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Soumya Sankar

Publications and source records attributed to Soumya Sankar.

17 recordsLinked to original sources
arXiv2026

Intrinsic anomalous Hall response in the bilayer kagome ferromagnet Co$_3$Sn

Transition-metal kagome magnets provide a rich platform for investigating the interplay between layer stacking, magnetic order, and band topology. Here, we report the molecular beam epitaxy and experimental investigation of high-quality thin films of the kagome metal Co$_3$Sn, which has not been synthesized in bulk form yet. Structural and chemical analyses confirm a hexagonal lattice structure ($P6_3/mmc$) composed of direct A-B stacked Co$_3$Sn kagome bilayers. Magnetometry reveals robust easy-plane ferromagnetism with a Curie temperature exceeding $300\,\text{K}$. Magneto-transport measurements demonstrate metallic behavior (carrier density $n\approx5.01\times10^{22}\,\text{cm}^{-3}$) alongside a temperature-independent anomalous Hall conductivity of $σ_{\rm AHE}\approx90\,Ω^{-1}\cdot{\rm cm}^{-1}$, extending from $2\,\text{K}$ up to room temperature. Results from first-principles density functional theory calculations attribute this anomalous Hall response to intrinsic Berry curvature hotspots near the Fermi level in the spin-split band structure. Our results establish Co$_3$Sn as a room-temperature kagome ferromagnet and highlight the impact of the layer stacking sequence on the material properties of kagome metals from the CoSn family.

cond-mat.mtrl-sci↗
arXiv2026

Active learning molecular beam epitaxy of complex quantum materials

The integration of machine learning (ML) into materials science offers a transformative pathway toward fully autonomous synthesis workflows. For precise thin-film deposition techniques like molecular beam epitaxy (MBE), this automation is critical to overcome the time-consuming, manual navigation of high-dimensional thermodynamic phase spaces. Existing approaches for ML-assisted thin film growth predominantly rely on continuous Bayesian optimization (BO) models that assume smooth parameter landscapes. Consequently, they struggle to capture the abrupt crystallographic phase boundaries and narrow growth windows inherent to binary quantum materials. Here, we demonstrate an active learning protocol based on Sequential Model-Based Optimization (SMBO) designed specifically for the closed-loop MBE of such compounds. To overcome the limitations of continuous models while retaining the efficient exploration-exploitation logic of traditional BO, we combine a random forest surrogate model capable of capturing highly non-linear phase transitions and thermodynamics constraints of the growth process with an expected improvement function to predict optimum growth parameters. We apply this combined SMBO framework to the MBE of the topological Weyl ferromagnet Fe$_3$Sn, which exists as a metastable line compound. Using a small initial training set of fewer than twenty growth iterations, our active learning loop rapidly navigates a complex optimization landscape to identify an optimum growth window bounded by sharp transitions. Within only four active learning iterations, the absolute predictive error is halved to $\approx10\%$. This data-efficient framework paves the way for the autonomous discovery and thin-film synthesis of functional quantum materials.

cond-mat.mtrl-sci↗
arXiv2026

Conic bundle threefolds differing by a constant Brauer class and connections to rationality

A double cover $Y$ of $\mathbb{P}^1 \times \mathbb{P}^2$ ramified over a general $(2,2)$-divisor will have the structure of a geometrically standard conic bundle ramified over a smooth plane quartic $Δ\subset \mathbb{P}^2$ via the second projection. These threefolds are rational over algebraically closed fields; however, over nonclosed fields, including $\mathbb{R}$, their rationality is an open problem. In this paper, we characterize rationality over $\mathbb{R}$ when $Δ(\mathbb{R})$ has at least two connected components (extending work of M. Ji and the second author) and over local fields when all odd degree fibers of the first projection have nonsquare discriminant. We obtain these applications by proving general results comparing the conic bundle structure on $Y$ with the conic bundle structure on a well-chosen intersection of two quadrics. The difference between these two conic bundles is encoded by a constant Brauer class, and we prove that this class encodes the obstruction to the existence of a section of the first projection $Y\to\mathbb{P}^1$.

