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Steven Flynn

Publications and source records attributed to Steven Flynn.

11 recordsLinked to original sources
arXiv2025

Synthesis of Cobalt Grown from Co-S Eutectic in High Magnetic Fields

Samples of Co were grown directly in the ferromagnetic state under equilibrium conditions using a cobalt sulfide flux. Magnetic fields up to 9 T were applied during growth, and isolated Co products exhibit progressively elongated morphologies, from cubes to rectangular rods to needle-like tendrils with poorly-defined facets. The degree of elongation of the major axis was found to correlate with magnetic field direction, strength, and gradient. Two-dimensional X-ray diffraction data indicate some level of polycrystalline-like samples, and quantitative analyses (Le Bail and Rietveld) of the one-dimensional data confirm the presence of hcp and fcc phases. The magnetic responses indicate a partial alignment of the magnetic easy-axis of the hcp phase along the magnetic field present during growth.

cond-mat.mtrl-sci↗
arXiv2025

Refined Strichartz Estimates for sub-Laplacians in Heisenberg and $H$-type groups

We obtain refined Strichartz estimates for the sub-Riemannian Schr\"{o}dinger equation on $H$-type Carnot groups using Fourier restriction techniques. In particular, we extend the previously known Strichartz estimates previously obtained for the Heisenberg group also to non radial initial data. The same arguments permits to obtain refined Strichartz estimates for the wave equation on $H$-type groups. Our proof is based on estimates for the spectral projectors for sub-Laplacians and reinterprets Strichartz estimates as Fourier restriction theorems for nilpotent groups in the context of trace-class operator valued measures.

math.AP↗
arXiv2024

Quantization on filtered manifolds

In this article, we develop a pseudodifferential calculus on a general filtered manifold M . The symbols are fields of operators $\sigma$(x, $\pi$) parametrised by x $\in$ M and the unitary dual G x M of the osculating Lie group G x M . We define classes of symbols and a local quantization formula associated to a local frame adapted to the filtration. We prove that the collection of operators on M coinciding locally with the quantization of symbols enjoys the essential properties of a pseudodifferential calculus: composition, adjoint, parametrices, continuity on adapted Sobolev spaces. Moreover, we show that the polyhomogeneous subcalculus coincides with the calculus constructed by van Erp and Yuncken via groupoids.

math.FA↗
arXiv2023

The sub-Riemannian X-ray transform on $H$-type groups: Fourier slice theorems, injectivity sets and frequency support

We study the X-ray transform along sub-Riemannian geodesics of $H$-type groups, a setting in which every geodesic apart from the horizontal lines carries conjugate points. The geodesics are helices labelled by a charge $\lambda$ in the dual of the center. Using the group Fourier transform we prove a Fourier slice theorem, which identifies the transform restricted to the geodesics of charge $\lambda$ as a Fourier restriction to their visible frequencies $\Gamma_\lambda^*$, a family of parallel hyperplanes of central frequencies dual to the central advance of the helices, followed by an explicit operator-valued multiplier. We characterize the sets of charges $Z$ whose geodesics determine an integrable function, one direction for each $\lambda\in Z$ sufficing, as exactly those for which $\bigcup_{\lambda\in Z}\Gamma_\lambda^*$ is dense. In particular the full transform is injective, and when the center has dimension at least two, charges of a single magnitude suffice provided their directions fill a circle. Averaging the normal operator over the horizontal directions gives a joint spectral multiplier of the sub-Laplacian and the central derivatives, whose eigenvalues we compute. This yields, outside the first Heisenberg group, a sharp stability estimate at fixed charge and central frequency with the loss of exactly half a derivative in the sub-Laplacian, as for the Euclidean X-ray transform. Finally we describe which central frequencies of $f$ are determined by a band or a cap of charges, namely all sufficiently high ones, the bounded remainder being recovered only by analytic continuation, in contrast with Euclidean limited-angle tomography.

math.DG↗
arXiv2022

Some remarks on semi-classical analysis on two-step Nilmanifolds

In this paper, we present recent results about the developement of a semiclassical approach in the setting of nilpotent Lie groups and nilmanifolds. We focus on two-step nilmanifolds and exhibit some properties of the weak limits of sequence of densities associated with eigenfunctions of a sub-Laplacian. We emphasize the influence of the geometry on these properties.

math.AP↗
arXiv2021

Geometric invariance of the semi-classical calculus on nilpotent graded Lie groups

