The electronic properties of graphene, a two-dimensional crystal of carbon atoms, are exceptionally novel. For instance, the low-energy quasiparticles in graphene behave as massless chiral Dirac fermions which has led to the experimental observation of many interesting effects similar to those predicted in the relativistic regime. Graphene also has immense potential to be a key ingredient of new devices, such as single molecule gas sensors, ballistic transistors and spintronic devices. Bilayer graphene, which consists of two stacked monolayers and where the quasiparticles are massive chiral fermions, has a quadratic low-energy band structure which generates very different scattering properties from those of the monolayer. It also presents the unique property that a tunable band gap can be opened and controlled easily by a top gate. These properties have made bilayer graphene a subject of intense interest. In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene f...

Properties of graphene: a theoretical perspective

We present a review, through selected illustra- tive examples, of the physics of classical vibrational modes in phononic lattices, which elaborates on the theo- ry, the formalism, the methods, and mainly on the numer- ical and experimental results related to phononic crystals. Most of the topics addressed here, are written in a self- consistent way and they can be read as independent indi- vidual parts.

http://esperia.iesl.forth.gr/~ppm/PUBLICATIONS/ZfKv220p765_2005.pdf

Classical vibrational modes in phononic lattices: theory and experiment

We study theoretically the propagation of lower-order Lamb waves in one-dimensional composite thin plates. The dispersion curves of Lamb modes propagating parallel to the surfaces of the thin plates in the periodic direction are calculated based on the plane wave expansion method. The existence of band gaps for low-order Lamb wave modes is demonstrated in the systems made of alternating strips of tungsten materials and silicon resin. The finite element method is employed to calculate the transmitted power spectra, which is in good agreement with the results by plane wave exposition. A crucial parameter, i.e., the ratio of the plate thickness $(L)$ to the lattice spacing $(D)$, is discussed in detail for the influence of formation of band gaps.

Stopbands for lower-order Lamb waves in one-dimensional composite thin plates

Revisiting the classical acoustics problem of rectangular side-branch cavities in a two-dimensional duct of infinite length we use the finite element method to numerically compute the acoustic resonances as well as the sound transmission and reflection for an incoming fundamental duct mode. To satisfy the requirement of outgoing waves in the far field we use two different forms of absorbing boundary conditions, namely the complex scaling method and the Hardy space method. In general the resonances are
damped due to radiation losses, but there also exist various types of localized trapped modes with nominally zero radiation loss. The most common type of trapped mode is antisymmetric about the duct axis and becomes quasi-trapped with very low damping if the symmetry about the duct axis is broken. In this case a Fano resonance results with resonance and antiresonance features and drastic changes in the sound transmission
and reflection coefficient. Two other types of trapped modes, termed embedded trapped modes, result from the interaction of neighbouring modes or Fabry–P´erot interference in multi-cavity systems. These embedded trapped modes occur only for very particular geometry parameters and frequencies and become highly localized quasi-trapped modes as soon as the geometry is perturbed. We show that all three types of trapped modes are possible in duct-cavity systems and that embedded trapped modes continue to exist when a cavity is moved off centre. If several cavities interact the single-cavity trapped mode splits into several trapped supermodes which might be useful for the design of low-frequency acoustic filters.

Trapped modes and Fano resonances in two-dimensional acoustical duct-cavity systems

We investigate the influence of a perpendicular magnetic field on the spectral and spin properties of a ballistic quasi-one-dimensional electron system with Rashba effect. The magnetic field strongly alters the spin-orbit induced modification to the subband structure when the magnetic length becomes comparable to the lateral confinement. A subband-dependent energy splitting at $k=0$ is found which can be much larger than the Zeeman splitting. This is due to the breaking of a combined spin orbital-parity symmetry.

