Complex behavior of the conductance of quantum wires with a long quantum-dot array F. Domı ´nguez-Adame a, * , I. Go ´mez a , P.A. Orellana b , M.L. Ladro ´n de Guevara b a GISC, Departamento de Fı ´sica de Materiales, Facultad de Fı ´sica, Universidad Complutense, E-28040 Madrid, Spain b Departamento de Fı ´sica, Universidad Cato ´lica del Norte, Casilla 1280, Antofagasta, Chile Abstract We consider electron transport through a quantum wire with an attached quantum-dot array, when the number of dots is large. To this end, we use a noninteracting Anderson Hamiltonian. The conductance at zero temperature shows a complex behavior as a function of the Fermi energy. In particular, two well-defined energy regions are observed. Far from the site-energy of the quantum dots, the conductance depends smoothly on the Fermi energy. On the contrary, at the center of the band the conductance develops an oscillating pattern with resonances and antiresonances due to constructive and destructive interference in the ballistic channel, respectively. We discuss analytically in detail the physical origin of this complex behavior. q 2004 Elsevier Ltd. All rights reserved. Keywords: Quantum wires; Quantum-dot array; Fermi energy 1. Introduction Latest advances in nanofabrication of quantum devices make it possible to obtain quantum dots (QDs) in a controllable way [1]. We have recently proposed a new quantum device based on a quantum wire (QW) with an attached QD array [2]. In this case the QD array acts as scattering center for transmission through the QW. This configuration can be regarded as a quantum wave guide with side-stub structures, similar to those reported in Ref. [3]. The conductance at zero temperature through the QW shows a complex behavior as a function of the Fermi energy, being strongly dependent on the number of QDs in the attached array. For a uniform QD array, we found that the conductance develops an oscillating pattern with resonances (perfect transmission) and antiresonances (perfect reflec- tion). In addition, we found an odd–even symmetry related to the number of QDs in the array, namely perfect transmission takes place if this number is even ðG ¼ 2e 2 =hÞ but perfect reflection arises for an odd number ðG ¼ 0Þ: These results indicate the feasibility of tuning the QW transport properties through the QD array. In this work we report further progress along the lines indicated above. In particular, we study in detail the complex behavior of the conductance of the QW when the number of QDs in the attached array is large. 2. Model Hamiltonian and conductance We model the system by using a noninteracting Anderson tunneling Hamiltonian that can be written as H ¼ H QW þ H N QD þ H QD–QW ; where H QW ¼ v X i ðc † i c iþ1 þ c † iþ1 c i Þ; ð1Þ H N QD ¼ 1 0 X N l¼1 d † l d l þ V c X N21 l¼1 ðd † l d lþ1 þ d † lþ1 d l Þ; H QD–QW ¼ V 0 ðd † 1 c 0 þ c † 0 d 1 Þ: The operators c † i and d † l create an electron at sites i and l; respectively. Here v and V c are the hoppings in the QW and in the array with N QDs, respectively. V 0 is the hopping between the QW and the amay. Finally, 1 0 is the energy level of each QD. Notice that we are assuming uniform hopping and identical QDs in the array, although this is not an essential requirement of the model since more general situations can be handled [2]. Fig. 1 shows a schematic view of the system. The experimentally accessible quantity is the linear conductance G, which is related to the transmission 0026-2692/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/S0026-2692(03)00229-5 Microelectronics Journal 35 (2004) 87–89 www.elsevier.com/locate/mejo * Corresponding author. Tel.: þ 34-91-394-4488; fax: þ34-91-394-4547. E-mail address: adame@fis.ucm.es (F. Domı ´nguez-Adame).