Quasiparticle states in superconducting superlattices

The energy bands and the global density of states are computed for superconductor / normal-metal superlattices in the clean limit. Dispersion relations are derived for the general case of insulating interfaces, including the mismatch of Fermi velocities and effective band masses. We focus on the influence of finite interface transparency and compare our results with those for transparent superlattices and trilayers. Analogously to the rapid variation on the atomic scale of the energy dispersion with layer thicknesses in transparent superlattices, we find strong oscillations of the almost flat energy bands (transmission resonances) in the case of finite transparency. In small-period transparent superlattices the BCS coherence peak disappears and a similar subgap peak is formed due to the Andreev process. With decreasing interface transparency the characteristic double peak structure in the global density of states develops towards a gapless BCS-like result in the tunnel limit. This effect can be used as a reliable STM probe for interface transparency.     

Wannier-Stark states in finite superlattices

Individual Wannier-Stark states are resolved in a current experiment over a wide electric-field range for a 5 and 4 period finite superlattice utilizing a hot-electron transistor. The observed field dependence of the tunneling transmission through the various states directly resembles the progressive localization of the wave functions. The basic transport through Wannier-Stark states in short-period superlattices is identified to be coherent. By tuning the Wannier-Stark state splitting with electric field into the optical phonon energy, the opening of new LO-phonon mediated transport paths is observed.     

Phonon-polariton density of states in semiconductor superlattices

An interesting property of modulated semiconductor materials is that their reflectance and absorption spectra can nearly be chosen at will by adjusting the layer geometry. Introducing the concept of phonon-polariton density of states, this paper is aimed at investigating spectral properties of multilayered materials in the infra-red frequency range. Using powerful analytical methods, we will successively consider the cases of infinite and semi-infinite superlattices. The local density of states of polariton modes is obtained using a Green's function technique. Complete information is then available on allowed radiative and non-radiative electromagnetic excitations, (as a function of frequency and wavelength), at any depth in the stratified material. This approach will depict the essential role played by the surface, which changes significantly the polariton density of states as compared to ideal unbounded materials. In multilayered materials, in addition to the effect induced by the surface, one can similarly investigate the influence of the internal interfaces on the polariton local density of states and, from these, on the optical properties of those systems. Electromagnetic eigenmodes arising from the accumulation of interfaces are crucial to assess the spectral properties involving TM-polarized radiations. Effects related to the TE-polarized radiations are explained from the macroscopic anisotropy due to the alternate growth of different semiconductors. These results will be used to discuss reflectance experiments and simulated ATR spectra.     

2D chaotic quantum states in superlattices

The semiclassical motion of an electron along the axis of a superlattice may be calculated from the miniband dispersion curve. Under a weak electric field the electron executes Bloch oscillations which confines the motion along the superlattice axis. When a magnetic field, tilted with respect to the superlattice axis, is applied the electron orbits become chaotic. The onset of chaos is characterised by a complex mixed stable-chaotic phase space and an extension of the orbital trajectories along the superlattice axis. This delocalisation of the orbits is also reflected in the quantum eigenstates of the system some of which show well-defined patterns of high probability density whose shapes resemble certain semiclassical orbits. This suggests that the onset of chaos will be manifest in electron transport through a finite superlattice. We also propose that these phenomena may be observable in the motion of trapped ultra-cold atoms in an optically induced superlattice potential and magnetic quadrupole potential whose axis is tilted relative to the superlattice axis.     

Diamond-like and graphite-like carbon states in short-period superlattices

The Raman and luminescence spectra are studied in superlattices consisting of carbon layers separated by thin SiC barrier layers. It is shown experimentally that, upon the avalanche annealing of an initially amorphous superlattice, the carbon layers can crystallize into either a diamond-like or graphite-like structure, depending on the geometrical parameters of the superlattice. A method is proposed for obtaining carbon films with a specified crystal modification within a unified technology.     

Zero-energy bound states in superconductor/ferromagnet superlattices

Andreev bound states in monoatomic superconductor–ferromagnet (S/F) superlattices are studied theoretically, assuming tunneling between S and F layers in perpendicular direction. Andreev reflection at S/F interfaces is strongly affected by the exchange interaction h in F layers. In the ground state, only for h≠0 zero-energy states (ZES) are formed on S and F layers. For h=0, corresponding to superconductor–normal metal (S/N) superlattices, ZES may appear in the nonequilibrium phase, =π. This is found both for s-wave and d-wave symmetry of the order parameter in S. The conditions for ZES are obtained as a function of h, of the transfer integral t for movement of quasiparticles (QPs) between S and F layers, and of the corresponding ground state phase difference _eq between two neighboring S layers.     