Rashba effect and magnetic field in semiconductor quantum wires

Ballistic spin transport through waveguides, with symmetric or asymmetric double stubs attached to them periodically, is studied systematically in the presence of a weak spin-orbit coupling that makes the electrons precess. By an appropriate choice of the waveguide length and of the stub parameters injected spin-polarized electrons can be blocked completely and the transmission shows a periodic and nearly-square-type behavior, with values 1 and 0, with wide gaps when only one mode is allowed to propagate in the waveguide. A similar behavior is possible for a certain range of the stub parameters even when two modes can propagate in the waveguide and the conductance is doubled. Such a structure is a good candidate for establishing a realistic spin transistor. A further modulation of the spin current can be achieved by inserting defects in a finite-number stub superlattice. Finite-temperature effects on the spin conductance are also considered.

https://arxiv.org/pdf/cond-mat/0204415.pdf

Spin-current modulation and square-wave transmission through periodically stubbed electron waveguides

We study ballistic transport of spin-polarized electrons through quantum wires in which the Rashba spin-orbit interaction (SOI) is spatially modulated Subband mixing, due to SOI, between the two lowest subbands is taken into account Simplified approximate expressions for the transmission are obtained for electron energies close to the bottom of the first subband and near the value for which anticrossing of the two lowest subbands occurs In structures with periodically varied SOI strength, square-wave modulation on the spin transmission is found when only one subband is occupied and its possible application to the spin transistor is discussed When two subbands are occupied the transmission is strongly affected by the existence of SOI interfaces as well as by the subband mixing

http://export.arxiv.org/pdf/cond-mat/0401344

Spin transport of electrons through quantum wires with a spatially modulated Rashba spin-orbit interaction

The dielectric function and plasmon modes of a two-dimensional electron gas (2DEG) are studied in single- and double-quantum-well structures with Rashba spin-orbit interaction (RSOI) in the framework of the random-phase approximation. The RSOI splits each parabolic energy subband of a 2DEG into two nonparabolic spin branches and affects the electronic many-body correlation and dielectric properties of the 2DEG. The influence of the RSOI on the 2DEG plasmon spectrum in single quantum wells appears mainly in three ways: (1) an overall frequency lowering due to the energy band deformation; (2) a weak frequency oscillation stemming from the spin-split energy band; and (3) an enhancement of the Landau damping as a result of the emerging of the interbranch single-particle-excitation spectrum. In double quantum wells, the above effects are enhanced for the optic plasmon mode but diminished for the acoustic one.

Plasmon spectrum of two-dimensional electron systems with Rashba spin-orbit interaction

Ballistic spin transport is studied through electronic tuners with double stubs attached to them. The spins precess due to the spin–orbit interaction. Injected polarized spins can exit the structure polarized in the opposite direction. A nearly square-wave spin transmission, with values 1 and 0, can be obtained using a periodic system of symmetric stubs and changing their length or width. The gaps in the transmission can be widened using asymmetric stubs. An additional modulation is obtained upon combining stub structures with different values of the spin–orbit strength.

Ballistic spin transport through electronic stub tuners: Spin precession, selection, and square-wave transmission

Ballistic spin transport is studied through electronic tuners with double stubs attached to them. The spins precess due to the spin-orbit interaction. Injected polarized spins can exit the structure polarized in the opposite direction. A nearly square-wave spin transmission, with values 1 and 0, can be obtained using a periodic system of symmetric stubs and changing their length or width. The gaps in the transmission can be widened using asymmetric stubs. An additional modulation is obtained upon combining stub structures with different values of the spin-orbit strength.

http://arxiv.org/pdf/cond-mat/0204391.pdf

X. F. Wang

Papers

Spin-current modulation and square-wave transmission through periodically stubbed electron waveguides

Spin transport of electrons through quantum wires with a spatially modulated Rashba spin-orbit interaction

Plasmon spectrum of two-dimensional electron systems with Rashba spin-orbit interaction

Ballistic spin transport through electronic stub tuners: Spin precession, selection, and square-wave transmission

Ballistic spin transport through electronic stub tuners: spin precession, selection, and square-wave transmission