math.AG↗
arXiv2026

Refined obstructions to local-global principles for 0-cycles

We introduce new `refined' obstructions to local-global principles for 0-cycles on algebraic varieties over number fields. Assuming finiteness of relevant Tate--Shafarevich groups, we show that the Hasse principle and weak approximation for 0-cycles on generalised Kummer varieties and bielliptic surfaces are controlled by obstructions of this new type. As an additional application of our refined obstructions, we answer a question of Zhang about the relationship between the Brauer--Manin and connected descent obstructions for 0-cycles. We also show that a Corwin--Schlank style refined obstruction set coincides with the set of global 0-cycles, conditionally on the Section Conjecture.

math.AG↗
arXiv2026

Distinguishing and Separating In-Plane Hall Responses

Electric Hall effects generated by an in-plane magnetic field have recently gained attention owing to their intrinsic origin in topological electronic states and potential application in magnetic field sensing. In pratice, the measured transverse electric voltage typically combines contributions from multiple phenomena, such as anisotropy and Berry curvature effects, leading to interpretative ambiguities of the measurement signal. Here, we introduce a universal framework that disentangles these contributions via their distinct field-reversal symmetries and angular dependencies. Leveraging a 12-terminal Hall bar for independent control of the electric and in-plane magnetic field directions, we exemplify this method by analyzing the transverse electric voltage recorded on the the ferromagnetic Weyl semimetal Fe3Sn in an in-plane geometry. The standardized approach presented in this work will guide future studies of in-plane Hall responses in magnetic and topological materials.

cond-mat.mes-hall↗
arXiv2025

Broadband nonlinear Hall response and multiple wave mixing in a room temperature altermagnet

Crystalline symmetries determine the linear and nonlinear response of materials to external stimuli such as mechanical pressure and electromagnetic fields, governing phenomena such as piezoelectricity, optical activity, and multiple wave mixing with wide ranging technological applications. Altermagnets present a new class of materials with magnetic crystalline order where specific crystal symmetry operations connect antiferromagnetic sublattices, leading to non-relativistic spin-splitting of the electronic band structure. Hence, the electric material properties of altermagnets should uniquely mirror these underlying symmetry properties, potentially giving rise to novel phenomena in response to external driving fields. Here, we report the discovery of a broadband third-order nonlinear anomalous Hall effect in altermagnetic CrSb at room temperature. The comparison of our observations with symmetry analyses and model calculations shows that this nonlinear Hall response is induced by the nonlinear electric susceptibility of a Berry curvature quadrupole, which exists within the spin-split band structure of CrSb and is characterized by the underlying crystalline and magnetic symmetries. We then utilize this third-order nonlinear electric susceptibility of CrSb to realize a multiple wave mixing device with pronounced four wave mixing output, which could, in principle, be extended to THz frequencies. Our study discovers that the crystalline magnetic order of altermagnets determines their nonlinear electric material properties, which could facilitate applications in high-frequency electronics, THz generation, communication networks, and energy harvesting.

cond-mat.mes-hall↗
arXiv2025

Room temperature observation of the anomalous in-plane Hall effect in epitaxial thin films of a Weyl ferromagnet

Topologically nontrivial electronic states can give rise to novel anomalous Hall effects. The potential appearance of these effects at room temperature holds promise for their application in magnetic sensing, spintronics, and energy harvesting technology. The anomalous in-plane Hall effect (IPHE) is predicted to arise in topological magnetic materials when an external magnetic field is applied within the sample plane. Because of stringent symmetry requirements, the conclusive detection of the anomalous IPHE induced by topological electronic states remains challenging, and the study of anomalous Hall effects is often confined to cryogenic conditions. Combining molecular beam epitaxy of the kagome metal Fe$_3$Sn with measurements of the electric Hall effect and theoretical calculations, we propose and experimentally demonstrate that the interplay of the kagome lattice motif with spin-orbit coupling and canted ferromagnetism with large exchange interactions gives rise to the anomalous IPHE at room temperature that is induced by topological Weyl points in the electronic band structure. Synthesizing a topological heterostructure including layers of Fe$_3$Sn and ferromagnetic CoFeB, we further show the enhancement of the anomalous IPHE through the magnetic stray field of the CoFeB layer. Our work establishes a design paradigm for topological magnets and heterostructures to discover and control novel anomalous Hall effects toward their use in technological applications.

