Strain dependent conductivity in biased bilayer graphene

Intrinsic bilayer graphene is a gapless semimetal. Under the application of a bias field it becomes a semiconductor with a direct band gap that is proportional to the applied field. Under a layer-asymmetric strain (where the upper layer undergoes compression and lower layer tension or visa-versa) we find that the band gap of a biased bilayer graphene ribbon becomes indirect and, for higher strains, becomes negative returning the material its original semimetal state. As a result, the conductivity of the ribbon increases and can be almost an order of magnitude larger that of the intrinsic unbiased material - a change that can be induced with a strain of only ~2-3%. The conductivity is proportional to the applied strain and the magnitude of the effect is tunable with the bias field. Such layer-asymmetric strains can be achieved by bending, with forces on the order of ~1nN resulting in a layer-asymmetric strain of ~1%. This new electromechanical effect has a wide potential for application in the areas of nano-force microscopy and pressure sensing on the atomic scale.Comment: Updated to journal version with new title and revised figures. 8 pages, 6 figure

Large displacement strain theory and its application to graphene

Under the application of a force, a material will deform and, hence, the crystal lattice will experience strain. This induced strain will alter the electronic properties of the material. In particular, strain in graphene generates an artificial vector potential which, if spatially varying, admits a pseudo-magnetic field. Current theories for spatially varying strain use linear or finite strain theory whose derivation is based on small displacements of infinitesimal length vectors. Here we apply a differential geometry method to derive a strain theory for large displacements of finite length vectors. This method gives a finite displacement term whose contribution is comparable to that of the linear strain term. Further to this, we show that a 'domain wall'-like pseudo-magnetic field profile can be generated when a wide graphene ribbon is subjected to a pair of opposing point forces (point stretch). The resulting field is a function of the new finite displacement term only and displays a maximum strength of over three times that which is predicted by the linear strain theory. These results extend the current theories of strain, which are based on the transformation of infinitesimal length vectors, to finite length vectors, thus providing an accurate description of pseudo-magnetic field structures in strained materials.Comment: Updated to journal version with revised figure 3 and new title. 7 pages, 5 figure

Optical properties of topological insulator Bragg gratings: Faraday rotation enhancement for TM polarized light at large incidence angles

Using the transfer matrix formalism, we study the transmission properties of a Bragg grating constructed from a layered axionic material. Such a material can be realized by a topological insulator subject to a time-symmetry breaking perturbation, such as an external magnetic field or surface magnetic impurities. Whilst the reflective properties of the structure are only negligibly changed by the presence of the axionic material, the grating induces a Faraday rotation and ellipticity in the transmitted light. We find that for TM polarized light incident on a 16 layer structure at 76 degrees to the normal the Faraday rotation can approach ~232 mrad (~13 degrees), whilst interference from the multi-layered structure ensures high transmission. This is significantly higher than Faraday rotations for the TM polarization at normal incidences or the TE polarization at any incident angle. Thus, Bragg gratings in this geometry show a strong optical signal of the magneto-electric and, hence, provide an ideal system in which to observe this effect by optical means.Comment: Updated to journal version with new title and new results. 8 pages, 6 figure

Quantum coherence induced second plateau in high-sideband generation

Optically excited electron-hole pairs, driven by a strong terahertz (THz) field, create high-sidebands in the optical spectrum. The sideband spectrum exhibits a 'plateau' up to a cutoff of 3.17Up, where Up is the ponderomotive energy. This cutoff is determined, semi-classically, from the maximum kinetic energy an electron-hole pair can gain from the THz field along a closed trajectory. A full quantum treatment reveals a second, classically forbidden, plateau with a cutoff of 8Up, the maximum kinetic energy an electron-hole pair can gain from the THz field along an open trajectory. The second plateau appears because a spatially separated electron and hole can still recombine if the classical excursion is within the coherence length of the electron-hole wavefunction or, equivalently, the coherence time is longer than the excursion time (half the THz field period). This effect broadens the range of materials and excitation conditions where high-sideband generations can occur, thereby providing a wealth of novel systems for ultrafast electro-optical applications.Comment: Updated to journal version with revised figure 1. 5 pages, 3 figure

The Electromagnetic Green's Function for Layered Topological Insulators

The dyadic Green's function of the inhomogeneous vector Helmholtz equation describes the field pattern of a single frequency point source. It appears in the mathematical description of many areas of electromagnetism and optics including both classical and quantum, linear and nonlinear optics, dispersion forces (such as the Casimir and Casimir-Polder forces) and in the dynamics of trapped atoms and molecules. Here, we compute the Green's function for a layered topological insulator. Via the magnetoelectric effect, topological insulators are able to mix the electric, E, and magnetic induction, B, fields and, hence, one finds that the TE and TM polarizations mix on reflection from/transmission through an interface. This leads to novel field patterns close to the surface of a topological insulator.Comment: 16 pages, 9 figure

