arXiv subjects

J. A. Crosse

Publications and source records attributed to J. A. Crosse.

18 recordsLinked to original sources

arXiv2021

Trigonal Quasicrystalline States in $30^\circ$ Rotated Double Moiré Superlattices

We study the lattice configuration and electronic structure of a double moiré superlattice, which is composed of a graphene layer encapsulated by two other layers in a way such that the two hexagonal moiré 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 moiré 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.

cond-mat.mes-hall↗

arXiv2021

Faraday rotations, ellipticity and circular dichroism in the magneto-optical spectrum of moiré 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.

cond-mat.mes-hall↗

arXiv2021

Strong geometry dependence of the Casimir force between interpenetrated rectangular gratings

Quantum fluctuations give rise to Casimir forces between two parallel conducting plates, the magnitude of which increases monotonically as the separation decreases. By introducing nanoscale gratings to the surfaces, recent advances have opened opportunities for controlling the Casimir force in complex geometries. Here, we measure the Casimir force between two rectangular gratings in regimes not accessible before. Using an on-chip detection platform, we achieve accurate alignment between the two gratings so that they interpenetrate as the separation is reduced. Just before interpenetration occurs, the measured Casimir force is found to have a geometry dependence that is much stronger than previous experiments, with deviations from the proximity force approximation reaching a factor of ~500. After the gratings interpenetrate each other, the Casimir force becomes non-zero and independent of displacement. This work shows that the presence of gratings can strongly modify the Casimir force to control the interaction between nanomechanical components.

quant-ph↗

arXiv2020

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 $θ=45^\circ$ and a pair of hexagonal lattices with a relative twist angle of $θ=30^\circ$, 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.

cond-mat.mes-hall↗

arXiv2020

Hofstadter butterfly and the quantum Hall effect in twisted double bilayer graphenes

We study the energy spectrum and quantum Hall effects of the twisted double bilayer graphene in uniform magnetic field. We investigate two different arrangements, AB-AB and AB-BA, which differ in the relative orientation but have very similar band structures in the absence of a magnetic field. For each system, we calculate the energy spectrum and quantized Hall conductivities at each spectral gap by using a continuum Hamiltonian that satisfies the magneto-translation condition. We show that the Hofstadter butterfly spectra of AB-AB and AB-BA stackings differ significantly, even though their zero magnetic field band structures closely resemble; the spectrum of AB-AB has valley degeneracy, which can be lifted by applying interlayer potential asymmetry, while the spectrum of AB-BA has no such degeneracy in any case. We explain the origin of the difference from the perspectives of lattice symmetry and band topology.

cond-mat.mes-hall↗

arXiv2019

Mapping the twist angle and unconventional Landau levels in magic angle graphene

The emergence of flat electronic bands and of the recently discovered strongly correlated and superconducting phases in twisted bilayer graphene crucially depends on the interlayer twist angle upon approaching the magic angle $θ_M \approx 1.1°$. Although advanced fabrication methods allow alignment of graphene layers with global twist angle control of about 0.1$°$, little information is currently available on the distribution of the local twist angles in actual magic angle twisted bilayer graphene (MATBG) transport devices. Here we map the local $θ$ variations in hBN encapsulated devices with relative precision better than 0.002$°$ and spatial resolution of a few moir$é$ periods. Utilizing a scanning nanoSQUID-on-tip, we attain tomographic imaging of the Landau levels in the quantum Hall state in MATBG, which provides a highly sensitive probe of the charge disorder and of the local band structure determined by the local $θ$. We find that even state-of-the-art devices, exhibiting high-quality global MATBG features including superconductivity, display significant variations in the local $θ$ with a span close to 0.1$°$. Devices may even have substantial areas where no local MATBG behavior is detected, yet still display global MATBG characteristics in transport, highlighting the importance of percolation physics. The derived $θ$ maps reveal substantial gradients and a network of jumps. We show that the twist angle gradients generate large unscreened electric fields that drastically change the quantum Hall state by forming edge states in the bulk of the sample, and may also significantly affect the phase diagram of correlated and superconducting states. The findings call for exploration of band structure engineering utilizing twist-angle gradients and gate-tunable built-in planar electric fields for novel correlated phenomena and applications.

cond-mat.mes-hall↗

arXiv2016

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.

physics.optics↗

arXiv2016

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.

quant-ph↗

arXiv2015

Theory of topological insulator waveguides: polarization control and the enhancement of the magneto-electric effect

