Arunava Chakrabarti

Role of a new type of correlated disorder in extended electronic states in the Thue-Morse lattice.

A new type of correlated disorder is shown to be responsible for the appearance of extended electronic states in one-dimensional aperiodic systems like the Thue-Morse lattice. Our analysis leads to an understanding of the underlying reason for the extended states in this system, for which only numerical evidence is available in the literature so far. The present work also sheds light on the restrictive conditions under which the extended states are supported by this lattice.

Magneto-transport in a mesoscopic ring with Rashba and Dresselhaus spin-orbit interactions

Electronic transport in a one-dimensional mesoscopic ring threaded by a magnetic flux is studied in the presence of Rashba and Dresselhaus spin-orbit interactions. A completely analytical technique within a tight-binding formalism unveils the spin-split bands in the presence of the spin-orbit interactions and leads to a method of determining the strength of the Dresselhaus interaction. In addition to this, the persistent currents for ordered and disordered rings have been investigated numerically. It is observed that the presence of the spin-orbit interaction, in general, leads to an enhanced amplitude of the persistent current. Numerical results corroborate the respective analytical findings.

Extended states in one-dimensional lattices : application to the quasiperiodic copper-mean chain

The question of the conditions under which one-dimensional systems support extended electronic eigenstates is addressed in a very general context. Using real-space renormalization-group arguements we discuss the precise criteria for determining the entire spectrum of extended eigenstates and the corresponding eigenfunctions in disordered as well as quasiperiodic systems. For purposes of illustration we calculate a few selected eigenvalues and the corresponding extended eigenfunctions for the quasiperiodic copper-mean chain. So far, for the infinite copper-mean chain, only a single energy has been numerically shown to support an extended eigenstate [J. Q. You, J. R. Yan, T. Xie, X. Zeng, and J. X. Zhong, J. Phys.: Condens. Matter 3, 7255 (1991)]: we show analytically that there is in fact an infinite number of extended eigenstates in this lattice which form fragmented minibands.

Metal-Insulator Transition in an Aperiodic Ladder Network : An Exact Result

We prove that a tight-binding ladder network composed of atomic sites with on-site potentials distributed according to the quasiperiodic Aubry model can exhibit a metal-insulator transition at multiple values of the Fermi energy. For specific values of the first and second neighbor electron hopping, the result is obtained exactly. With a more general model, we numerically calculate the two-terminal conductance. The numerical results corroborate the analytical findings.

Ladder network as a mesoscopic switch: An exact result

We investigate the possibilities of a tight-binding ladder network as a mesoscopic switching device. Several cases have been discussed in which any one or both arms of the ladder can assume random, ordered, or quasiperiodic distribution of atomic potentials. We show that, for a special choice of the Hamiltonian parameters, it is possible to prove exactly the existence of mobility edges in such a system, which plays a central role in the switching action. We also present numerical results for the two-terminal conductance of a general model of a quasiperiodically grown ladder, which support the general features of the electron states in such a network. The analysis might be helpful in fabricating mesoscopic or DNA switching devices.

Magnetotransport in periodic and quasiperiodic arrays of mesoscopic rings

We study theoretically the transmission properties of serially connected mesoscopic rings threaded by a magnetic flux. Within a tight-binding formalism we derive exact analytical results for the transmission through periodic and quasiperiodic Fibonacci arrays of rings of two different sizes. The role played by the number of scatterers in each arm of the ring is analyzed in some detail. The behavior of the transmission coefficient at a particular value of the energy of the incident electron is studied as a function of the magnetic flux (and vice versa) for both periodic and quasiperiodic arrays of rings having different number of atoms in the arms. We find interesting resonance properties at specific values of the flux, as well as a power-law decay in the transmission coefficient as the number of rings increases, when the magnetic field is switched off. For the quasiperiodic Fibonacci sequence we discuss various features of the transmission characteristics as functions of energy and flux, including one special case where, at a special value of the energy and in the absence of any magnetic field, the transmittivity changes periodically as a function of the system size.

Electronic transmission in a model quantum wire with side-coupled quasiperiodic chains : Fano resonance and related issues

We present exact results for the transmission coefficient of a linear lattice at one or more sites of which we attach a Fibonacci quasiperiodic chain. Two cases have been discussed\char22{}viz., when a single quasiperiodic chain is coupled to a site of the host lattice and when more than one dangling chain is grafted periodically along the backbone. Our interest is to observe the effect of increasing the size of the attached quasiperiodic chain on the transmission profile of the model wire. We find clear signature that, with a side-coupled semi-infinite Fibonacci chain, the Cantor set structure of its energy spectrum should generate interesting multifractal character in the transmission spectrum of the host lattice. This gives us an opportunity to control the conductance of such systems and to devise a switching mechanism that can act over arbitrarily small scales of energy. The Fano profiles in resonance are observed at various intervals of energy as well. Moreover, an increase in the number of such dangling chains may lead to the design of a kind of spin filters. This aspect is discussed.

Renormalization-group analysis of extended electronic states in one-dimensional quasiperiodic lattices

We present a detailed analysis of the nature of electronic eigenfunctions in one-dimensional quasi-periodic chains based on a clustering idea recently introduced by us [Sil et al., Phys. Rev. {\bf B 48}, 4192 (1993) ], within the framework of the real-space renormalization group approach. It is shown that even in the absence of translational invariance, extended states arise in a class of such lattices if they possess a certain local correlation among the constituent atoms. We have applied these ideas to the quasi-periodic period-doubling chain, whose spectrum is found to exhibit a rich variety of behaviour, including a cross-over from critical to an extended regime, as a function of the hamiltonian parameters. Contrary to prevailing ideas, the period-doubling lattice is shown to support an infinity of extended states, even though the polynomial invariant associated with the trace map is non-vanishing. Results are presented for different parameter regimes, yielding both periodic as well as non-periodic eigenfunctions. We have also extended the present theory to a multi-band model arising from a quasi-periodically arranged array of

On the nature of eigenstates of quasiperiodic lattices in one dimension

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Flux-induced semiconducting behavior of a quantum network

-function potentials on the atomic sites. Finally, we present a multifractal analysis of these wavefunctions following the method of Godreche and Luck [ C. Godreche and J. M. Luck, J. Phys. A :Math. Gen. {\bf 23},