arXiv subjects

Shubham Sinha

Publications and source records attributed to Shubham Sinha.

17 recordsLinked to original sources

arXiv2026

High-pressure stabilization of Mg2IrH7: Structural proximity to high-Tc superconductivity

Mg$_2$IrH$_6$ is a metastable complex metal hydride with a predicted superconducting transition temperature as high as 170 K at ambient pressure. Following the synthesis of isomorphic, insulating Mg$_2$IrH$_5$ at low pressure, higher-pressure studies were conducted to investigate the phase behavior and compound formation in this system. X-ray diffraction and Raman spectroscopic measurements indicate that cubic Mg$_2$IrH$_7$ is stabilized above ca. 40 GPa and coexists with a related hexagonal hydride with likely composition near Mg$_2$IrH$_5$. Electrical transport measurements show that the cubic Mg$_2$IrH$_7$ is insulating, in agreement with ab initio predictions, and persists during room-temperature decompression until $\sim$20 GPa before reverting back to the cubic Mg$_2$IrH$_5$. The experimental results confirm ground-state structure predictions in the Mg-Ir-H system, and the formation of two nearly identical phases with surrounding compositions opens new opportunities to access superconducting Mg$_2$IrH$_6$ through non-equilibrium processing pathways.

cond-mat.supr-con↗

arXiv2026

Inverse Isotope Effect in the Ternary Perovskite Hydride SrPdH/D$_{2.9}$: A Signature of Quantum Zero-Point Fluctuations

Guided by first-principles calculations, we demonstrate superconductivity in the ternary perovskite hydride SrPdH$_{3-x}$, synthesized at low pressure. Structural characterization via neutron diffraction reveals the near-stoichiometric composition SrPdD$_{2.9(2)}$ with 96\% deuterium site occupancy. Subsequent transport and magnetic susceptibility measurements establish onset superconducting transitions at $T_\text{c} = \SI{2.1}{K} $ (H) and $T_\text{c} = \SI{2.2}{K} $ (D), exhibiting an inverse isotope effect that our first-principles calculations attribute predominantly to quantum zero-point motion. The excellent agreement between theory and experiment with respect to thermodynamic stability and superconducting properties provides important validation for theory-guided superconductor discovery. This work establishes superconductivity in the perovskite hydride structural prototype -- expanding the limited family of experimentally realized ternary hydride superconductors -- and demonstrates the importance of quantum nuclear motion on the accurate theoretical treatment of low-pressure hydride superconductors.

cond-mat.supr-con↗

arXiv2025

Intersection Theory of Hyperquot Schemes on curves

We study the virtual intersection theory of Hyperquot schemes parameterizing sequences of quotient sheaves of a vector bundle on a smooth projective curve. Our results generalize the Vafa--Intriligator formula for Quot schemes and provide a closed formula for virtual counts of maps from the curve to a partial flag variety.

math.AG↗

arXiv2025

A Borel--Weil--Bott theorem for Quot schemes on $\mathbb{P}^1$

We study the cohomology groups of tautological bundles on Quot schemes over the projective line, which parametrize rank $r$ quotients of a vector bundle $V$ on $\mathbb{P}^1$. Our main result is an analogue of the Borel--Weil--Bott theorem for Quot schemes. As a corollary, we prove recent conjectures of Marian, Oprea, and Sam on the exterior and symmetric powers of tautological bundles.

math.AG↗

arXiv2025

A short way of counting maps to hypersurfaces in Grassmannians

Using a Quot scheme compactification, we calculate the virtual count of maps of degree $d$ from a smooth projective curve of genus $g$ to a hypersurface in a Grassmannian, sending specified points of the curve to special Schubert subvarieties restricted to the hypersurface. We study the question of whether this virtual count is in fact enumerative under suitable conditions on the hypersurface, in the regime when the map degree $d$ is large.

math.AG↗

arXiv2025

Prediction and Synthesis of Mg$_4$Pt$_3$H$_6$: A Metallic Complex Transition Metal Hydride Stabilized at Ambient Pressure

