arXiv subjects

Christian Pauly

Publications and source records attributed to Christian Pauly.

At least 19 recordsLinked to original sources

arXiv2025

Abelianization of the $\operatorname{SL}_2$ Hitchin connection at level four

We prove that the Hitchin connection for $\operatorname{SL}_2$ at level four can be understood in terms of the Mumford-Welters connections on bundles of abelian theta functions for Prym torsors of all unramified double covers, and use this to show that its monodromy is finite. This builds on earlier works, for individual curves, of the last named author with Oxbury and Ramanan. The key ingredients in making this work on the level of connections are equivariant conformal embeddings, and anti-invariant level-rank duality.

math.AG↗

arXiv2025

Neutron irradiation damage on Silicon Photomultipliers and electrical annealing studies for the CBM RICH detector

Limited radiation hardness is the primary drawback to implementing Silicon Photomultipliers (SiPMs) in high-luminosity environments, such as the Compressed Baryonic Matter (CBM) experiment. Hadron irradiation generates defects in the silicon lattice of SiPMs, increasing dark current, dark count rate (DCR), crosstalk, and afterpulsing, while degrading gain and photon resolution. The expected radiation dose in the photon camera of the Ring Imaging Cherenkov detector of the CBM experiment ranges from $8\times 10^9$ to $5\times 10^{10}$ n$_{\text{eq}}$/cm$^2$ after two-months of operation at maximum beam energy and intensity. In this work, we evaluated the radiation hardness of three different SiPMs: AFBR-S4N66P024M, S14160-6050HS, and MICROFC-60035. The samples were exposed to neutron irradiation with doses ranging from $3\times 10^8$ to $1\times 10^{11}$ n$_{\text{eq}}$/cm$^2$. The neutron radiation damage was found to increase the SiPM dark current up to $10^3$ times, DCR up to $10^2$ times, and afterpulsing up to $10\%$ while decreasing their gain and photon resolution. We performed electrical annealing (250 $^{\circ}$C/30 min) on the samples to recover the photon resolution and decrease the DCR and dark current.

physics.ins-det↗

arXiv2025

Hecke transformation for orthogonal bundles over curves

Given an orthogonal bundle $E$ over a smooth projective curve $X$ we define a Hecke transformation in the moduli space of orthogonal bundles by performing an elementary transformation with respect to a Lagrangian submodule $L \subset E_{2x}$ at some point $x \in X$. We show that the analogue of Tyurin's duality theorem holds for orthogonal bundles. Special cases of orthogonal bundles of ranks $2,3,4$ and $6$ are studied in detail.

math.AG↗

arXiv2024

The Prym-Hitchin Connection and Anti-Invariant Level-Rank Duality

We construct a "Hitchin-type" connection on bundles of non-abelian theta functions on higher-rank Prym varieties, for unramified double covers of curves. We formulate a version of level-rank duality in this Prym setting (building on work of Zelaci), show it holds for level one, and establish that the duality respects the flat connections at all levels.

math.AG↗

arXiv2023

Hitchin map for the moduli space of $Λ$-modules in positive characteristic

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.

math.AG↗

arXiv2023

Parabolic opers and differential operators

Parabolic SL(r,C)-opers were defined and investigated in [BDP] 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 and with fixed parabolic weights satisfying the condition that all parabolic weights at any point $x_i$ in S are integral multiples of $\frac{1}{2N_i+1}$, where $N_i > 1$ 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 $N_i$) 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.

math.AG↗

arXiv2022

The Hitchin connection in arbitrary characteristic

We give an algebro-geometric construction of the Hitchin connection, valid also in positive characteristic (with a few exceptions). A key ingredient is a substitute for the Narasimhan-Atiyah-Bott Kähler form that realizes the Chern class of the determinant-of-cohomology line bundle on the moduli space of bundles on a curve. As replacement we use an explicit realisation of the Atiyah class of this line bundle, based on the theory of the trace complex due to Beilinson-Schechtman and Bloch-Esnault.

math.AG↗

arXiv2022

Infinitesimal deformations of parabolic connections and parabolic opers

We compute the infinitesimal deformations of quadruples $(X, S, E_*, D)$, where $(X, S)$ is a compact Riemann surface with $n$ marked points, $E_*$ is a parabolic vector bundle on $X$ with parabolic structure over $S$, and $D$ is a parabolic connection on $E_*$. Using it we compute the infinitesimal deformations of $(X, S, D)$, where $D$ is a parabolic SL(r, C)-oper on $(X, S)$. It is shown that the monodromy map, from the moduli space of triples $(X, S, D)$, where $D$ is a parabolic SL(r, C)-oper on $(X, S)$, to the SL(r, C)-character variety of X - S, is an immersion.

math.AG↗

arXiv2020

Strong and Weak Three-Dimensional Topological Insulators Probed by Surface Science Methods

We review the contributions of surface science methods to discover and improve 3D topological insulator materials, while illustrating with examples from our own work. In particular, we demonstrate that spin-polarized angular-resolved photoelectron spectroscopy is instrumental to evidence the spin-helical surface Dirac cone, to tune its Dirac point energy towards the Fermi level, and to discover novel types of topological insulators such as dual ones or switchable ones in phase change materials. Moreover, we introduce procedures to spatially map potential fluctuations by scanning tunneling spectroscopy and to identify topological edge states in weak topological insulators.

cond-mat.mtrl-sci↗

arXiv2019

Parabolic SL(r)-opers

We define SL(r)-opers in the set-up of vector bundles on curves with a parabolic structure over a divisor. Basic properties of these objects are investigated.

