Design of Superconductor in Quantum Dot Superlattices
Hiroyuki Tamura and Hideaki Takayanagi
Materials Science Laboratory
The electronic properties of solids are closely related to their crystal structure which is strictly determined by the atomic nature of the individual elements. However, the imposition of a superstructure on a given lattice makes the controlled fabrication of structures with chosen properties possible. One approach discussed more recently is to place quantum dot (QD), also known as artificial atoms, on the points of a lattice to form an artificial crystal called a quantum-dot superlattice (QDSL) [1,2].
Here, we propose a method for forming QDSLs in a quantum wire network of square and plaquette lattices shown in Fig. 1 . The plaquette lattice has a square plaquette in each unit cell with four lattice-points at the vertices, as shown in the inset of Fig. 2. We have used the spin dependent local density approximation to obtain the band structure of the wire network. It can be shown that both QDSLs are well represented by the Hubbard model. An interesting difference between the two QDSLs is that the Fermi surface of the plaquette QDSL has disconnected pieces whereas the square QDSL is formed of one piece. To find a correlation effect that reflects both the Coulomb interaction and the structures of the Fermi surface, we studied the existence of superconductivity for both lattices within the framework of the Hubbard model. We found a superconducting ground state where the transition temperature Tc of the plaquette lattice is more than double that of the square lattice as shown in Fig. 2, and is sufficiently high to allow superconductivity to be observed experimentally.
 H. Tamura, K. Shiraishi, T. Kimura, and H. Takayanagi, Phys. Rev. B 65 (2002) 085324.  K. Shiraishi, H. Tamura, and H. Takayanagi, Appl. Phys. Lett. 78 (2001) 3702.  T. Kimura, H. Tamura, K. Kuroki, K. Shiraishi, H. Takayanagi, and R. Arita, Phys. Rev. B 66 (2002) 132508.
Fig. 1. Diagram of a quantum wire network with spacings a and b between adjacent wires. We assume InAs quantum wires buried in In0.776Ga0.224As barrier regions. The case where a=b (a<b) corresponds to the square (plaquette) lattice.
Fig. 2. Superconducting transition temperature Tc plotted as a function of the transfer energy ta. Tc of the plaquette lattice (ta=1.5, tb=0.5) is more than double that of the square lattice (ta=tb=1). Inset: Corresponding tight-binding model with hopping parameters ta and tb.
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