The generic isogeny decomposition of the Prym Variety of a cyclic branched covering

Let $$f:S'\longrightarrow S$$ f : S ′ ⟶ S be a cyclic branched covering of smooth projective surfaces over $${\mathbb {C}}$$ C whose branch locus $$\Delta \subset S$$ Δ ⊂ S is a smooth ample divisor. Pick a very ample complete linear system $$|{\mathcal {H}}|$$ | H | on S, such that the polarized surface $$(S, |{\mathcal {H}}|)$$ ( S , | H | ) is not a scroll nor has rational hyperplane sections. For the general member $$[C]\in |{\mathcal {H}}|$$ [ C ] ∈ | H | consider the $$\mu _{n}$$ μ n -equivariant isogeny decomposition of the Prym variety $${{\,\mathrm{Prym}\,}}(C'/C)$$ Prym ( C ′ / C ) of the induced covering $$f:C'{:}{=}f^{-1}(C)\longrightarrow C$$ f : C ′ : = f - 1 ( C ) ⟶ C : $$\begin{aligned} {{\,\mathrm{Prym}\,}}(C'/C)\sim \prod _{d|n,\ d\ne 1}{\mathcal {P}}_{d}(C'/C). \end{aligned}$$ Prym ( C ′ / C ) ∼ ∏ d | n , d ≠ 1 P d ( C ′ / C ) . We show that for the very general member $$[C]\in |{\mathcal {H}}|$$ [ C ] ∈ | H | the isogeny component $${\mathcal {P}}_{d}(C'/C)$$ P d ( C ′ / C ) is $$\mu _{d}$$ μ d -simple with $${{\,\mathrm{End}\,}}_{\mu _{d}}({\mathcal {P}}_{d}(C'/C))\cong {\mathbb {Z}}[\zeta _{d}]$$ End μ d ( P d ( C ′ / C ) ) ≅ Z [ ζ d ] . In addition, for the non-ample case we reformulate the result by considering the identity component of the kernel of the map $${\mathcal {P}}_{d}(C'/C)\subset {{\,\mathrm{Jac}\,}}(C')\longrightarrow {{\,\mathrm{Alb}\,}}(S')$$ P d ( C ′ / C ) ⊂ Jac ( C ′ ) ⟶ Alb ( S ′ ) .

The Generation of Switchable Polarized Currents in Nodal Ring Semimetals Using High-Frequency Periodic Driving

A nodal ring semimetal (NRSM) can be driven to a spin-polarized NRSM or a spin-polarized Weyl semimetal (SWSM) by a high-frequency electromagnetic field. We investigate the conditions in realizing these phases and propose a switchable spin-polarized currents generator based on periodically driven NRSMs. Both bulk and surface polarized currents are investigated. The polarization of bulk current is sensitive to the amplitude of the driving field and robust against the direction and polarization of the driving, the opaqueness of the lead-device interface and the misalignment between the nodal ring and the interface, which provides sufficient flexibility in manipulating the devices. Similar switchable polarized surface currents are also expected, which is contributed by the Fermi arc surface state associated with the Weyl semimetal (WSM) phases. The generation of polarized currents and the polarization switching effect offer opportunities to design periodic driving controlled topological spintronics devices based on NRSMs.

Wiring Up Along Electrodes for Biofilm Formation

Millimeter-length cables of bacteria were discovered growing along a graphite-rod electrode serving as an anode of a microbial electrolysis cell (MEC). The MEC had been inoculated with a culture of Fe-reducing microorganisms enriched from a polluted river sediment (Reconquista river, Argentina) and was operated at laboratory controlled conditions for 18 days at an anode poised potential of 240 mV (vs. Ag/AgCl), followed by 23 days at 480 mV (vs. Ag/AgCl). Anode samples were collected for scanning electron microscopy, phylogenetic and electrochemical analyses. The cables were composed of a succession of bacteria covered by a membranous sheath and were distinct from the known “cable-bacteria” (family Desulfobulbaceae). Apparently, the formation of the cables began with the interaction of the cells via nanotubes mostly located at the cell poles. The cables seemed to be further widened by the fusion between them. 16S rRNA gene sequence analysis confirmed the presence of a microbial community composed of six genera, including Shewanella, a well-characterized electrogenic bacteria. The formation of the cables might be a way of colonizing a polarized surface, as determined by the observation of electrodes extracted at different times of MEC operation. Since the cables of bacteria were distinct from any previously described, the results suggest that bacteria capable of forming cables are more diverse in nature than already thought. This diversity might render different electrical properties that could be exploited for various applications.

Double-bowl state in photonic Dirac nodal line semimetal

The past decade has seen a proliferation of topological materials for both insulators and semimetals in electronic systems and classical waves. Topological semimetals exhibit topologically protected band degeneracies, such as nodal points and nodal lines. Dirac nodal line semimetals (DNLS), which own four-fold line degeneracy, have drawn particular attention. DNLSs have been studied in electronic systems but there is no photonic DNLS. Here in this work, we provide a new mechanism, which is unique for photonic systems to investigate a stringent photonic DNLS. When truncated, the photonic DNLS exhibits double-bowl states (DBS), which comprise two sets of perpendicularly polarized surface states. In sharp contrast to nondegenerate surface states in other photonic systems, here the two sets of surface states are almost degenerate over the whole-spectrum range. The DBS and the bulk Dirac nodal ring (DNR) dispersion along the relevant directions, are experimentally resolved.

