Uniaxial materials whose axial and tangential permittivities have opposite signs are referred to as indefinite or hyperbolic media. In such materials light propagation is unusual, leading to novel and often non-intuitive optical phenomena. Here we re
port infrared nano-imaging experiments demonstrating that crystals of hexagonal boron nitride (hBN), a natural mid-infrared hyperbolic material, can act as a hyper-focusing lens and as a multi-mode waveguide. The lensing is manifested by subdiffractional focusing of phonon-polaritons launched by metallic disks underneath the hBN crystal. The waveguiding is revealed through the modal analysis of the periodic patterns observed around such launchers and near the sample edges. Our work opens new opportunities for anisotropic layered insulators in infrared nanophotonics complementing and potentially surpassing concurrent artificial hyperbolic materials with lower losses and higher optical localization.
Hexagonal boron nitride (h-BN) is a natural hyperbolic material, for which the dielectric constants are the same in the basal plane (epsilon^t = epsilon^x = epsilon^y) but have opposite signs (epsilon^t*epsilon^z < 0) from that in the normal plane (e
psilon^z). Due to this property, finite-thickness slabs of h-BN act as multimode waveguides for propagation of hyperbolic phonon polaritons - collective modes that originate from the coupling between photons and electric dipoles in phonons. However, control of these hyperbolic phonon polaritons modes has remained challenging, mostly because their electrodynamic properties are dictated by the crystal lattice of h-BN. Here we show by direct nano-infrared imaging that these hyperbolic polaritons can be effectively modulated in a van der Waals heterostructure composed of monolayer graphene on h-BN. Tunability originates from the hybridization of surface plasmon polaritons in graphene with hyperbolic phonon polaritons in h-BN, so that the eigenmodes of the graphene/h-BN heterostructure are hyperbolic plasmon-phonon polaritons. Remarkably, the hyperbolic plasmon-phonon polaritons in graphene/h-BN suffer little from ohmic losses, making their propagation length 1.5-2.0 times greater than that of hyperbolic phonon polaritons in h-BN. The hyperbolic plasmon-phonon polaritons possess the combined virtues of surface plasmon polaritons in graphene and hyperbolic phonon polaritons in h-BN. Therefore, graphene/h-BN structures can be classified as electromagnetic metamaterials since the resulting properties of these devices are not present in its constituent elements alone.
We measured the in-plane resistivity anisotropy in the underdoped Ca$_{1-x}$Na$_x$Fe$_2$As$_2$ single crystals. The anisotropy (indicated by $rho_{rm b} - rho_{rm a}$) appears below a temperature well above magnetic transition temperature $T_{rm N}$,
being positive ($rho_{rm b} - rho_{rm a} > 0$) as $xleq$ 0.14. With increasing the doping level to $x$ = 0.19, an intersection between $rho_{rm b}$ and $rho_{rm a}$ is observed upon cooling, with $rho_{rm b} - rho_{rm a} < 0$ at low-temperature deep inside a magnetically ordered state, while $rho_{rm b} - rho_{rm a}> 0$ at high temperature. Subsequently, further increase of hole concentration leads to a negative anisotropy $rho_{rm b} - rho_{rm a} < 0$ in the whole temperature range. These results manifest that the anisotropic behavior of resistivity in the magnetically ordered state depends strongly on the competition of the contributions from different mechanisms, and the competition between the two contributions results in a complicated evolution of the anisotropy of in-plane resistivity with doping level.
We examine the behavior of a one-dimensional superconducting wire exposed to an applied electric current. We use the time-dependent Ginzburg-Landau model to describe the system and retain temperature and applied current as parameters. Through a combi
nation of spectral analysis, asymptotics and canonical numerical computation, we divide this two-dimensional parameter space into a number of regions. In some of them only the normal state or a stationary state or an oscillatory state are stable, while in some of them two states are stable. One of the most interesting features of the analysis is the evident collision of real eigenvalues of the associated PT-symmetric linearization, leading as it does to the emergence of complex elements of the spectrum. In particular this provides an explanation to the emergence of a stable oscillatory state. We show that part of the bifurcation diagram and many of the emerging patterns are directly controlled by this spectrum, while other patterns arise due to nonlinear interaction of the leading eigenfunctions.
