Unified theory of the anomalous and topological Hall effects with phase-space Berry curvatures.

Spontaneously broken time-reversal symmetry in magnetic materials leads to a Hall response, with a nonzero voltage transverse to an applied current, even in the absence of external magnetic fields. It is common to analyze the Hall resistivity of chiral magnets as the sum of two terms: an anomalous Hall effect arising from spin-orbit coupling and a topological Hall signal coming from skyrmions, which are topologically nontrivial spin textures. The theoretical justification for such a decomposition has long remained an open problem. Using a controlled semiclassical approach that includes all phase-space Berry curvatures, we show that the solution of the Boltzmann equation leads to a Hall resistivity that is just the sum of an anomalous term arising from momentum-space curvature and a topological term related to the real-space curvature. We also present numerically exact results from a Kubo formalism that complement the semiclassical approach.

Floquet Topological Phases in One-Dimensional Nonlinear Photonic Crystals.

We report on a theoretical analysis of the Floquet topological crystalline phases in driven one-dimensional photonic crystals mediated by second-order optical nonlinearity. We define the photonic Berry connection and photonic polarization in such systems using different methods and prove their equivalence. We present two examples of topological phase transitions in which two Floquet bands cross and open new gaps under the driving field. Finally, we analyze the physical consequences of each topological phase transition by examining edge states and filling anomalies. Our study presents routes toward the realization of robust reconfigurable photonic cavities with topologically protected light confinement.

Quadrupole topological photonic crystals.

Quadrupole topological phases, exhibiting protected boundary states that are themselves topological insulators of lower dimensions, have recently been of great interest. Extensions of these ideas from current tight binding models to continuum theories for realistic materials require the identification of quantized invariants describing the bulk quadrupole order. Here we identify the analog of quadrupole order in Maxwell's equations for a gyromagnetic photonic crystal (PhC) through a double-band-inversion process. The quadrupole moment is quantized by the simultaneous presence of crystalline symmetry and broken time-reversal symmetry, which is confirmed using three independent methods: analysis of symmetry eigenvalues, numerical calculations of the nested Wannier bands and the expectation value of the quadrupole operator. Furthermore, we reveal the boundary manifestations of quadrupole phases as quantized edge polarizations and fractional corner charges. The latter are the consequence of a filling anomaly of energy bands as first predicted in electronic systems.

Optically Controlled Orbitronics on a Triangular Lattice.

The propagation of electrons in an orbital multiplet dispersing on a lattice can support anomalous transport phenomena deriving from an orbitally induced Berry curvature. In striking contrast to the related situation in graphene, we find that anomalous transport for an L=1 multiplet on the primitive 2D triangular lattice is activated by easily implemented on site and optically tunable potentials. We demonstrate this for dynamics in a Bloch band where point degeneracies carrying opposite winding numbers are generically offset in energy, allowing both an anomalous charge Hall conductance with the sign selected by off-resonance coupling to circularly polarized light and a related anomalous orbital Hall conductance activated by layer buckling.

Floquet Chern insulators of light.

Achieving topologically-protected robust transport in optical systems has recently been of great interest. Most studied topological photonic structures can be understood by solving the eigenvalue problem of Maxwell's equations for static linear systems. Here, we extend topological phases into dynamically driven systems and achieve a Floquet Chern insulator of light in nonlinear photonic crystals (PhCs). Specifically, we start by presenting the Floquet eigenvalue problem in driven two-dimensional PhCs. We then define topological invariant associated with Floquet bands, and show that topological band gaps with non-zero Chern number can be opened by breaking time-reversal symmetry through the driving field. Finally, we numerically demonstrate the existence of chiral edge states at the interfaces between a Floquet Chern insulator and normal insulators, where the transport is non-reciprocal and uni-directional. Our work paves the way to further exploring topological phases in driven optical systems and their optoelectronic applications.

Spatially dispersive circular photogalvanic effect in a Weyl semimetal.

Weyl semimetals (WSMs) are gapless topological states of matter with broken inversion and/or time reversal symmetry. WSMs can support a circulating photocurrent when illuminated by circularly polarized light at normal incidence. Here, we report a spatially dispersive circular photogalvanic effect (s-CPGE) in a WSM that occurs with a spatially varying beam profile. Our analysis shows that the s-CPGE is controlled by a symmetry selection rule combined with asymmetric carrier excitation and relaxation dynamics. By evaluating the s-CPGE for a minimal model of a WSM, a frequency-dependent scaling behaviour of the photocurrent is obtained. Wavelength-dependent measurements from the visible to mid-infrared range show evidence of Berry curvature singularities and band inversion in the s-CPGE response. We present the s-CPGE as a promising spectroscopic probe for topological band properties, with the potential for controlling photoresponse by patterning optical fields on topological materials to store, manipulate and transmit information.

Plasmon Reflections by Topological Electronic Boundaries in Bilayer Graphene.

Domain walls separating regions of AB and BA interlayer stacking in bilayer graphene have attracted attention as novel examples of structural solitons, topological electronic boundaries, and nanoscale plasmonic scatterers. We show that strong coupling of domain walls to surface plasmons observed in infrared nanoimaging experiments is due to topological chiral modes confined to the walls. The optical transitions among these chiral modes and the band continua enhance the local conductivity, which leads to plasmon reflection by the domain walls. The imaging reveals two kinds of plasmonic standing-wave interference patterns, which we attribute to shear and tensile domain walls. We compute the electronic structure of both wall varieties and show that the tensile wall contains additional confined bands which produce a structure-specific contrast of the local conductivity, in agreement with the experiment. The coupling between the confined modes and the surface plasmon scattering unveiled in this work is expected to be common to other topological electronic boundaries found in van der Waals materials. This coupling provides a qualitatively new pathway toward controlling plasmons in nanostructures.