Observation of a giant mass enhancement in the ultrafast electron dynamics of a topological semimetal

Topological phases of matter offer exciting possibilities to realize lossless charge and spin information transport on ultrafast time scales. However, this requires detailed knowledge of their nonequilibrium properties. Here, we employ time-, spin- and angle-resolved photoemission to investigate the ultrafast response of the Sb(111) spin-polarized surface state to femtosecond-laser excitation. The surface state exhibits a giant mass enhancement which is observed as a kink structure in its energy-momentum dispersion above the Fermi level. The kink structure, originating from the direct coupling of the surface state to the bulk continuum, is characterized by an abrupt change in the group velocity by ~70%, in agreement with our GW-based band structure calculations. Our observation of this connectivity in the transiently occupied band structure enables the unambiguous experimental verification of the topological nature of the surface state. The influence of bulk-surface coupling is further confirmed by our measurements of the electron dynamics, which show that bulk and surface states behave as a single thermalizing electronic population with distinct contributions from low-k electron-electron and high-k electron-phonon scatterings. These findings are important for future applications of topological semimetals and their excitations in ultrafast spintronics.

Topological insulator metamaterial with giant circular photogalvanic effect

One of the most notable manifestations of electronic properties of topological insulators is the dependence of the photocurrent direction on the helicity of circularly polarized optical excitation. The helicity-dependent photocurrents, underpinned by spin-momentum locking of surface Dirac electrons, are weak and easily overshadowed by bulk contributions. Here, we show that the chiral response can be enhanced by nanostructuring. The tight confinement of electromagnetic fields in the resonant nanostructure enhances the photoexcitation of spin-polarized surface states of topological insulator Bi1.5Sb0.5Te1.8Se1.2, leading to an 11-fold increase of the circular photogalvanic effect and a previously unobserved photocurrent dichroism (ρcirc = 0.87) at room temperature. The control of spin transport in topological materials by structural design is a previously unrecognized ability of metamaterials that bridges the gap between nanophotonics and spin electronics, providing opportunities for developing polarization-sensitive photodetectors.

Efficient generation of complex vectorial optical fields with metasurfaces

Vectorial optical fields (VOFs) exhibiting arbitrarily designed wavefronts and polarization distributions are highly desired in photonics. However, current methods to generate them either require complicated setups or exhibit limited functionalities, which is unfavorable for integration-optics applications. Here, we propose a generic approach to efficiently generate arbitrary VOFs based on metasurfaces exhibiting full-matrix yet inhomogeneous Jones-matrix distributions. We illustrate our strategy with analytical calculations on a model system and an experimental demonstration of a meta-device that can simultaneously deflect light and manipulate its polarization. Based on these benchmark results, we next experimentally demonstrate the generation of a far-field VOF exhibiting both a vortex wavefront and an inhomogeneous polarization distribution. Finally, we design/fabricate a meta-device and experimentally demonstrate that it can generate a complex near-field VOF—a cylindrically polarized surface plasmon wave possessing orbital angular momentum—with an efficiency of ~34%. Our results establish an efficient and ultracompact platform for generating arbitrary predesigned VOFs in both the near- and far-fields, which may find many applications in optical manipulation and communications.

Hidden bulk and surface effects in the spin polarization of the nodal-line semimetal ZrSiTe

In non-magnetic materials the combination of inversion symmetry breaking (ISB) and spin-orbit coupling (SOC) determines the spin polarization of the band structure. However, a local spin polarization can also arise in centrosymmetric crystals containing ISB subunits. This is namely the case for the nodal-line semimetal ZrSiTe where, by combining spin- and angle-resolved photoelectron spectroscopy with ab initio band structure calculations, we reveal a complex spin polarization. In the bulk, the valence and conduction bands exhibit opposite spin orientations in two spatially separated two-dimensional ZrTe sectors within the unit cell, yielding no net polarization. We also observe spin-polarized surface states that are well separated in energy and momentum from the bulk bands. A layer-by-layer analysis of the spin polarization allows us to unveil the complex evolution of the signal in the bulk states near the surface, thus bringing the intertwined nature of surface and bulk effects to the fore.

High-frequency rectifiers based on type-II Dirac fermions

The advent of topological semimetals enables the exploitation of symmetry-protected topological phenomena and quantized transport. Here, we present homogeneous rectifiers, converting high-frequency electromagnetic energy into direct current, based on low-energy Dirac fermions of topological semimetal-NiTe2, with state-of-the-art efficiency already in the first implementation. Explicitly, these devices display room-temperature photosensitivity as high as 251 mA W−1 at 0.3 THz in an unbiased mode, with a photocurrent anisotropy ratio of 22, originating from the interplay between the spin-polarized surface and bulk states. Device performances in terms of broadband operation, high dynamic range, as well as their high sensitivity, validate the immense potential and unique advantages associated to the control of nonequilibrium gapless topological states via built-in electric field, electromagnetic polarization and symmetry breaking in topological semimetals. These findings pave the way for the exploitation of topological phase of matter for high-frequency operations in polarization-sensitive sensing, communications and imaging.