math.AG↗

arXiv2019

Opers of higher types, Quot-schemes and Frobenius instability loci

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.

math.AG↗

arXiv2018

The wobbly divisors of the moduli space of rank-$2$ vector bundles

Let $X$ be a smooth projective complex curve of genus $g \geq 2$ and let $\M_X(2,Λ)$ be the moduli space of semi-stable rank-$2$ vector bundles over $X$ with fixed determinant $Λ$. 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 $\Ww_k \subset \M_X(2,Λ)$. We show that on one wobbly divisor the set of maximal subbundles is degenerate. We also compute the class of the divisors $\Ww_k$ in the Picard group of $\M_X(2,Λ)$.

math.AG↗

arXiv2018

Mapping the band structure of GeSbTe phase change alloys around the Fermi level

Phase change alloys are used for non-volatile random access memories exploiting the conductivity contrast between amorphous and metastable, crystalline phase. However, this contrast has never been directly related to the electronic band structure. Here, we employ photoelectron spectroscopy to map the relevant bands for metastable, epitaxial GeSbTe films. The constant energy surfaces of the valence band close to the Fermi level are hexagonal tubes with little dispersion perpendicular to the (111) surface. The electron density responsible for transport belongs to the tails of this bulk valence band, which is broadened by disorder, i.e., the Fermi level is 100 meV above the valence band maximum. This result is consistent with transport data of such films in terms of charge carrier density and scattering time. In addition, we find a state in the bulk band gap with linear dispersion, which might be of topological origin.

cond-mat.mtrl-sci↗

arXiv2017

Very stable bundles and properness of the Hitchin map

Let $X$ be a smooth complex projective curve of genus $g\geq 2$ and let $K$ be its canonical bundle. In this note we show that a stable vector bundle $E$ on $X$ is very stable, i.e. $E$ has no non-zero nilpotent Higgs field, if and only if the restriction of the Hitchin map to the vector space of Higgs fields $H^0(X, \mathrm{End}(E) \otimes K)$ is a proper map.

math.AG↗

arXiv2016

Electronic Structure of the Dark Surface of the Weak Topological Insulator Bi14Rh3I9

The compound Bi14Rh3I9 consists of ionic stacks of intermetallic [(Bi4Rh)3I]2+ and insulating [Bi2I8]2- 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 towards the bulk. In contrast, the anionic "spacer" layer shows a gap at the Fermi level, both, on the surface and in the bulk, i.e. 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 non-trivial surface layer which is traced back to the coupling with the underlying zigzag chain structure of the spacer layer.

cond-mat.mtrl-sci↗

arXiv2015

Spatially resolved Landau level spectroscopy of the topological Dirac cone of bulk-type Sb2Te3(0001): potential fluctuations and quasiparticle lifetime

Using low temperature scanning tunneling spectroscopy, we probe the Landau levels of the topologically protected state of Sb2Te3(0001) after in-situ cleavage of a single crystal. Landau levels are visible for magnetic fields B > 2 T at energies, which confirm the Dirac type dispersion including the zeroth Landau level. We find different Dirac velocities for the lower and the upper part of the Dirac cone in reasonable agreement with previous density functional theory data. The Dirac point deduced from the zeroth Landau level shifts by about 40 meV between different areas of the sample indicating long range potential fluctuations. The local potentials are correlated to different local defect densities varying slightly stronger than expected from a statistical distribution. The quasiparticle lifetime deduced from the width of the Landau level peaks decreases close to inversely with the electron energy with respect to the Fermi level. Consequently, we attribute the peak width to a dominating scattering of the hot quasiparticles by electron-electron interaction.

cond-mat.mes-hall↗

arXiv2015

Sub-nm wide electron channels protected by topology

Helical locking of spin and momentum and prohibited backscattering are the key properties of topologically protected states. They are expected to enable novel types of information processing such as spintronics by providing pure spin currents, or fault tolerant quantum computation by using the Majorana fermions at interfaces of topological states with superconductors. So far, the required helical conduction channels used to realize Majorana fermions are generated through application of an axial magnetic field to conventional semiconductor nanowires. Avoiding the magnetic field enhances the possibilities for circuit design significantly. Here, we show that sub-nanometer wide electron channels with natural helicity are present at surface step-edges of the recently discovered topological insulator Bi14Rh3I9. Scanning tunneling spectroscopy reveals the electron channels to be continuous in both energy and space within a large band gap of 200 meV, thereby, evidencing its non-trivial topology. The absence of these channels in the closely related, but topologically trivial insulator Bi13Pt3I7 corroborates the channels' topological nature. The backscatter-free electron channels are a direct consequence of Bi14Rh3I9's structure, a stack of 2D topologically insulating, graphene-like planes separated by trivial insulators. We demonstrate that the surface of Bi14Rh3I9 can be engraved using an atomic force microscope, allowing networks of protected channels to be patterned with nm precision.

cond-mat.mes-hall↗

arXiv2015

Hitchin-Mochizuki morphism, Opers and Frobenius-destabilized vector bundles over curves

Let X be a smooth projective curve of genus g \textgreater{}1 defined over an algebraically closed field k of characteristic p \textgreater{}0. For p sufficiently large (explicitly given in terms of r,g) we construct an atlas for the locus of all Frobenius-destabilized bundles (i.e. we construct all Frobenius-destabilized bundles of 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 a recent preprint by Chen and Zhu. In particular we prove a generalization of a result of Mochizuki to higher ranks.

math.AG↗