arXiv subjects

Arunava Chakrabarti

Publications and source records attributed to Arunava Chakrabarti.

At least 37 records · Page 2Linked to original sources

arXiv2016

Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi-one dimensionality

It is shown that, an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight binding model can be tailored to generate absolutely continuous energy bands. It can be achieved if linear atomic clusters of an appropriate size are side coupled to a suitable subset of sites in the backbone, and if the nearest neighbor hopping integrals, in the backbone and in the side coupled cluster bear a certain ratio. We work out the precise relationship between the number of atoms in one of the building blocks in the backbone, and that in the side attachment. In addition, we also evaluate the definite correlation between the numerical values of the hopping integrals at different subsections of the chain, that can convert an otherwise point spectrum (or, a singular continuous one for deterministically disordered lattices) with exponentially (or power law ) localized eigenfunctions to an absolutely continuous spectrum comprising one or more bands (subbands) populated by extended, totally transparent eigenstates. The results, which are analytically exact, put forward a non-trivial variation of the Anderson localization [P. W. Anderson, Phys. Rev. 109, 1492 (1958)], pointing towards its unusual sensitivity to the numerical values of the system parameters and, go well beyond the other related models such as the Random Dimer Model (RDM) [Dunlap et al., Phys. Rev. Lett. 65, 88 (1990)].

cond-mat.dis-nn↗

arXiv2016

Spin filter for arbitrary spins by substrate engineering

We design spin filters for particles with potentially arbitrary spin S (= 1/2, 1, 3/2,....) using a one-dimensional periodic chain of magnetic atoms as a quantum device. Describing the system within a tight-binding formalism we present an analytical method to unravel the analogy between a one-dimensional magnetic chain and a multi-strand ladder network. This analogy is crucial, and is subsequently exploited to engineer gaps in the energy spectrum by an appropriate choice of the magnetic substrate. We obtain an exact correlation between the magnitude of the spin of the incoming beam of particles and the magnetic moment of the substrate atoms in the chain desired for opening up of a spectral gap. Results of spin polarized transport, calculated within a transfer matrix formalism, are presented for particles having half-integer as well as higher spin states. We find that the chain can be made to act as a quantum device which opens a transmission window only for selected spin components over certain ranges of the Fermi energy, blocking them in the remaining part of the spectrum. The results appear to be robust even when the choice of the substrate atoms deviates substantially from the ideal situation, as verified by extending the ideas to the case of a spin spiral. Interestingly, the spin spiral geometry, apart from exhibiting the filtering effect, is also seen to act as a device flipping spins - an effect that can be monitored by an interplay of the system size and the period of the spiral. Our scheme is applicable to ultracold quantum gases, and might inspire future experiments in this direction.

cond-mat.mes-hall↗

arXiv2015

Engineering slow light and mode crossover in a fractal-kagome waveguide network

We present an analytically exact scheme of unraveling a multitude of flat, dispersionless photonic bands in a kagome waveguide strip where each elementary plaquette hosts a deterministic fractal geometry of arbitrary size. The number of non-dispersive eigenmodes grows as higher and higher order fractal geometry is embedded in the kagome motif. Such eigenmodes are found to be localized with finite support in the kagome strip and exhibit a hierarchy of localization areas. The onset of localization can, in principle, be delayed in space by an appropriate choice of frequency of the incident wave. The length scale at which the onset of localization for each mode occurs, can be tuned at will as prescribed here using a real space renormalization method. Conventional methods of extracting the non-dispersive modes in such geometrically frustrated lattices fail as a non-translationally invariant fractal decorates the unit cells in the transverse direction. The scheme presented here circumvents this difficulty, and thus may inspire the experimentalists to design similar fractal incorporated kagome or Lieb class of lattices to observe a multifractal distribution of flat photonic bands.

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arXiv2015

Engineering flat electronic bands in quasiperiodic and fractal loop geometries

Exact construction of one electron eigenstates with flat, non-dispersive bands, and localized over clusters of various sizes is reported for a class of quasi-one dimensional looped networks. Quasiperiodic Fibonacci and Berker fractal geometries are embedded in the arms of the loop threaded by a uniform magnetic flux. We work out an analytical scheme to unravel the localized single particle states pinned at various atomic sites or over clusters of them. The magnetic field is varied to control, in a subtle way, the extent of localization and the location of the flat band states in energy space. In addition to this we show that, an appropriate tuning of the field can lead to a re-entrant behavior of the effective mass of the electron in a band, with a periodic flip in its sign.

