Biplab Pal

Publications (6) View all

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  Article: Complete absence of localization in a family of disordered lattices

  Biplab Pal, Santanu K. Maiti, Arunava Chakrabarti
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  ABSTRACT: We present analytically exact results to show that certain quasi–one-dimensional lattices, where the building blocks are arranged in a random fashion, can have an absolutely continuous part in the energy spectrum when special correlations are introduced among some of the parameters describing the corresponding Hamiltonians. We explicitly work out two prototype cases, one being a disordered array of a simple diamond network and isolated dots, and the other an array of triangular plaquettes and dots. In the latter case, a magnetic flux threading each plaquette plays a crucial role in converting the energy spectrum into an absolutely continuous one. A flux controlled enhancement in the electronic transport is an interesting observation in the triangle-dot system that may be useful while considering prospective devices. The analytical findings are comprehensively supported by extensive numerical calculations of the density of states and transmission coefficient in each case.
  EPL (Europhysics Letters) 04/2013; 102(1):17004. · 2.17 Impact Factor
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  Article: Engineering wave localization in a fractal waveguide network

  Biplab Pal, Pinaki Patra, Jyoti Prasad Saha, Arunava Chakrabarti
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  ABSTRACT: We present an exact analytical method of engineering the localization of classical waves in a fractal waveguide network. It is shown that a countable infinity of localized eigenmodes with a multitude of localization lengths can exist in a Vicsek fractal geometry built with diamond-shaped monomode waveguides as the "unit cells." The family of localized modes forms clusters of increasing size. The length scale at which the onset of localization for each mode takes place can be engineered at will, following a well-defined prescription developed within the framework of a real space renormalization group. The scheme leads to an exact evaluation of the wave vector for every such localized state, a task that is nontrivial, if not impossible for any random or deterministically disordered waveguide network.
  Physical Review A 02/2013; 87(2):023814. · 2.88 Impact Factor
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  Conference Proceeding: Absolutely continuous spectrum and ballistic transport in a one-dimensional quasiperiodic system

  Biplab Pal, Arunava Chakrabarti
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  ABSTRACT: We analyse a quasiperiodic arrangement of four atomic sites sitting at the vertices of a diamond shaped plaquette and single isolated sites, occupying a one dimensional backbone following a Fibonacci quasicrystal pattern. We work within a tight binding formalism. It is shown that, even with this simple deviation from pure one dimension, a definite relation between the numerical values of the system parameters will render all the single particle states completely extended. The spectrum will be absolutely continuous with the transmission completely ballistic throughout the band, completely violating the Cantor set character of the usual Fibonacci quasiperiodic chains.
  57th DAE Solid State Physics Symposium 2012, Indian Institute of Technology, Bombay, Mumbai, India; 12/2012
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  Article: Staggered and extreme localization of electron states in fractal space

  Biplab Pal, Arunava Chakrabarti
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  ABSTRACT: We present exact analytical results revealing the existence of a countable infinity of unusual single-particle states, which are localized with a multitude of localization lengths in a Vicsek fractal network with diamond-shaped loops as the "unit cells." The family of localized states forms clusters of increasing size, much in the sense of Aharonov-Bohm cages [J. Vidal et al., Phys. Rev. Lett. 81, 5888 (1998)], but now without a magnetic field. The length scale at which the localization effect for each of these states sets in can be uniquely predicted following a well-defined prescription developed within the framework of a real-space renormalization group. The scheme allows an exact evaluation of the energy eigenvalue for every such state which is ensured to remain in the spectrum of the system even in the thermodynamic limit. In addition, we discuss the existence of a perfectly conducting state at the band center of this geometry and the influence of a uniform magnetic field threading each elementary plaquette of the lattice on its spectral properties. Of particular interest is the case of extreme localization of single-particle states when the magnetic flux equals half the fundamental flux quantum.
  Physical Review B 06/2012; 85(21):214203. · 3.69 Impact Factor
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  Article: On the extendedness of eigenstates in a hierarchical lattice: A critical view

  Biplab Pal, Arunava Chakrabarti, Nitai Bhattacharya
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  ABSTRACT: We take a critical view at the basic definition of extended single particle states in a non-translationally invariant system. For this, we present the case of a hierarchical lattice and incorporate long range interactions that are also distributed in a hierarchical fashion. We show that it is possible to explicitly construct eigenstates with constant amplitudes (normalized to unity) at every lattice point for special values of the electron-energy. However, the end-to-end transmission, corresponding to the above energy of the electron in such a hierarchical system depends strongly on a special correlation between the numerical values of the parameters of the Hamiltonian. Keeping the energy and the distribution of the amplitudes invariant, one can transform the lattice from conducting to insulating simply by tuning the numerical values of the long range interaction. The values of these interactions themselves display a fractal character.
  Solid State Communications 10/2011; 151(24):1894-1898. · 1.65 Impact Factor