Weyl semimetals are gapless topological states of matter [1][2][3][4][5][6][7][8][9][10][11][12] with broken inversion and/or time reversal symmetry, which can support unconventional responses to externally applied electrical, optical and magnetic fields. Here we report a new photogalvanic effect in type-II WSMs, MoTe2 and Mo0.9W0.1Te2, which are observed to support a circulating photocurrent when illuminated by circularly polarized light at normal incidence. This effect occurs exclusively in the inversion broken phase, where crucially we find that it is associated with a spatially varying
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.
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.
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.
We study the Fermi surface contribution to the nonlinear DC photocurrent at quadratic order in a spatially uniform optical field in the ultra-clean limit. In addition to injection and ballistic currents, we find that circularly-polarized light incident on a time-reversal invariant metallic system generates an intrinsic contribution to the bulk photogalvanic effect deriving from photoinduced electronic transitions on the Fermi surface. In velocity gauge, this contribution originates in both the coherent band off-diagonal and diagonal parts of the density matrix, describing respectively, the coherent wave function evolution and the carrier dynamics of an excited population. We derive a formula for the intrinsic Fermi surface contribution for a chiral Weyl semimetal. At low frequency, this response is proportional to the frequency of the driving field, with its sign determined by the topological charge of the Weyl nodes and with its magnitude being comparable to the recently discovered quantized circular photogalvanic effect.
Orbital polarization is an internal attribute of an electronic Bloch state in a crystal that, in addition to spin, can endow band structure with nontrivial geometry and manifest itself in unique responses to applied fields. Here we identify this physics in a generic model for an orbital multiplet propagating on a two dimensional Bravais lattice. The theory features nontrivial fully orbitally-derived quantum geometry applicable to materials containing only light elements and without support from a nonprimitive space group. We obtain line-node degeneracies protected by a perpendicular mirror symmetry and two types of point degeneracies protected by PT symmetry. Crucially, and in contrast to the well-studied problem on the honeycomb lattice [1,2], here point degeneracies with opposite winding numbers are generically offset in energy which allows the activation of anomalous transport responses using readily-implemented spatially-uniform local potentials. We demonstrate this by calculations of an anomalous Hall conductance (AHC) coherently controlled by a circularly-polarized optical field and a related anomalous orbital Hall conductance (AOHC) activated by layer buckling. The model provides a prototypical demonstration of orbitally-induced topological responses in crystals with applications in many other lattice structures.Momentum-space Berry curvature in an electronic band structure can manifest in anomalous responses to applied fields [3]. This is understood at the semiclassical level by including the anomalous velocity in the equations of motion for a wavepacket [4,5], and at the quantum level by formulating linear and nonlinear response functions in terms of the Berry curvature [6][7][8]. Physical realizations on the honeycomb lattice [1, 2] present an essential complication in practice. At half filling, the band structure has point degeneracies protected by PT symmetry that carry opposite winding numbers. Breaking these symmetries to gap this spectrum liberates a Berry curvature into the Brillouin zone but its integrated strength vanishes unless the mass parameter also has a valley asymmetry that compensates the sign change of the winding number. This k-dependence inevitably requires sitenonlocality in the mass terms [1,2] that is difficult to implement in practical settings [9,10]. A notable work-around occurs in two-dimensional (2D) transition metal dichalcogenides where inversion symmetry is broken due to sublattice asymmetry, and the spectrum is instead gapped by a valleysymmetric mass [11]. In this case, anomalous charge transport can be activated by a valley asymmetry in the nonequilibrium population of excited carriers produced by circularly-polarized light [11][12][13][14].In this work, we consider a different scenario applicable to a family of simpler lattice models and illustrate it with an implementation on the primitive triangular lattice. Band degeneracies in the model arise from an on-site L = 1 orbital multiplet and are lifted by dispersion on the lattice. This model is motivated by a recent work...
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