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arXiv2015

Flat band analogues and flux driven extended electronic states in a class of geometrically frustrated fractal networks

We demonstrate, by explicit construction, that a single band tight binding Hamiltonian defined on a class of deterministic fractals of the b = 3N Sierpinski type can give rise to an infinity of dispersionless, flat-band like states which can be worked out analytically using the scale invariance of the underlying lattice. The states are localized over clusters of increasing sizes, displaying the existence of a multitude of localization areas. The onset of localization can, in principle, be delayed in space by an appropriate choice of the energy of the electron. A uniform magnetic field threading the elementary plaquettes of the network is shown to destroy this staggered localization and generate absolutely continuous sub-bands in the energy spectrum of these non-translationally invariant networks.

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arXiv2014

Engineering bands of extended electronic states in a class of topologically disordered and quasiperiodic lattices

We show that a discrete tight-binding model representing either a random or a quasiperiodic array of bonds, can have the entire energy spectrum or a substantial part of it absolutely continuous, populated by extended eigenfunctions only, when atomic sites are coupled to the lattice locally, or non-locally from one side. The event can be fine-tuned by controlling only the host-adatom coupling in one case, while in two other cases cited here an additional external magnetic field is necessary. The delocalization of electronic states for the group of systems presented here is sensitive to a subtle correlation between the numerical values of the Hamiltonian parameters - a fact that is not common in the conventional cases of Anderson localization. Our results are analytically exact, and supported by numerical evaluation of the density of states and electronic transmission coefficient.

cond-mat.dis-nn↗

arXiv2014

Exotic electron states and tunable magneto-transport in a fractal Aharonov-Bohm interferometer

A Sierpinski gasket fractal network model is studied in respect of its electronic spectrum and magneto-transport when each arm of the gasket is replaced by a diamond shaped Aharonov-Bohm interferometer, threaded by a uniform magnetic flux. Within the framework of a tight binding model for non-interacting, spinless electrons and a real space renormalization group method we unravel a class of extended and localized electronic states. In particular, we demonstrate the existence of extreme localization of electronic states at a special finite set of energy eigenvalues, and an infinite set of energy eigenvalues where the localization gets delayed in space (staggered localization). These eigenstates exhibit a multitude of localization areas. The two terminal transmission coefficient and its dependence on the magnetic flux threading each basic Aharonov-Bohm interferometer is studied in details. Sharp switch on- switch off effects that can be tuned by controlling the flux from outside, are discussed. Our results are analytically exact.

cond-mat.mes-hall↗

arXiv2014

Absolutely continuous energy bands in the electronic spectrum of quasiperiodic ladder networks

The energy spectra of quasi-one dimensional quasiperiodic ladder networks are analyzed within a tight binding description. In particular, we show that if a selected set of sites in each strand of a ladder is tunnel-coupled to quantum dots attached from a side, absolutely continuous subbands can be generated in the spectrum if one tunes the dot potential and the dot-strand coupling appropriately. Typical cases with two and three strand Fibonacci ladders in the off diagonal model are discussed in details. We also discuss the possibility of re-entrant insulator-metal transition for a general n-strand ladder network when n becomes large. The observations remain valid even in the case of a disordered ladder network with the same constituents. The results are analytically exact.

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arXiv2013

Complete absence of localization in a family of disordered lattices

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.

cond-mat.dis-nn↗

arXiv2012

Engineering light localization in a fractal waveguide network

We present an exact analytical method of engineering the localization of electromagnetic waves in a fractal waveguide network. It is shown that, a countable infinity of localized electromagnetic modes 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 form 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 non-trivial, if not impossible for any random or deterministically disordered waveguide network.

cond-mat.dis-nn↗

arXiv2012

Controlled engineering of extended states in disordered systems

We describe how to engineer wavefunction delocalization in disordered systems modelled by tight-binding Hamiltonians in d>1 dimensions. We show analytically that a simple product structure for the random onsite potential energies, together with suitably chosen hopping strengths, allows a resonant scattering process leading to ballistic transport along one direction, and a controlled coexistence of extended Bloch states and anisotropically localized states in the spectrum. We demonstrate that these features persist in the thermodynamic limit for a continuous range of the system parameters. Numerical results support these findings and highlight the robustness of the extended regime with respect to deviations from the exact resonance condition for finite systems. The localization and transport properties of the system can be engineered almost at will and independently in each direction. This study gives rise to the possibility of designing disordered potentials that work as switching devices and band-pass filters for quantum waves, such as matter waves in optical lattices.

