1,2,…∞: From Bilayer to Superlattice

Physical Review B, 2014

We show that in layered systems with electronic phase separation tendency, the long-range Coulomb interaction can drive the spontaneous formation of unidirectional superlattices of electronic charge in a completely homogeneous crystalline background. In this self-organized electronic heterostructure, the ratio among the number of crystalline planes in the minority and majority electronic phases corresponds to Farey fractions with the superlattice period controlled by the background charge density and the frustrating Coulomb interaction strength. The phase diagram displays Arnold tongues obeying a modified Farey tree hierarchy and a devil's staircase, typical of systems with frustration among different scales. We further discuss the competition of these electronic superlattices, recently observed in iron-based superconductors and mixed valence compounds, with in-plane electronically modulated phases.

Physical review. B, Condensed matter, 1994

We have analyzed the influence of the topmost two layers on the properties of the collective excitations of a jinite superlattice structure. For semi inj-inite superlattices the effect of the topmost layers on the collective excitations was discussed by Streight and Mills [Phys. Rev. B 29, 6337 (1987)]. We extend the discussion to the case of a superlattice with a finite number of periods, in which the thickness and the dielectric constant of the topmost two layers may differ from those of the layers below. A general dispersion relation for the finite superlattice is derived and applied to finite GaAs-A1As superlattices. The dispersion curves and the electrostatic potentials show that several modes change in character with varied thickness of the topmost two layers. This change of the mode character is reflected in the electron-energy-loss spectra calculated in the framework of the dielectric theory.

Proceedings of the Royal Society of …, 1938

Solid State Communications, 2007

Naturally occuring or man-made systems displaying periodic spatial modulations of their properties on a nanoscale constitute superlattices. Such modulated structures are important both as prototypes of simple nanotechnological devices and as particular examples of emerging spatial inhomogeneity in interacting many-electron systems. Here we investigate the effect different types of modulation of the system parameters have on the ground-state energy and the charge-density distribution of the system. The superlattices are described by the inhomogeneous attractive Hubbard model, and the calculations are performed by density-functional and densitymatrix renormalization group techniques. We find that modulations in local electric potentials are much more effective in shaping the system's properties than modulations in the attractive on-site interaction. This is the same conclusions we previously (Phys. Rev. B 71, 125130) obtained for repulsive interactions, suggesting that it is not an artifact of a specific state, but a general property of modulated structures.

Physical Review B, 1990

A terminated Kronig-Penney-like model is proposed for studying electronic surface states in compositional {potential-modulation) and in effective-mass {mass-modulation) superlattices. The existence of surface states in the minigaps of both types of superlattices is shown explicitly and their properties are discussed.

Journal of Experimental and Theoretical Physics, 2011

We investigate the dynamic susceptibility and one dimensional density of states in an initially sinusoidal superlattice containing simultaneously 2D phase inhomogeneities simulating correlated rough nesses of superlattice interfaces and 3D amplitude inhomogeneities of the superlattice layer materials. The analytic expression for the averaged Green's function of the sinusoidal superlattice with two phase inho mogeneities is derived in the Bourret approximation. It is shown that the effect of increasing asymmetry in the peak heights of dynamic susceptibility at the Brillouin zone boundary of the superlattice, which was dis covered earlier upon an increase in root mean square (rms) fluctuations, also takes place upon an increase in the correlation wavenumber of inhomogeneities. However, the peaks in this case also become closer, and the width and depth of the gap in the density of states decrease thereby. It is shown that the enhancement of rms fluctuations of 3D amplitude inhomogeneities in a superlattice containing 2D phase inhomogeneities suppresses the effect of dynamic susceptibility asymmetry and leads to a slight broadening of the gap in the density of states and a decrease in its depth. Targeted experiments aimed at detecting the effects studied here would facilitate the development of radio spectroscopic and optical methods for identi fying the presence of inhomogeneities of various dimensions in multilayer magnetic and optical structures.

Physical Review Letters, 2009

In a unified approach, we study the transport properties of periodic-on-average bi-layered photonic crystals, metamaterials and electron superlattices. Our consideration is based on the analytical expression for the localization length derived for the case of weakly fluctuating widths of layers, that also takes into account possible correlations in disorder. We analyze how the correlations lead to anomalous properties of transport. In particular, we show that for quarter stack layered media specific correlations can result in a ω 2 -dependence of the Lyapunov exponent in all spectral bands.

Surface Science Reports, 2002

The existence and properties of localised electronic states are described in binary (two layers per period) and polytype (multiple layers per period) semiconductor superlattices. Special attention is paid to surface effects, due to the superlattice potential termination by a clad layer, and the resulting Tamm-like surface states localised at the superlattice/clad-layer interface. The effect of the Bragg con®nement of electrons in coupled superlattices, particularly the formation of above-barrier bound states at the junction of superlattices or the spacer layer embedded in a superlattice, is also discussed. Based on peculiar properties of localised superlattices states, with respect to extended miniband states, their importance for both the fundamental research and various device applications is stressed out. The most frequently used Kronig±Penney-like approaches within the framework of effective-mass and envelope-function approximation, namely, the direct-matching procedure and the transfermatrix technique, are described for bulk-and surface-electronic-structure calculations of terminated binary and polytype superlattices, as well as for coupled superlattices. Comparison of the results with experimental data and/ or more advanced computations indicates that these simple models are versatile and accurate (within their domain of validity), when applied to AlGaAs-based heterostructures. Two Green-function techniques, one based on the combined factorisation and Wronskian methods, and the other on the interface-response theory, are presented for the purpose of density-of-states analysis. For terminated binary GaAs/AlGaAs superlattices, an appropriate choice of the superlattice and clad-layer parameters, as well as the surface location within the superlattice period, enables a surface state with desired energy position inside the minigap, and required extension into the superlattice bulk, to be achieved. Introduction of additional layers into the superlattice sequence, resulting in a polytype superlattice, offers a further means of in¯uencing the energies and localisation properties of surface states, but, more importantly, creates an opportunity for surface states to occur under classical Shockley conditions, which is not possible in binary superlattices, where only Tamm-like surface states can exist. The Surface Science Reports 47 (2002) 93±196

Physical Review B, 1998

The problem of superlattice symmetry, i.e., the question of periodicity along the growth direction ͑surface normal͒ in magnetic multilayer systems, is discussed using discrete Fourier transformations for the anisotropy energy, as well as, for the antiparallel and perpendicular interface exchange coupling. We analyze the system Cu͑100͒/͑Cu 3 Ni 3) n , where n is the number of repetitions, for the case of free surfaces and surfaces capped semi-infinitely by Cu͑100͒. It will be shown that for some magnetic properties, and only in certain situations, ͑almost͒ periodic behavior with respect to n applies, while for other properties an oscillatory behavior is characteristic. Also discussed are implications with respect to typical experimental situations and with respect to traditional supercell approaches. ͓S0163-1829͑98͒00313-0͔

Applied Physics Letters, 1987