Photoelectron spectroscopy in combination with piezoforce microscopy reveals that the helicity of Rashba bands is coupled to the nonvolatile ferroelectric polarization of GeTe(111). A novel surface ...Rashba band is found and fingerprints of a bulk Rashba band are identified by comparison with density functional theory calculations.
Let X be a smooth projective curve of genus g≥2 defined over an algebraically closed field k of characteristic p>0. For p>r(r−1)(r−2)(g−1) we construct an atlas for the locus of all ...Frobenius-destabilized bundles of rank r (i.e. we construct all Frobenius-destabilized bundles of rank r and degree zero up to isomorphism). This is done by exhibiting a surjective morphism from a certain Quot-scheme onto the locus of stable Frobenius-destabilized bundles. Further we show that there is a bijective correspondence between the set of stable vector bundles E over X such that the pull-back F⁎(E) under the Frobenius morphism of X has maximal Harder–Narasimhan polygon and the set of opers having zero p-curvature. We also show that, after fixing the determinant, these sets are finite, which enables us to derive the dimension of certain Quot-schemes and certain loci of stable Frobenius-destabilized vector bundles over X. The finiteness is proved by studying the properties of the Hitchin–Mochizuki morphism; an alternative approach to finiteness has been realized in 3. In particular we prove a generalization of a result of Mochizuki to higher ranks.
In this paper we continue our study of the Frobenius instability locus in the
coarse moduli space of semi-stable vector bundles of rank $r$ and degree $0$
over a smooth projective curve defined over ...an algebraically closed field of
characteristic $p>0$. In a previous paper we identified the "maximal" Frobenius
instability strata with opers (more precisely as opers of type $1$ in the
terminology of the present paper) and related them to certain Quot-schemes of
Frobenius direct images of line bundles. The main aim of this paper is to
describe for any integer $q \geq 1$ a conjectural generalization of this
correspondence between opers of type $q$ (which we introduce here) and
Quot-schemes of Frobenius direct images of vector bundles of rank $q$. We also
give a conjectural formula for the dimension of the Frobenius instability
locus.
Compound Bi14Rh3I9 consists of ionic stacks of intermetallic (Bi4Rh)3I2+ and insulating Bi2I82– layers and has been identified to be a weak topological insulator. Scanning tunneling microscopy ...revealed the robust edge states at all step edges of the cationic layer as a topological fingerprint. However, these edge states are found 0.25 eV below the Fermi level, which is an obstacle for transport experiments. Here, we address this obstacle by comparing results of density functional slab calculations with scanning tunneling spectroscopy and angle-resolved photoemission spectroscopy. We show that the n-type doping of the intermetallic layer is intrinsically caused by the polar surface and is well-screened toward the bulk. In contrast, the anionic “spacer” layer shows a gap at the Fermi level, both on the surface and in the bulk; that is, it is not surface-doped due to iodine desorption. The well-screened surface dipole implies that a buried edge state, probably already below a single spacer layer, is located at the Fermi level. Consequently, a multilayer step covered by a spacer layer could provide access to the transport properties of the topological edge states. In addition, we find a lateral electronic modulation of the topologically nontrivial surface layer, which is traced back to the coupling with the underlying zigzag chain structure of the spacer layer.
Building on Simpson's original definition over the complex numbers, we introduce the notion of restricted sheaf Λ of rings of differential operators on a variety defined over a field of positive ...characteristic. We define the notion of p-curvature for Λ-modules and the analogue of the Hitchin map on the moduli space of Λ-modules. We show that under certain conditions this Hitchin map descends under the Frobenius map of the underlying variety and we give examples.
We show that Nori's fundamental group scheme \pi(X,x) does not base change correctly under extension of the base field for certain smooth projective ordinary curves X of genus 2 defined over a field ...of characteristic 2.
Fast detection of near-infrared (NIR) photons with high responsivity remains a challenge for photodetectors. Germanium (Ge) photodetectors are widely used for near-infrared wavelengths but suffer ...from a trade-off between the speed of photodetection and quantum efficiency (or responsivity). To realize a high-speed detector with high quantum efficiency, a small-sized photodetector efficiently absorbing light is required. In this paper, we suggest a realization of a dielectric metasurface made of an array of subwavelength germanium PIN photodetectors. Due to the subwavelength size of each pixel, a high-speed photodetector with a bandwidth of 65 GHz has been achieved. At the same time, high quantum efficiency for near-infrared illumination can be obtained by the engineering of optical resonant modes to localize optical energy inside the intrinsic Ge disks. Furthermore, small junction capacitance and the possibility of zero/low bias operation have been shown. Our results show that all-dielectric metasurfaces can improve the performance of photodetectors.
Let
be a smooth projective complex curve of genus
≥ 2 and let M
(2,
) be the moduli space of semi-stable rank-2 vector bundles over
with fixed determinant
. We show that the wobbly locus, i.e. the ...locus of semi-stable vector bundles admitting a non-zero nilpotent Higgs field, is a union of divisors 𝓦
⊂ M
(2,
). We show that on one wobbly divisor the set of maximal subbundles is degenerate. We also compute the class of the divisors 𝓦
in the Picard group of M
(2,
).
Strange duality revisited Pauly, Christian
Mathematical research letters,
2014, Letnik:
21, Številka:
6
Journal Article
Recenzirano
Odprti dostop
We give a proof of the strange duality or rank-level duality of the WZW models of conformal blocks by extending the genus-0 result, obtained by Nakanishi-Tsuchiya in 1992, to higher genus curves via ...the sewing procedure. The new ingredient of the proof is an explicit use of the branching rules of the conformal embedding of the affine Lie algebras sl(r) x sl(l) in sl(rl). We recover the strange duality of spaces of generalized theta functions obtained by Belkale, Marian-Oprea, as well as by Oudompheng in the parabolic case.
Parabolic SL(r,C)–opers were defined and investigated in 9 in the set-up of vector bundles on curves with a parabolic structure over a divisor. Here we introduce and study holomorphic differential ...operators between parabolic vector bundles over curves. We consider the parabolic SL(r,C)–opers on a Riemann surface X with given singular divisor S⊂X and with fixed parabolic weights satisfying the condition that all parabolic weights at any xi∈S are integral multiples of 12Ni+1, where Ni>1 are fixed integers. We prove that this space of opers is canonically identified with the affine space of holomorphic differential operators of order r between two natural parabolic line bundles on X (depending only on the divisor S and the weights Ni) satisfying the conditions that the principal symbol of the differential operators is the constant function 1 and the sub-principal symbol vanishes identically. The vanishing of the sub-principal symbol ensures that the logarithmic connection on the rank r bundle is actually a logarithmic SL(r,C)–connection.
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