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arXiv2012

Interplay of magnetic field and geometry in magneto-transport of mesoscopic loops with Rashba and Dresselhaus spin-orbit interactions

Electronic transport in closed loop structures is addressed within a tight-binding formalism and in the presence of both the Rashba and Dresselhaus spin-orbit interactions. It has been shown that any one of the spin-orbit fields can be estimated precisely if the other one is known, by observing either the transmission resonance or anti-resonance of unpolarized electrons. The result is obtained through an exact analytic calculation for a simple square loop, and through a numerically exact formulation for a circular ring. The sensitivity of the transport properties on the geometry of the interferometer is discussed in details.

cond-mat.mes-hall↗

arXiv2012

A proposal for the measurement of Rashba and Dresselhaus spin-orbit interaction strengths in a single sample

We establish an exact analytical treatment for the determination of the strengths of the Rashba and Dresselhaus spin-orbit interactions in a single sample by measuring persistent spin current. A hidden symmetry is exploited in the Hamiltonian to show that the spin current vanishes when the strength of the Dresselhaus interaction becomes equal to the strength of the Rashba term. The results are sustained even in the presence of disorder and thus an experiment in this regard will be challenging.

cond-mat.mes-hall↗

arXiv2012

Staggered and extreme localization of electron states in fractal space

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 form 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 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.

cond-mat.dis-nn↗

arXiv2012

Multi-terminal magneto-transport in an interacting fractal network: a mean field study

Magneto-transport of interacting electrons in a Sierpinski gasket fractal is studied within a mean field approach. We work out the three-terminal transport and study the interplay of the magnetic flux threading the planar gasket and the dephasing effect introduced by the third lead. For completeness we also provide results of the two-terminal transport in presence of electron-electron interaction. It is observed that dephasing definitely reduces the transport, while the magnetic field generates a continuum in the transmission spectrum signaling a band of extended eigenstates in this non-translationally invariant fractal structure. The Hubbard interaction and the dephasing introduced by the third lead play their parts in reducing the average transmission, and opens up gaps in the spectrum, but can not destroy the continuum in the spectrum.

cond-mat.mes-hall↗

arXiv2011

A Fibonacci atomic chain with side coupled quantum dots: crossover from a singular continuous to a continuous spectrum and related issues

Interaction of bound states with a singular continuous spectrum is studied using a one dimensional Fibonacci quasicrystal as a prototype example. Single level quantum dots are attached from a side to a subset of atomic sites of the quasiperiodic chain. The proximity of the dots to the chain is modeled by introducing a tunnel hopping between a dot and the backbone. It is shown that, depending upon the proximity of the side coupled dot, the spectrum of an infinite quasiperiodic chain can display radical changes from its purely one dimensional characteristics. Absolutely continuous parts in the spectrum can be generated as well as isolated resonant eigenstates whose positions in the spectrum are sensitive to the proximity of the quantum dots. The cycles of the matrix map and the two terminal transport are discussed in details.

cond-mat.dis-nn↗

arXiv2011

Electron states and magneto-transport in a graphene geometry with a fractal distribution of holes

We consider an infinite graphene geometry where bonds and sites have been removed selectively to map it onto an effective Sierpinski gasket comprising of hexagons. We show that such a structure is capable of sustaining an infinite number of extended single particle states inspite of the absence of any translational order. When each basic hexagonal plaquette in the Sierpinski geometry is threaded by a magnetic flux, the spectrum exhibits bands of extended eigenstates. The bands persist for any arbitrary value of the flux but disappear again as the flux becomes equal to half the fundamental flux quantum. The localization - de-localization issues are discussed thoroughly along with the computation of two terminal magneto-transport of finite versions of the lattice. The numerical results corroborate our analytical findings.

cond-mat.mes-hall↗

arXiv2011

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 presence of Rashba and Dresselhaus spin-orbit interactions. A completely analytical technique within a tight-binding formalism unveils the spin-split bands in 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.

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