In this paper, we consider the semi-classical setting constructed on nilpotent graded Lie groups by means of representation theory. We analyze the effects of the pull-back by diffeomorphisms on pseudodifferential operators. We restrict to diffeomorphisms that preserve the filtration and prove that they are Pansu differentiable. We show that the pull-back of a semi-classical pseudodifferential operator by such a diffeomorphism has a semi-classical symbol that is expressed at leading order in terms of the Pansu differential. We interpret the geometric meaning of this invariance in the setting of filtered manifolds.

math.FA↗
arXiv2020

Injectivity of the Heisenberg X-ray Transform

We initiate the study of X-ray tomography on sub-Riemannian manifolds, for which the Heisenberg group exhibits the simplest nontrivial example. With the language of the group Fourier Transform, we prove an operator-valued incarnation of the Fourier Slice Theorem, and apply this new tool to show that a sufficiently regular function on the Heisenberg group is determined by its line integrals over sub-Riemannian geodesics. We also consider the family of taming metrics $g_\epsilon$ approximating the sub-Riemannian metric, and show that the associated X-ray transform is injective for all $\epsilon>0$. This result gives a concrete example of an injective X-ray transform in a geometry with an abundance of conjugate points.

math.DG↗
arXiv2015

The Effect of Dopants on the Magnetoresistance of WTe2

Elucidating the nature of the large, non-saturating magnetoresistance in WTe2 is a significant step in functionalizing this phenomenon for applications. Here, Mo, Re, and Ta doped WTe2 are compared to determine whether isovalent and aliovalent substitutions have different effects on the large magnetoresistance. By 1% substitution, isoelectronic doping reduces the magnetoresistance by a factor of 1.2 with an apparent linear trend, whereas aliovalent doping reduces the effect by over an order of magnitude while following a higher-order decay. The apparent increased sensitivity of the magnetoresistive effect to aliovalent doping over simple isoelectronic disorder supports the conclusion that the large magnetoresistance in WTe2 arises from interactions between balanced hole and electron populations.

cond-mat.mtrl-sci↗
arXiv2015

Correlation of Crystal Quality and Extreme Magnetoresistance of WTe$_2$

High quality single crystals of WTe$_2$ were grown using a Te flux followed by a cleaning step involving self-vapor transport. The method is reproducible and yields consistently higher quality single crystals than are typically obtained via halide assisted vapor transport methods. Magnetoresistance (MR)values at 9 Tesla and 2 Kelvin as high as 1.75 million \%, nearly an order of magnitude higher than previously reported for this material, were obtained on crystals with residual resistivity ratio (RRR) of approximately 1250. The MR follows a near B$^2$ law (B = 1.95(1)) and, assuming a semiclassical model, the average carrier mobility for the highest quality crystal was found to be ~167,000 cm$^2$/Vs at 2 K. A correlation of RRR, MR ratio and average carrier mobility ($\mu_{avg}$) is found with the cooling rate during the flux growth.

cond-mat.mtrl-sci↗
arXiv2014

Titanic Magnetoresistance in WTe2

Magnetoresistance is the change of a material's electrical resistance in response to an applied magnetic field. In addition to its intrinsic scientific interest, it is a technologically important property, placing it in "Pasteur's quadrant" of research value: materials with large magnetorsistance have found use as magnetic sensors 1, in magnetic memory 2, hard drives 3, transistors 4, and are the subject of frequent study in the field of spintronics 5, 6. Here we report the observation of an extremely large one-dimensional positive magnetoresistance (XMR) in the layered transition metal dichalcogenide (TMD) WTe2; 452,700 percent at 4.5 Kelvin in a magnetic field of 14.7 Tesla, and 2.5 million percent at 0.4 Kelvin in 45 Tesla, with no saturation. The XMR is highly anisotropic, maximized in the crystallographic direction where small pockets of holes and electrons are found in the electronic structure. The determination of the origin of this effect and the fabrication of nanostructures and devices based on the XMR of WTe2 will represent a significant new direction in the study and uses of magnetoresistivity. *The published version of the paper includes co-authors Tian Liang and Max Hirschberger. **This paper has been published with new MR data to 60T where the MR of WTe2 reaches 13 million percent (at 0.5K) and still shows no signs of saturation. We also have new electron diffraction patterns to lower temperature (10K). We discuss the possible origin of the MR as coming from an electron-hole 'resonance' condition established by a perfect n/p ratio of 1 (more details in a new "extended data" section). This makes WTe2, possibly, the first realization of a perfectly balanced semimetal. ***The paper is published as "Large non-saturating magnetoresistance in WTe2" in Nature (2014), DOI:10.1038/nature13763

cond-mat.mtrl-sci↗