Extended two-parameter squeezed states

In a recent paper, a new λ-dependent squeezed states was proposed [J. Beckers, N. Debergh and F.H. Szafraniec, Phys. Lett. A 243 (1998) 256–260] in which the usual Fock-space creation operator has been modified by introducing a simple translational term. In this paper, we generalize this approach by adding a new term proportional to the creation operator using exponential quadratic operators.     

Stark states in semiconductor quantum wells and superlattices

The quasi-bound states of electrons and holes in coupled GaAsAlGaAs quantum wells in the presence of an applied electric field perpendicular to the wells are determined by the exact solution of the Schroedinger equation using the iteration matrix formalism. The transmission probability in a finite superlattice is also calculated taking into account the exact wave functions in the barriers and wells. The method can be useful to interpret recent tunneling-current measurements.     

The nontrivial states in one-dimensional nonlinear bichromatic superlattices

We study topological properties of one-dimensional nonlinear bichromatic superlattices and unveil the effect of nonlinearity on topological states. We find the existence of nontrivial edge solitions, which distribute on the boundaries of the lattice with their chemical potential located in the linear gap regime and are sensitive to the phase parameter of the superlattice potential. We further demonstrate that the topological property of the nonlinear Bloch bands can be characterized by topological Chern numbers defined in the extended two-dimensional parameter space. In addition, we discuss that the composition relations between the nolinear Bloch waves and gap solitions for the nonlinear superlattices. The stabilities of edge solitons are also studied.     

Localized electronic states in -layer-based superlattices with structural defects

Using an effect-barrier height method, we study the properties of the localized electronic states in an N-layer-based superlattice with structural defects within the framework of effective-mass theory. The coupling effect between normal and lateral degrees of freedom of an electron on the localized electronic states in both symmetric and asymmetric triple layer superlattices with structural defects has been considered numerically. The results show that the localized states display different behaviors in both symmetric and asymmetric structures in spite of the minibands being not influenced by the structural symmetry. Moreover, the coupling effect causes the minibands, minigaps and localized electron levels to depend on the transverse wave number k_xy. A brief physical analysis is given.     

Extended nature of coupled optical interface modes in Thue-Morse dielectric superlattices

We investigate coupled optical interface modes in Thue-Morse (TM) dielectric superlattices composed of two kinds of materials with frequency-dependent dielectric functions. Four basic transfer matrices are derived in the dielectric continuum approximation. By a standard matrix operation method, the trace map of the global transfer matrix in this configuration is obtained. Under Born-von Kármán boundary conditions, the frequency spectra are calculated and their branching rules together with the quartet property are elucidated. It is further proved rigorously that nearly all eigenmodes in this framework have extended nature. The quartet of the eigenmodes is illuminated analytically. The common features and pronounced differences compared with coupled optical interface modes in periodic and Fibonacci dielectric superlattices as well as with other collective elementary excitations in TM structures are also revealed. Received 24 September 2002 / Received in final form 11 January 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: gjin@nju.edu.cn     

Vertical hopping conduction via virtual states in intentionally disordered superlattices

A new mechanism of vertical conduction in intentionally disordered superlattices is examined. It is shown that low-temperature conduction due to phonon-assisted tunneling between distant quantum wells of a superlattice is determined mainly by hopping processes via virtual intermediate states. Under standard conditions a weak temperature dependence of vertical conduction is obtained for this mechanism. The characteristic behavior of the conductivity as a function of disorder amplitude is found for this mechanism. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 12, 879–884 (25 June 1999)     

Two types of extended states in random dimer barrier superlattices

We study numerically the effects of short-range correlated disorder on the electronic and transport properties of intentionally disordered GaAs–Al_xGa_1−xAs superlattices. We consider layers having identical thickness where the Al concentration x takes at random two different values with the constraint that one of them appears only in pairs, i.e. the random dimer barrier. Various physical quantities such as the conductance, the universal fluctuation conductance, the localization length, the resistance and its probability distribution are statistically computed by means of the transfer matrix formalism to discriminate the nature of the electronic states. In spite of the presence of disorder, the system exhibits two kinds of sets of propagating states lying below the barrier due to the characteristic structure of the superlattice. The states close to the resonance can be viewed as consisting of weakly localized states with very large localization length. In the band tails, i.e. for vanishing conductance, the states are strongly localized. The nature of the transition between these two regimes is quantitatively investigated through relevant physical quantities.