Stationary, dynamical, and spectral electronic properties of a correlated random ladder model with coexisting extended and localized states

Abstract

We study some stationary, dynamical, and spectral properties of a tight-binding Hamiltonian model for noninteracting electrons in a random two-channels ladder with correlated disorder that presents superposed bands of localized and extended states. We compute the participation number, Kubo-Greenwood conductance, Lyapunov exponent, the spread of an initially localized wave packet, as well as the level-spacing statistics in the band of coexisting localized and extended states. All stationary quantities show a metallic character at the coexistence energy band, such as a finite conductance and vanishing Lyapunov exponent. The wave packet exhibits a ballistic spread due to the Bloch-type nature of the extended states. On the other hand, the levelspacing statistics is characterized by a new distribution function which accounts for the superposition of uniformly distributed Bloch-type states and Poissonian-distributed localized states.

Controlled engineering of extended states in disordered systems

“…Let us remark that these choices, particularly for L y ≪ L x , resemble and generalise quasi-1D "ladder" models currently discussed in the literature to describe electronic transport in DNA 42,43 and mesoscopic devices. [44][45][46] However we believe that a faithful realization of our model can be implemented using optical potentials and matter waves, where single-site resolution and control has already been demonstrated. [47][48][49][50][51][52][53][54] C. Reduction to decoupled channels Equations ( 4) and ( 5) allow us to factorize the ǫ x matrix as…”

Robust entanglement transfer through a disordered qubit ladder

“…In [33] (see also [34]) it was shown that when n,1 , n,2 , and γ n obey constant proportions between each other across the chain, one is able to choose an appropriate basis set that decouples both legs. Moreover, it is possible to turn one of them completely free of disorder [33].…”

“…They also put forward the possibility of spanning a band of disorder-free states coexisting with exponentially-localized modes given the on-site energies and interchain hopping strenghts follow constant proportions along the ladder [33]. de Moura et al further found out a novel level-spacing statistics associated to it [34]. A generalized version of this wavefunction delocalization engineering for N -leg ladder systems has also been put forward [35].…”

Bloch oscillation in correlated aperiodic ladders

“…Recently, Sil et al have shown that a finite spectrum of delocalized states can appear in double‐strand systems for a special choice of the Hamiltonian parameters (). Moreover, contrary to previous examples of systems which present mobility edges, those extended states lie down in the same energy region of localized states ().…”