arXiv subjects

S. N. Karmakar

Publications and source records attributed to S. N. Karmakar.

44 records · Page 3Linked to original sources

arXiv2005

On the role of electron correlation and disorder on persistent currents in isolated one-dimensional rings

To understand the role of electron correlation and disorder on persistent currents in isolated 1D rings threaded by magnetic flux $ϕ$, we study the behavior of persistent currents in aperiodic and ordered binary alloy rings. These systems may be regarded as disordered systems with well-defined long-range order so that we do not have to perform any configuration averaging of the physical quantities. We see that in the absence of interaction, disorder suppresses persistent currents by orders of magnitude and also removes its discontinuity as a function of $ϕ$. As we introduce electron correlation, we get enhancement of the currents in certain disordered rings. Quite interestingly we observe that in some cases, electron correlation produces kink-like structures in the persistent current as a function of $ϕ$. This may be considered as anomalous Aharonov-Bohm oscillations of the persistent current and recent experimental observations support such oscillations. We find that the persistent current converges with the size of the rings.

cond-mat.mes-hall↗

arXiv2004

Strange behavior of persistent currents in small Hubbard rings

We show exactly that small Hubbard rings exhibit unusual kink-like structures giving anomalous oscillations in persistent current. Singular behavior of persistent current disappears in some cases. In half-filled systems mobility gradually drops to zero with interaction, while it converges to some finite value in non-half-filled cases.

cond-mat.mes-hall↗

arXiv1998

Physical nature of all the electronic states in the Thue-Morse chain

We present an analytical method for finding all the electronic eigenfunctions and eigenvalues of the aperiodic Thue-Morse lattice. We prove that this system supports only extended electronic states which is a very unusual behavior for this class of systems, and so far as we know, this is the only example of a quasiperiodic or aperiodic system in which critical or localized states are totally absent in the spectrum. Interestingly we observe that the symmetry of the lattice leads to the existence of degenerate eigenstates and all the eigenvalues excepting the four global band edges are doubly degenerate. We show exactly that the Landauer resistivity is zero for all the degenerate eigenvalues and it scales as $\sim L^2$ ($L=$ system size) at the global band edges. We also find that the localization length $ξ$ is always greater than the system size.

cond-mat↗

arXiv1998

Periodic features in the Dynamic Structure Factor of the Quasiperiodic Period-doubling Lattice

We present an exact real-space renormalization group (RSRG) method for evaluating the dynamic structure factor of an infinite one-dimensional quasiperiodic period-doubling (PD) lattice. We observe that for every normal mode frequency of the chain, the dynamic structure factor $S(q,ω)$ always exhibits periodicity with respect to the wave vector $q$ and the presence of such periodicity even in absence of translational invariance in the system is quite surprising. Our analysis shows that this periodicity in $S(q,ω)$ actually indicates the presence of delocalized phonon modes in the PD chain. The Brillouin Zones of the lattice are found to have a hierarchical structure and the dispersion relation gives both the acoustic as well as optical branches. The phonon dispersion curves have a nested structure and we have shown that it is actually the superposition of the dispersion curves of an infinite set of periodic lattices.

cond-mat↗

arXiv1994

On the 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.

cond-mat↗

arXiv1994

A renormalization group analysis of extended electronic states in 1d 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 $δ$-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},

cond-mat↗

arXiv1993

Extended electronic states in disordered 1-d lattices: an example

We discuss a very simple model of a 1-d disordered lattice, in which {\em all} the electronic eigenstates are extended. The nature of these states is examined from several viewpoints, and it is found that the eigenfunctions are not Bloch functions although they extend throughout the chain. Some typical wavefunctions are plotted. This problem originated in our earlier study of extended states in the quasiperiodic copper-mean lattice [ Sil, Karmakar, Moitra and Chakrabarti, Phys. Rev. B (1993) ]. In the present investigation extended states are found to arise from a different kind of correlation than that of the well-known dimer-type.

cond-mat↗

arXiv1993

Extended states in 1D lattices: application to quasiperiodic copper-mean chain

The question of the conditions under which 1D systems support extended electronic eigenstates is addressed in a very general context. Using real space renormalisation group arguments we discuss the precise criteria for determining the entire spertrum 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 [ You et al. (1991)] : we show analytically that there is in fact an infinite number of extended eigenstates in this lattice which form fragmented minibands.

cond-mat↗