Comment on ``Periodic wave functions and number of extended states in random dimer systems'

There are no periodic wave-functions in the RDM but close to the critical energies there exist periodic envelopes. These envelopes are given by the non-disordered properties of the system.Comment: RevTex file, 1 page, Comment X. Huang, X. Wu and C. Gong, Phys. Rev. B 55, 11018 (1997

Nanowires: A route to efficient thermoelectric devices

Miniaturization of electronic devices aims at manufacturing ever smaller products, from mesoscopic to nanoscopic sizes. This trend is challenging because the increased levels of dissipated power demands a better understanding of heat transport in small volumes. A significant amount of the consumed energy is transformed into heat and dissipated to the environment. Thermoelectric materials offer the possibility to harness dissipated energy and make devices less energy-demanding. Heat-to-electricity conversion requires materials with a strongly suppressed thermal conductivity but still high electronic conduction. Nanowires can meet nicely these two requirements because enhanced phonon scattering at the surface and defects reduces the lattice thermal conductivity while electric conductivity is not deteriorated, leading to an overall remarkable thermoelectric efficiency. Therefore, nanowires are regarded as a promising route to achieving valuable thermoelectric materials at the nanoscale. In this paper, we present an overview of key experimental and theoretical results concerning the thermoelectric properties of nanowires. The focus of this review is put on the physical mechanisms by which the efficiency of nanowires can be improved. Phonon scattering at surfaces and interfaces, enhancement of the power factor by quantum effects and topological protection of electron states to prevent the degradation of electrical conductivity in nanowires are thoroughly discussed

Localisation and finite-size effects in graphene flakes

We show that electron states in disordered graphene, with an onsite potential that induces inter-valley scattering, are localised for all energies at disorder as small as of the band width of clean graphene. We clarify that, in order for this Anderson-type localisation to be manifested, graphene flakes of size or larger are needed. For smaller samples, due to the surprisingly large extent of the electronic wave functions, a regime of apparently extended (or even critical) states is identified. Our results complement earlier studies of macroscopically large samples and can explain the divergence of results for finite-size graphene flakes

Interactions and thermoelectric effects in a parallel-coupled double quantum dot

We investigate the nonequilibrium transport properties of a double quantum dot system connected in parallel to two leads, including intradot electron-electron interaction. In the absence of interactions the system supports a bound state in the continuum. This state is revealed as a Fano antiresonance in the transmission when the energy levels of the dots are detuned. Using the Keldysh nonequilibrium Green's function formalism, we find that the occurrence of the Fano antiresonance survives in the presence of Coulomb repulsion. We give precise predictions for the experimental detection of bound states in the continuum. First, we calculate the differential conductance as a function of the applied voltage and the dot level detuning and find that crossing points in the diamond structure are revealed as minima due to the transmission antiresonances. Second, we determine the thermoelectric current in response to an applied temperature bias. In the linear regime, quantum interference gives rise to sharp peaks in the thermoelectric conductance. Remarkably, we find interaction induced strong current nonlinearities for large thermal gradients that may lead to several nontrivial zeros in the thermocurrent. The latter property is especially attractive for thermoelectric applications.Comment: 9 pages, 8 figure

FIBONACCI SUPERLATTICES OF NARROW-GAP III-V SEMICONDUCTORS

We report theoretical electronic structure of Fibonacci superlattices of narrow-gap III-V semiconductors. Electron dynamics is accurately described within the envelope-function approximation in a two-band model. Quasiperiodicity is introduced by considering two different III-V semiconductor layers and arranging them according to the Fibonacci series along the growth direction. The resulting energy spectrum is then found by solving exactly the corresponding effective-mass (Dirac-like) wave equation using tranfer-matrix techniques. We find that a self-similar electronic spectrum can be seen in the band structure. Electronic transport properties of samples are also studied and related to the degree of spatial localization of electronic envelope-functions via Landauer resistance and Lyapunov coefficient. As a working example, we consider type II InAs/GaSb superlattices and discuss in detail our results in this system.Comment: REVTeX 3.0, 16 pages, 8 figures available upon request. To appear in Semiconductor Science and Technolog

Enhancing thermoelectric properties of graphene quantum rings

We study the thermoelectric properties of rectangular graphene rings connected symmetrically or asymmetrically to the leads. A side-gate voltage applied across the ring allows for the precise control of the electric current flowing through the system. The transmission coefficient of the rings manifests Breit-Wigner line-shapes and/or Fano line-shapes, depending on the connection configuration, the width of nanoribbons forming the ring and the side-gate voltage. We find that the thermopower and the figure of merit are greatly enhanced when the chemical potential is tuned close to resonances. Such enhancement is even more pronounced in the vicinity of Fano like anti-resonances which can be induced by a side-gate voltage independently of the geometry. This opens a possibility to use the proposed device as a tunable thermoelectric generator.Comment: 6 pages, 5 figures, accepted for publication in Physical Review

Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect

We calculate numerically the localization length critical index within the Chalker-Coddington (CC) model for plateau-plateau transitions in the quantum Hall effect. Lyapunov exponents have been calculated with relative errors on the order $10^{-3}$. Such high precision was obtained by considering the distribution of Lyapunov exponents for large ensembles of relatively short chains and calculating the ensemble average values. We analyze thoroughly finite size effects and find the localization length critical index $\nu= 2.517\pm 0.018$.Comment: 4 pages, 4 figure

Dynamical phenomena in Fibonacci Semiconductor Superlattices

We present a detailed study of the dynamics of electronic wavepackets in Fibonacci semiconductor superlattices, both in flat band conditions and subject to homogeneous electric fields perpendicular to the layers. Coherent propagation of electrons is described by means of a scalar Hamiltonian using the effective-mass approximation. We have found that an initial Gaussian wavepacket is filtered selectively when passing through the superlattice. This means that only those components of the wavepacket whose wavenumber belong to allowed subminibands of the fractal-like energy spectrum can propagate over the entire superlattice. The Fourier pattern of the transmitted part of the wavepacket presents clear evidences of fractality reproducing those of the underlying energy spectrum. This phenomenon persists even in the presence of unintentional disorder due to growth imperfections. Finally, we have demonstrated that periodic coherent-field induced oscillations (Bloch oscillations), which we are able to observe in our simulations of periodic superlattices, are replaced in Fibonacci superlattices by more complex oscillations displaying quasiperiodic signatures, thus sheding more light onto the very peculiar nature of the electronic states in these systems.Comment: 7 pagex, RevTex, 5 Postscript figures. Physical Review B (in press

Transmission resonances and supercritical states in a one dimensional cusp potential

We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric cusp potential. We compute the scattering and bound states solutions and we derive the conditions for transmission resonances as well as for supercriticality.Comment: 10 pages. Revtex 4. To appear in Phys Rev.

Fluorescence decay in aperiodic Frenkel lattices

We study motion and capture of excitons in self-similar linear systems in which interstitial traps are arranged according to an aperiodic sequence, focusing our attention on Fibonacci and Thue-Morse systems as canonical examples. The decay of the fluorescence intensity following a broadband pulse excitation is evaluated by solving the microscopic equations of motion of the Frenkel exciton problem. We find that the average decay is exponential and depends only on the concentration of traps and the trapping rate. In addition, we observe small-amplitude oscillations coming from the coupling between the low-lying mode and a few high-lying modes through the topology of the lattice. These oscillations are characteristic of each particular arrangement of traps and they are directly related to the Fourier transform of the underlying lattice. Our predictions can be then used to determine experimentally the ordering of traps.Comment: REVTeX 3.0 + 3PostScript Figures + epsf.sty (uuencoded). To appear in Physical Review