cond-mat.mes-hall↗
arXiv2024

Frobenius distributions of low dimensional abelian varieties over finite fields

Given a $g$-dimensional abelian variety $A$ over a finite field $\mathbf{F}_q$, the Weil conjectures imply that the normalized Frobenius eigenvalues generate a multiplicative group of rank at most $g$. The Pontryagin dual of this group is a compact abelian Lie group that controls the distribution of high powers of the Frobenius endomorphism. This group, which we call the Serre--Frobenius group, encodes the possible multiplicative relations between the Frobenius eigenvalues. In this article, we classify all possible Serre--Frobenius groups that occur for $g \le 3$. We also give a partial classification for simple ordinary abelian varieties of prime dimension $g>3$.

math.NT↗
arXiv2024

Cascade of strongly correlated quantum states in a partially filled kagome flat band

Coulomb interactions among charge carriers that occupy an electronic flat band have a profound impact on the macroscopic properties of materials. At sufficient strength, these interactions can give rise to captivating phenomena such as quantum criticality, Mott-Hubbard states, and unconventional superconductivity. The appearance of these characteristics sensitively depends on the number of electrons occupying the flat band states. In this work, we present experimental evidence obtained from scanning tunneling microscopy measurements for a cascade of strongly correlated states appearing in the partially occupied kagome flat bands of Co$_{1-x}$Fe$_x$Sn whose filling can be controlled by the Fe-doping level $x$. At elevated temperatures ($T\geq16\,K$), we detect a nematic electronic state across a broad doping range $0.05 100\,$meV) blend the states of two $3d$-orbital derived flat bands and impart a nematic order parameter. This state serves as the parent phase of a strongly correlated phase diagram: At lower temperatures $T<16\,$K, we find spectroscopic evidence for an orbital-selective Mott state enabled by the $3d$-orbital degeneracy of the Co atom. This state can only be detected in samples with ideal Fe doping ($x=0.17$) and descends into pseudogap phases upon electron and hole doping. At $T<8\,$K, the pseudogap phase evolves into another nematic low temperature state. Our observations demonstrate that the electronic ground state of a kagome flat band depends on the complex interplay between strong Coulomb repulsion, $3d$-orbital degeneracy, and flat band filling fraction at different temperatures.

cond-mat.str-el↗
arXiv2024

On rational points on classifying stacks and Malle's conjecture

In this expository article, we compare Malle's conjecture on counting number fields of bounded discriminant with recent conjectures of Ellenberg--Satriano--Zureick-Brown and Darda--Yasuda on counting points of bounded height on classifying stacks. We illustrate the comparisons via the classifying stacks $B(\mathbb{Z}/n\mathbb{Z})$ and $B{μ_n}$.

math.NT↗
arXiv2023

Experimental evidence for Berry curvature multipoles in antiferromagnets

Berry curvature multipoles appearing in topological quantum materials have recently attracted much attention. Their presence can manifest in novel phenomena, such as nonlinear anomalous Hall effects (NLAHE). The notion of Berry curvature multipoles extends our understanding of Berry curvature effects on the material properties. Hence, research on this subject is of fundamental importance and may also enable future applications in energy harvesting and high-frequency technology. It was shown that a Berry curvature dipole can give rise to a 2nd order NLAHE in materials of low crystalline symmetry. Here, we demonstrate a fundamentally new mechanism for Berry curvature multipoles in antiferromagnets that are supported by the underlying magnetic symmetries. Carrying out electric transport measurements on the kagome antiferromagnet FeSn, we observe a 3rd order NLAHE, which appears as a transverse voltage response at the 3rd harmonic frequency when a longitudinal a.c. current drive is applied. Interestingly, this NLAHE is strongest at and above room temperature. We combine these measurements with a scaling law analysis, a symmetry analysis, model calculations, first-principle calculations, and magnetic Monte-Carlo simulations to show that the observed NLAHE is induced by a Berry curvature quadrupole appearing in the spin-canted state of FeSn. At a practical level, our study establishes NLAHE as a sensitive probe of antiferromagnetic phase transitions in other materials, such as moiré superlattices, two-dimensional van der Waal magnets, and quantum spin liquid candidates, that remain poorly understood to date. More broadly, Berry curvature multipole effects are predicted to exist for 90 magnetic point groups. Hence, our work opens a new research area to study a variety of topological magnetic materials through nonlinear measurement protocols.

