Superlattices and Microstructures, Vol. 20, No. 4, 1996 Coherent electronic properties of coupled two-dimensional quantum dot arrays R. Kotlyar, S. Das Sarma Department of Physics, University of Maryland, College Park, Maryland 20742, U.S.A. (Received 20 May 1996) In this paper we review our recent study of coherent electronic properties of coupled two- dimensional quantum dot arrays using numerical exact-diagonalization methods on a Mott– Hubbard type correlated tight-binding model. We predict the existence of a novel kind of persistent current in a two-dimensional isolated array of quantum dots in a transverse magnetic field. We calculate the conductance spectrum for resonant tunneling transport through a coherent two-dimensional array of quantum dots in the Coulomb Blockade regime. We also calculate the effective two-terminal capacitance of an array coupled to bias leads. c  1996 Academic Press Limited Key words: Collective Coulomb Blockade, persistent current. 1. Introduction By tuning the tunnel barriers between the individual dots of a linear chain of semiconductor quantum dots, which have been electrostatically defined in a 2D electron gas [1], it is, in principle, possible to achieve various theoretically interesting [2] coupling regimes where interdot tunneling, Coulomb interaction, and intradot interlevel energies compete with each other. The transition from the single dot Coulomb Blockade (CB) conductance oscillations to their splitting into minibands due to coherent tunneling in the array can be identified with the formation of an ‘artificial molecule’ [2–4]. The suppression of conductance due to the Mott–Hubbard spin-polarization transition, which has no analogy within the classical charging model, has been predicted [3] to conclusively test the formation of a coherent many-body ‘molecular’ state. In this presentation we briefly review our extensive recent work [5] on the electronic properties of coupled and coherent two-dimensional (2D) quantum dot arrays using the Mott–Hubbard Hamiltonian approach. Our motivation is to investigate the characteristic signature of the formation of an artificial 2D quantum dot molecule in experimentally observable electronic properties. Recent fabrication of coherent quantum dot structures in several laboratories motivates our numerical investigation of the 2D L x × L y quantum dot arrays in the Collective Coulomb Blockade (CCB) regime [2]. We discuss the existence of an equilibrium persistent current in 2D arrays and contrast the situation with persistent current results in 1D rings. In general, the transport current-carrying states can be probed by measuring the low bias CCB conductance spectrum, which we calculate within a linear response theory. Finally, we also present our results on the two-terminal effective capacitance of a 2D quantum dot array. In Section 2, we define and describe our coherent 2D Mott–Hubbard model for the coupled quantum dot array, and in Sections 3, 4 and 5 we present our numerical results for the persistent current, the conductance, and the capacitance, respectively. A detailed discussion of our other results will be given elsewhere [5]. 0749–6036/96/080641 + 09 $25.00/0 c  1996 Academic Press Limited