Topological insulators subject to a time-symmetry-breaking perturbation are predicted to display a magneto-electric effect that causes the electric and magnetic induction fields to mix at the material's surface. This effect induces polarization rotations of between ~1-10 mrad per interface in incident plane-polarized light normal to a multilayered structure. Here we show, theoretically and numerically, that, using a waveguide geometry with a topological insulator guide layer and dielectric cladding, it is possible to achieve rotations of between ~100-1000 mrad and generate an elliptical polarization with only a three-layered structure. Both the rotation angle and ellipticity are dependent on the permittivity contrast of the guide and cladding layers and the strength of the time-symmetry-breaking perturbation. This geometry is beneficial, not only as a way to enhance the magneto-electric effect, rendering it easier to observe, but also as a method for controlling the polarization of light in the next generation of photonic devices.

physics.optics↗

arXiv2015

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.

physics.optics↗

arXiv2015

Theory of low power ultra-broadband terahertz sideband generation in bi-layer graphene

In a semiconductor illuminated by a strong terahertz field, optically excited electron-hole pairs can recombine to emit light in a broad frequency comb evenly spaced by twice the terahertz frequency. Such high-order terahertz sideband generation is of interest both as an example of extreme nonlinear optics and also as a method for ultrafast electro-optical modulation. So far, this phenomenon has only been observed with large field strengths (~10 kVcm-1), an obstacle for technological applications. Here we predict that bi-layer graphene generates high-order sidebands at much weaker terahertz fields. We find that a terahertz field of strength 1 kVcm-1 can produce a high-sideband spectrum of about 30 THz, 100 times broader than in GaAs. The sidebands are generated despite the absence of classical collisions, with the quantum coherence of the electron-hole pairs enabling recombination. These remarkable features lower the barrier to desktop electro-optical modulation at terahertz frequencies, facilitating ultrafast optical communications.

cond-mat.mes-hall↗

arXiv2014

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.

cond-mat.mes-hall↗

arXiv2014

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.

cond-mat.mes-hall↗

arXiv2014

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.

cond-mat.mes-hall↗

arXiv2011

Coincident count rates in absorbing dielectric media

A study of the effects of absorption on the nonlinear process of parametric down conversion is presented. Absorption within the nonlinear medium is accounted for by employing the framework of macroscopic QED and the Green tensor quantization of the electromagnetic field. An effective interaction Hamiltonian, which describes the nonlinear interaction of the electric field and the linear noise polarization field, is used to derive the quantum state of the light leaving a nonlinear crystal. The signal and idler modes of this quantum state are found to be a superpositions of the electric and noise polarization fields. Using this state, the expression for the coincident count rates for both Type I and Type II conversion are found. The nonlinear interaction with the noise polarization field were shown to cause an increase in the rate on the order of 10^{-12} for absorption of 10% per cm. This astonishingly small effect is found to be negligible compared to the decay caused by linear absorption of the propagating modes. From the expressions for the biphoton amplitude it can be seen the maximally entangled states can still be produced even in the presence of strong absorption.

quant-ph↗

arXiv2010

Atomic multipole relaxation rates near surfaces

The spontaneous relaxation rates for an atom in free space and close to an absorbing surface are calculated to various orders of the electromagnetic multipole expansion. The spontaneous decay rates for dipole, quadrupole and octupole transitions are calculated in terms of their respective primitive electric multipole moments and the magnetic relaxation rate is calculated for the dipole and quadrupole transitions in terms of their respective primitive magnetic multipole moments. The theory of electromagnetic field quantization in magnetoelectric materials is used to derive general expressions for the decay rates in terms of the dyadic Green function. We focus on the decay rates in free space and near an infinite half space. For the decay of atoms near to an absorbing dielectric surface we find a hierarchy of scaling laws depending on the atom-surface distance z.

quant-ph↗

arXiv2010

Effective nonlinear Hamiltonians in dielectric media

We derive an effective Hamiltonian for the nonlinear process of parametric down conversion in the presence of absorption. Based upon the Green function method for quantizing the electromagnetic field, we first set up Heisenberg's equations of motion for a single atom driven by an external electric field and in the presence of an absorbing dielectric material. The equations of motion are then solved to second order in perturbation theory which, in rotating-wave approximation, yields the standard effective interaction Hamiltonian known from free-space nonlinear optics. In a second step, we derive the local-field corrected Hamiltonian for an atom embedded in a dielectric host medium, i.e. a nonlinear crystal. Here we show that the resulting effective Hamiltonian is trilinear in the electric and noise polarization fields, and is thus capable of describing nonlinear noise processes. Furthermore, it reduces to the phenomonological nonlinear Hamiltonian for the cases where the noise polarization field, and hence absorption, vanishes.

quant-ph↗

arXiv2010

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.

quant-ph↗