Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

Ultimate performance of Quantum Well Infrared Photodetectors in the tunneling regime

Thanks to their wavelength diversity and to their excellent uniformity, Quantum Well Infrared Photodetectors (QWIP) emerge as potential candidates for astronomical or defense applications in the very long wavelength infrared (VLWIR) spectral domain. However, these applications deal with very low backgrounds and are very stringent on dark current requirements. In this paper, we present the full electro-optical characterization of a 15 micrometer QWIP, with emphasis on the dark current measurements. Data exhibit striking features, such as a plateau regime in the IV curves at low temperature (4 to 25 K). We show that present theories fail to describe this phenomenon and establish the need for a fully microscopic approach

Modular symbols in Iwasawa theory

This survey paper is focused on a connection between the geometry of $\mathrm{GL}_d$ and the arithmetic of $\mathrm{GL}_{d-1}$ over global fields, for integers $d \ge 2$. For $d = 2$ over $\mathbb{Q}$, there is an explicit conjecture of the third author relating the geometry of modular curves and the arithmetic of cyclotomic fields, and it is proven in many instances by the work of the first two authors. The paper is divided into three parts: in the first, we explain the conjecture of the third author and the main result of the first two authors on it. In the second, we explain an analogous conjecture and result for $d = 2$ over $\mathbb{F}_q(t)$. In the third, we pose questions for general $d$ over the rationals, imaginary quadratic fields, and global function fields.Comment: 43 page

Midwave infrared InAs/GaSb superlattice photodiode with a dopant-free p–n junction

Midwave infrared (MWIR) InAs/GaSb superlattice (SL) photodiode with a dopant-free p–n junction was fabricated by molecular beam epitaxy on GaSb substrate. Depending on the thickness ratio between InAs and GaSb layers in the SL period, the residual background carriers of this adjustable material can be either n-type or p-type. Using this flexibility in residual doping of the SL material, the p–n junction of the device is made with different non-intentionally doped (nid) SL structures. The SL photodiode processed shows a cut-off wavelength at 4.65 μm at 77 K, residual carrier concentration equal to 1.75 × 1015 cm−3, dark current density as low as 2.8 × 10−8 A/cm2 at 50 mV reverse bias and R0A product as high as 2 × 106 Ω cm2. The results obtained demonstrate the possibility to fabricate a SL pin photodiode without intentional doping the pn junction

Iterative Phase Retrieval Algorithms for Scanning Transmission Electron Microscopy

Scanning transmission electron microscopy (STEM) has been extensively used for imaging complex materials down to atomic resolution. The most commonly employed STEM imaging modality of annular dark field produces easily-interpretable contrast, but is dose-inefficient and produces little to no contrast for light elements and weakly-scattering samples. An alternative is to use phase contrast STEM imaging, enabled by high speed detectors able to record full images of a diffracted STEM probe over a grid of scan positions. Phase contrast imaging in STEM is highly dose-efficient, able to measure the structure of beam-sensitive materials and even biological samples. Here, we comprehensively describe the theoretical background, algorithmic implementation details, and perform both simulated and experimental tests for three iterative phase retrieval STEM methods: focused-probe differential phase contrast, defocused-probe parallax imaging, and a generalized ptychographic gradient descent method implemented in two and three dimensions. We discuss the strengths and weaknesses of each of these approaches using a consistent framework to allow for easier comparison. This presentation of STEM phase retrieval methods will make these methods more approachable, reproducible and more readily adoptable for many classes of samples.Comment: 25 pages, 11 figures, 1 tabl

Equidistribution of Heegner Points and Ternary Quadratic Forms

We prove new equidistribution results for Galois orbits of Heegner points with respect to reduction maps at inert primes. The arguments are based on two different techniques: primitive representations of integers by quadratic forms and distribution relations for Heegner points. Our results generalize one of the equidistribution theorems established by Cornut and Vatsal in the sense that we allow both the fundamental discriminant and the conductor to grow. Moreover, for fixed fundamental discriminant and variable conductor, we deduce an effective surjectivity theorem for the reduction map from Heegner points to supersingular points at a fixed inert prime. Our results are applicable to the setting considered by Kolyvagin in the construction of the Heegner points Euler system

Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fields

We study the arithmetic of Eisenstein cohomology classes (in the sense of G. Harder) for symmetric spaces associated to GL_2 over imaginary quadratic fields. We prove in many cases a lower bound on their denominator in terms of a special L-value of a Hecke character providing evidence for a conjecture of Harder that the denominator is given by this L-value. We also prove under some additional assumptions that the restriction of the classes to the boundary of the Borel-Serre compactification of the spaces is integral. Such classes are interesting for their use in congruences with cuspidal classes to prove connections between the special L-value and the size of the Selmer group of the Hecke character.Comment: 37 pages; strengthened integrality result (Proposition 16), corrected statement of Theorem 3, and revised introductio

Encoding multistate charge order and chirality in endotaxial heterostructures

Intrinsic resistivity changes associated with charge density wave (CDW) phase transitions in 1T-TaS$_2$ hold promise for non-volatile memory and computing devices based on the principle of phase change memory (PCM). High-density PCM storage is proposed for materials with multiple intermediate resistance states, which have been observed in 1T-TaS$_2$. However, the metastability responsible for this behavior makes the presence of multistate switching unpredictable in 1T-TaS$_2$ devices. Here, we demonstrate the synthesis of nanothick verti-lateral 1H-TaS$_2$/1T-TaS$_2$ heterostructures in which the number of endotaxial metallic 1H-TaS$_2$ monolayers dictates the number of high-temperature resistance transitions in 1T-TaS$_2$ lamellae. Further, we also observe optically active heterochirality in the CDW superlattice structure, which is modulated in concert with the resistivity steps. This thermally-induced polytype conversion nucleates at folds and kinks where interlayer translations that relax local strain favorably align 1H and 1T layers. This work positions endotaxial TaS$_2$ heterostructures as prime candidates for non-volatile device schemes implementing coupled switching of structure, chirality, and resistance

Radiometric and noise characteristics of InAs-rich T2SL MWIR pin photodiodes

We present a full characterization of the radiometric performances of a type-II InAs/GaSb superlattice pin photodiode operating in the mid-wavelength infrared domain. We first focused our attention on quantum efficiency, responsivity and angular response measurements: quantum efficiency reaches 23% at λ = 2.1 µm for 1 µm thick structure. Noise under illumination measurements are also reported: noise is limited by the Schottky contribution for reverse bias voltage smaller than 1.2 V. The specific detectivity, estimated for 2p field-of-view and 333 K background temperature, was determined equal to 2.29 x 10^10 Jones for -0,8 V bias voltage and 77 K operating temperature