levels suciently that quantiza- tion is no longer important in determining dot behav- ior [3]. Using self-consistent calculations to obtain the type of soft potentials expected in real quantum dots, we have found that an intermediate situation arises – the level quantization is preserved in the open dots, but is done so in a highly selective manner that de- pends strongly on the conguration of the QPCs. We have modeled a quantum dot that also has been studied experimentally [4]. As shown in the left panel of Fig. 1, the split-gate that denes the dot has QPCs that are staggered. This sits on top of a GaAs–AlGaAs heterostructure, which consists of a 5 nm undoped GaAs cap layer, a 40 nm Al x Ga 1-x As (x =0:26) Si-doped (N D =1:5 × 10 18 cm -3 ) bar- rier layer, and a 15 nm undoped Al x Ga 1-x As 1386-9477/00/$ - see front matter ? 2000 Elsevier Science B.V. All rights reserved. PII:S1386-9477(00)00050-3