Electronic properties of a Cantor lattice

✍ Scribed by Sheelan Sengupta; Arunava Chakrabarti; Samar Chattopadhyay

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 358 KB
• Volume: 344
• Category: Article
• ISSN: 0921-4526
• DOI: 10.1016/j.physb.2003.09.273

✦ Synopsis

We present results of some investigations on the electronic properties of a non-periodic self-similar structure based on the triadic Cantor set sequence. In particular, we examine the eigenvalue spectrum of a Cantor lattice using the trace map technique widely used for the conventional quasi-periodic sequences. In addition, we show that a Cantor lattice possesses a number of resonant extended wave functions, some of which exhibit a distribution that resembles the lattice itself. We present results for the transmission coefficient of finite, but arbitrarily large Cantor lattices. We also examine in some detail, the cycles of the matrix map for such a sequence, and the variety of cyclic behaviour that one may encounter depending on the specific choices of the Hamiltonian parameters.