J. C. Martinez

Theory of giant Faraday rotation and Goos-Hänchen shift in graphene

We give a quantum formulation of the recently observed giant Faraday rotation (FR) in monolayer graphene (Crassee I., Nat. Phys., 7 (2011) 48) which incorporates graphenes anomalous Hall effect and the resonant interplay between Landau levels and Floquet sidebands in the limit of large Fermi energy. The same formalism is then used to discuss the Goos-Hanchen (GH) shift at the interface of two media of different permittivity, with graphene at their interface. This last feature introduces current into the electromagnetic boundary conditions. For the s-polarization case, the presence of the graphene-induced surface charge causes a much larger GH shift than without charge, and its usual monotonic behavior is altered. In the p-polarization case, surface charge and current may alter the conventional GH shift in opposite ways. We predict new phenomena such as minimum GH shift and a lateral broadening of the reflected beam, all of which should be observable with current experimental capabilities.

Giant Faraday and Kerr rotation with strained graphene.

Polarized electromagnetic waves passing through (reflected from) a dielectric medium parallel to a magnetic field undergo Faraday (Kerr) rotation of their polarization. Recently, Faraday rotation angles as much as 0.1 rad were observed for terahertz waves propagating through graphene over a SiC substrate. We show that the same effect is observable with the magnetic field replaced by an in-plane strain field which induces a pseudomagnetic field in graphene. With two such sheets a rotation of π/4 can be achieved, which is the required rotation for an optical diode. Similarly a Kerr rotation of 1/4 rad is predicted from a single reflection from a strained graphene sheet.

Topological dynamics and current-induced motion in a skyrmion lattice

We study the Thiele equation for current-induced motion in a skyrmion lattice through two soluble models of the pinning potential. Comprised by a Magnus term, a dissipative term and a pinning force, Thieles equation resembles Newtons law but in virtue of the topological character to the first, it differs significantly from Newtonian mechanics and because the Magnus force is dominant, unlike its mechanical counterpart—the Coriolis force—skyrmion trajectories do not necessarily have mechanical counterparts. This is important if we are to understand skyrmion dynamics and tap into its potential for data-storage technology. We identify a pinning threshold velocity for the one-dimensional pinning potential and for a two-dimensional attractive potential we find a pinning point and the skyrmion trajectories toward that point are spirals whose frequency (compare Keplers second law) and amplitude-decay depend only on the Gilbert constant and potential at the pinning point. Other scenarios, e.g. other choices of initial spin velocity, a repulsive potential, etc are also investigated.

Tuning the Casimir force via modification of interface properties of three-dimensional topological insulators

The axion coupling in topological insulators (TI), which couples electric polarization (magnetization) with the magnetic (electric) field, is known to support a small-distance Casimir repulsion and a large-distance Casimir attraction with a zero-force stable equilibrium between TI plates. By enhancing the reflection properties of the TI interface through mirrors that introduce multiple reflections, we show that it is possible to maintain these trends while tuning the position of the zero-force point and its binding energy: the former by an order of magnitude and latter by over four orders. Moreover, surface charge on the TI allows for intermediate tuning of the zero-force point between coarse settings determined by the axion coupling.

Pseudospin filter for graphene via laser irradiation

We study graphene monolayer charge carriers irradiated by an electromagnetic vortex. From this, two scenarios are envisaged: canonical oscillator coherent states, which form for large particle numbers and from which a sublattice filter can be constructed, and pair-coherent states, which emerge when the carrier velocity is much less than the Fermi velocity and which can exhibit nonclassical properties. The first should be useful in the control (e.g., confinement and guided transport) of graphene electrons, while the second provides a physical system for examining nonclassical properties of wave packets.

Klein tunneling and zitterbewegung and the formation of a polarized p-n junction in graphene

The Klein tunneling of charge pairs in an electrostatically created p-n junction of monolayer graphene is shown to occur at an observable rate for moderate fields. The pairs undergo zitterbewegung (ZBW) in opposite directions leading to their separation and transverse dipole moment, since the valleys contribute constructively. The dipole moment depends critically on the exponential collimation characteristic of Klein tunneling and serves as a diagnostic signature of ZBW.

Robust localized modes in bilayer graphene induced by an antisymmetric kink potential

When bilayer graphene is gated with a kink potential, pair particle localization occurs at the kink where a particle (electron) and its chiral partner (hole) are held in balance by electrostatic coupling. Zero-energy states (zero modes) are always present in pairs and occur at the same point in the dispersion graph, regardless of kink strength. The robust and binary nature of the kink-induced modes, which are topologically protected against disorder, and the ease with which a kink is created suggest applications in switching devices or information storage.

Casimir force between metal and graphene sheets

The Casimir force between neutral plates is attractive. For the Casimir force to be really useful one must be able to switch from attraction to repulsion. Exploiting the experimentalist’s ability to change the sign of the charge carriers in graphene, we show how the sign of the Fresnel reflection coefficients can be reversed. This gives rise to a Casimir force between a metal sheet and graphene, which can be either attractive or repulsive; we illustrate it for a dielectric cylinder and graphene sheet.

Optical Faraday rotation with graphene

Plane polarized electromagnetic waves propagating through a dielectric medium parallel to a magnetic field undergo Faraday rotation (FR) of their polarization. “Giant” Faraday rotation by as much as 0.1 rad was recently observed for terahertz waves with graphene over a SiC substrate. We show that for the (more technologically useful) optical frequency range, the same effect may be achieved with interband transitions between Landau levels formed by application of real or pseudo-magnetic fields induced by strain. At some resonant condition, the FR angle shows a sharp transition and sign reversal, which may be used to rotate the polarizations of the sodium doublet D-lines so as to be perpendicular to each other.

Creation of “dark-soliton” atoms

Dark solitons are thought to always repel so that bound states of dark solitons do not form. We show that quantum fluctuations of the background induce attractive forces between dark optical solitons. We clarify the nature of these fluctuations. Together with the repulsive potential, this attractive force creates a potential similar to that in a diatomic molecule which allows for the formation of bound pairs of dark solitons. Such pairs can be useful in the creation of notch arrays and crystal-like structures.