Related papers: Engineering flat electronic bands in quasiperiodic…
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…
The spectrum of spinless, non-interacting electrons on a linear chain that is buckled in a non- uniform manner giving it a flavor of a topologically disordered lattice, is investigated within a tight binding formalism. We have addressed two…
The explicit construction of non-dispersive flat band modes and the tunability of has been reported for a hierarchical 3-simplex fractal geometry. A single band tight binding Hamiltonian defined for the deterministic self-similar…
Flat bands result in a divergent density of states and high sensitivity to interactions in physical systems. While such bands are well known in systems under magnetic fields, their realization and behavior in zero-field settings remain…
Exact one-electron eigenstates in finite parts of 1D periodic and Fibonacci chains of attractive and repulsive delta potentials are computed and analyzed. Bloch and bound state boundary conditions are related in terms of transfer matrices.…
Certain lattices with specific geometries have one or more spectral bands that are strictly flat, i.e. the electron energy is independent of the momentum. This can occur robustly irrespective of the specific couplings between the lattices…
The localization properties of electrons moving in a plane perpendicular to a spatially-correlated static magnetic field of random amplitude and vanishing mean are investigated. We apply the method of level statistics to the eigenvalues and…
One can confine the two-dimensional electron gas in semiconductor heterostructures electrostatically or by etching techniques such that a small electron island is formed. These man-made ``artificial atoms'' provide the experimental…
We discover a new wave localization mechanism in a periodic system without any disorder, which can produce a novel type of perfect flat band and is distinct from the known localization mechanisms, i.e., Anderson localization and flat band…
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…
We address the problem of analytically extracting a countable infinity of flat, non-dispersive bands in a periodic array of cells that comprise branching Vicsek geometries of higher and higher generations. Through a geometric construction,…
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…
The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides…
Finite strips, composed of a periodic stacking of infinite quasiperiodic Fibonacci chains, have been investigated in terms of their electronic properties. The system is described by a tight binding Hamiltonian. The eigenvalue spectrum of…
This short review presents a few case studies of finite electron systems for which strong correlations play a dominant role. In simple metal clusters, the valence electrons determine stability and shape of the clusters. The ionic skeleton…
Topological properties of energy spectra of general one-dimensional quasiperiodic systems, describing also Bloch electrons in magnetic fields, are studied for an infinity of irrational modulation frequencies corresponding to irrational…
I study the structure of the two-dimensional electron gas edge in the quantum Hall regime using the composite fermion approach. The electron density distribution and the composite fermion energy spectrum are obtained numerically in Hartree…
The existence of macroscopic shell structure of submicron metal clusters is known for several decades. Since the most studies provide theoretical analysis for clusters of spherical shape, the electron density inhomogeneities caused by shell…
Compact localized single particle eigenstates on a deterministic fractal substrate, modelled by a triangular Sierpinski gasket of arbitrarily large size, are unravelled and examined analytically. We prescribe an exact real space…
Flat magnetic nano-elements are an essential component of current and future spintronic devices. By shaping an element it is possible to select and stabilize chosen metastable magnetic states, control its magnetization dynamics. Here, using…