cond-mat.mes-hall↗
arXiv2023

Visualizing the Localized Electrons of a Kagome Flat Band

Destructive interference between electron wavefunctions on the two-dimensional (2D) kagome lattice induces an electronic flat band, which could host a variety of interesting many-body quantum states. Key to realize these proposals is to demonstrate the real space localization of kagome flat band electrons. In particular, the extent to which the often more complex lattice structure and orbital composition of realistic materials counteract the localizing effect of destructive interference, described by the 2D kagome lattice model, is hitherto unknown. We used scanning tunneling microscopy (STM) to visualize the non-trivial Wannier states of a kagome flat band at the surface of CoSn, a kagome metal. We find that the local density of states associated with the flat bands of CoSn is localized at the center of the kagome lattice, consistent with theoretical expectations for their corresponding Wannier states. Our results show that these states exhibit an extremely small localization length of two to three angstroms concomitant with a strongly renormalized quasiparticle velocity, which is comparable to that of moiré superlattices. Hence, interaction effects in the flat bands of CoSn could be much more significant than previously thought. Our findings provide fundamental insight into the electronic properties of kagome metals and are a key step for future research on emergent many-body states in transition metal based kagome materials.

cond-mat.mes-hall↗
arXiv2023

Curve classes on conic bundle threefolds and applications to rationality

We undertake a study of conic bundle threefolds $π\colon X\to W$ over geometrically rational surfaces whose associated discriminant covers $\tildeΔ\toΔ\subset W$ are smooth and geometrically irreducible. First, we determine the structure of the group $\mathrm{CH}^2 X_{\overline{k}}$ of rational equivalence classes of curves. Precisely, we construct a Galois-equivariant group homomorphism from $\mathrm{CH}^2X_{\overline{k}}$ to a group scheme associated to the discriminant cover $\tildeΔ\to Δ$ of $X$. The target group scheme is a generalization of the Prym variety of $\tildeΔ\toΔ$ and so our result can be viewed as a generalization of Beauville's result that the algebraically trivial curve classes on $X_{\overline{k}}$ are parametrized by the Prym variety. We apply our structural result on curve classes to study the refined intermediate Jacobian torsor (IJT) obstruction to rationality introduced by Hassett--Tschinkel and Benoist--Wittenberg. The first case of interest is $W = \mathbb P^2$ and $Δ$ is a smooth plane quartic. In this case, we show that the IJT obstruction characterizes rationality when the ground field has less arithmetic complexity (precisely, when the $2$-torsion in the Brauer group of the ground field is trivial). We also show that a hypothesis of this form is necessary by constructing, over any $k \subset\mathbb R$, a conic bundle threefold with $Δ$ a smooth quartic where the IJT obstruction vanishes, yet $X$ is irrational over $k$.

math.AG↗
arXiv2021

Derived equivalences of gerbey curves

We study derived equivalences of certain stacks over genus $1$ curves, which arise as connected components of the Picard stack of a genus $1$ curve. To this end, we develop a theory of integral transforms for these algebraic stacks. We use this theory to answer the question of when two stacky genus $1$ curves are derived equivalent. We use integral transforms and intersection theory on stacks to answer the following questions: if $C'=Pic^d(C)$, is $C=Pic^f(C')$ for some integer $f$? If $C'=Pic^d(C)$ and $C''=Pic^f(C')$, then is $C''=Pic^g(C)$ for some integer $g$?

math.AG↗
arXiv2020

Proportion of ordinarity in some families of curves over finite fields

A curve over a field of characteristic $p$ is called ordinary if the $p$-torsion of its Jacobian as large as possible, that is, an $\mathbb{F}_p$ vector space of dimension equal to its genus. In this paper we consider the following question: fix a finite field $\mathbb{F}_q$ and a family $\mathscr{F}$ of curves over $\mathbb{F}_q$. Then, what is the probability that a curve in this family is ordinary? We answer this question when $\mathscr{F}$ is either the Artin-Schreier family in any characteristic or a superelliptic family in characteristic 2.

math.NT↗
arXiv2020

Counting elliptic curves with a rational $N$-isogeny for small $N$

We count the number of rational elliptic curves of bounded naive height that have a rational $N$-isogeny, for $N \in \{2,3,4,5,6,8,9,12,16,18\}$. For some $N$, this is done by generalizing a method of Harron and Snowden. For the remaining cases, we use the framework of Ellenberg, Satriano and Zureick-Brown, in which the naive height of an elliptic curve is the height of the corresponding point on a moduli stack.

math.NT↗