Casimir-Polder Shift and Decay Rate in the Presence of Nonreciprocal Media

We calculate the Casimir-Polder frequency shift and decay rate for an atom in front of a nonreciprocal medium by using macroscopic quantum electrodynamics. The results are a generalization of the respective quantities for matter with broken time-reversal symmetry which does not fulfill the Lorentz reciprocity principle. As examples, we contrast the decay rates, the resonant and nonresonant frequency shifts of a perfectly conducting (reciprocal) mirror to those of a perfectly reflecting nonreciprocal mirror. We find different power laws for the distance dependence of all quantities in the retarded and nonretarded limits. As an example of a more realistic nonreciprocal medium, we investigate a topological insulator subject to a time-symmetry breaking perturbation.Comment: 11 pages, 6 figure

Faraday rotations, ellipticity and circular dichroism in the magneto-optical spectrum of moir\'e superlattices

We study the magneto-optical conductivity of a number of Van der Waals heterostructures, namely, twisted bilayer graphene, AB-AB and AB-BA stacked twisted double bilayer graphene and monolayer graphene and AB-stacked bilayer graphene on hexagonal boron nitride. As magnetic field increases, the absorption spectrum exhibits a self-similar recursive pattern reflecting the fractal nature of the energy spectrum. Whilst twisted bilayer graphene displays only weak circular dichroism, monolayer graphene and AB-stacked bilayer graphene on hexagonal boron nitride show specifically strong circular dichroism, owing to strong inversion symmetry breaking properties of the hexagonal boron nitride layer. As, the left and right circularly polarized light interact with these structures differently, plane polarized incident light undergoes a Faraday rotation and gains an ellipticity when transmitted. The size of the respective angles is on the order of a degree.Comment: 24 pages, 9 figure

Quasicrystalline electronic states in twisted bilayers and the effects of interlayer and sublattice symmetries

We study the electronic structure of quasicrystals composed of incommensurate stacks of atomic layers. We consider two systems: a pair of square lattices with a relative twist angle of $\theta=45^\circ$ and a pair of hexagonal lattices with a relative twist angle of $\theta=30^\circ$, with various interlayer interaction strengths. This constitutes every two-dimensional bilayer quasicrystal system. We investigate the resonant coupling governing the quasicrystalline order in each quasicrystal symmetry, and calculate the quasi-band dispersion. The resonant interaction emerges in bilayer quasicrystals if all the dominant interlayer interactions occur between the atomic orbitals that have the same magnetic quantum number. Thus, not only the quasicrystal composed of the widely studied graphene, but also those composed of transition metal dichalcogenides will exhibit the quasicrystalline states. We find that some quasicrystalline states, which are usually obscured by decoupled monolayer states, are more prominent, i.e., "exposed", in the systems with strong interlayer interaction. We also show that we can switch the states between quasicrystalline configuration and its layer components, by turning on and off the interlayer symmetry.Comment: 18 pages, 10 figure

Trigonal Quasicrystalline States in 30∘30^\circ Rotated Double Moir\'{e} Superlattices

We study the lattice configuration and electronic structure of a double moir\'{e} superlattice, which is composed of a graphene layer encapsulated by two other layers in a way such that the two hexagonal moir\'{e} patterns are arranged in a dodecagonal quasicrystalline configuration. We show that there are between 0 and 4 such configurations depending on the lattice mismatch between graphene and the encapsulating layer. We then reveal the resonant interaction, which is distinct from the conventional 2-, 3-, 4-wave mixing of moir\'{e} superlattices, that brings together and hybridizes twelve degenerate Bloch states of monolayer graphene. These states do not fully satisfy the dodecagonal quasicrystalline rotational symmetry due to the symmetry of the wave vectors involved. Instead, their wave functions exhibit trigonal quasicrystalline order, which lacks inversion symmetry, at the energies much closer to the charge neutrality point of graphene.Comment: 12 pages, 6 figure

Thermal Casimir-Polder shifts in Rydberg atoms near metallic surfaces

The Casimir-Polder (CP) potential and transition rates of a Rydberg atom above a plane metal surface at finite temperature are discussed. As an example, the CP potential and transition rates of a rubidium atom above a copper surface at room temperature is computed. Close to the surface we show that the quadrupole correction to the force is significant and increases with increasing principal quantum number n. For both the CP potential and decay rates one finds that the dominant contribution comes from the longest wavelength transition and the potential is independent of temperature. We provide explicit scaling laws for potential and decay rates as functions of atom-surface distance and principal quantum number of the initial Rydberg state.Comment: Updated to journal version with corrected figures. 4 Pages, 2 figure