The low-pressure stabilization of superconducting hydrides with high critical temperatures ($T_c$s) remains a significant challenge, and experimentally verified superconducting hydrides are generally constrained to a limited number of structural prototypes. Ternary transition-metal complex hydrides (hydrido complexes)-typically regarded as hydrogen storage materials-exhibit a large range of compounds stabilized at low pressure with recent predictions for high-$T_c$ superconductivity. Motivated by this class of materials, we investigated complex hydride formation in the Mg-Pt-H system, which has no known ternary hydride compounds. Guided by ab initio structural predictions, we successfully synthesized a novel complex transition-metal hydride, Mg$_4$Pt$_3$H$_6$, using laser-heated diamond anvil cells. The compound forms in a body-centered cubic structural prototype at moderate pressures between 8-25 GPa. Unlike the majority of known hydrido complexes, Mg$_4$Pt$_3$H$_6$ is metallic, with formal charge described as 4[Mg]$^{2+}$.3[PtH$_2$]$^{2-}$. X-ray diffraction (XRD) measurements obtained during decompression reveal that Mg$_4$Pt$_3$H$_6$ remains stable upon quenching to ambient conditions. Magnetic-field and temperature-dependent electrical transport measurements indicate ambient-pressure superconductivity with $T_c$ (50%) = 2.9 K, in reasonable agreement with theoretical calculations. These findings clarify the phase behavior in the Mg-Pt-H system and provide valuable insights for transition-metal complex hydrides as a new class of hydrogen-rich superconductors.

cond-mat.supr-con↗

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↗

arXiv2024

Quantum $K$-invariants via Quot schemes II

We derive a $K$-theoretic analogue of the Vafa--Intriligator formula, computing the (virtual) Euler characteristics of vector bundles over the Quot scheme that compactifies the space of degree $d$ morphisms from a fixed projective curve to the Grassmannian $\mathrm{Gr}(r,N)$. As an application, we deduce interesting vanishing results, used in our previous work to study the quantum $K$-ring of $\mathrm{Gr}(r,N)$. In the genus-zero case, we prove a simplified formula involving Schur functions, consistent with the Borel--Weil--Bott theorem in the degree-zero setting. These new formulas offer a novel approach for computing the structure constants of quantum $K$-products.

math.AG↗

arXiv2024

Bergman-Einstein metrics on two-dimensional Stein spaces

We show that the Bergman metric of the ball quotients $\mathbb{B}^2/Γ$, where $Γ$ is a finite and fixed point free group, is Kähler-Einstein if and only if $Γ$ is trivial. As a consequence, we characterize the unit ball $\mathbb{B}^2$, among 2 dimensional Stein spaces with isolated normal singularities, proving an algebraic version of Cheng's conjecture for 2 dimensional Stein spaces.

math.CV↗

arXiv2024

Quantum $K$-invariants via Quot schemes I

We study the virtual Euler characteristics of sheaves over Quot schemes of curves, establishing that these invariants fit into a topological quantum field theory (TQFT) valued in $\mathbb{Z}[[q]]$. We show that the three-pointed genus-zero $K$-theoretic stable map invariants of the Grassmannian coincide with the genus-zero $K$-theoretic invariants defined via the Quot scheme. Utilizing Quot scheme compactifications alongside the TQFT framework, we derive presentations of the small quantum $K$-ring of the Grassmannian. Our approach offers a new method for finding explicit formulas for quantum $K$-invariants.

math.AG↗

arXiv2024

Pressure induced metallization and loss of surface magnetism in FeSi

Single crystalline FeSi samples with a conducting surface state (CSS) were studied under high pressure ($\textit{P}$) and magnetic field ($\textit{B}$) by means of electrical resistance ($\textit{R}$) measurements to explore how the bulk semiconducting state and the surface state are tuned by the application of pressure. We found that the energy gap ($Δ$) associated with the semiconducting bulk phase begins to close abruptly at a critical pressure ($P_{cr}$) of ~10 GPa and the bulk material becomes metallic with no obvious sign of any emergent phases or non-Fermi liquid behavior in $\textit{R}$($\textit{T}$) in the neighborhood of $P_{cr}$ above 3 K. Moreover, the metallic phase appears to remain at near-ambient pressure upon release of the pressure. Interestingly, the hysteresis in the $\textit{R}$($\textit{T}$) curve associated with the magnetically ordered CSS decreases with pressure and vanishes at $P_{cr}$, while the slope of the $\textit{R}$($\textit{B}$) curve, d$\textit{R}$/d$\textit{B}$, which has a negative value for $\textit{P}$ < $P_{cr}$, decreases in magnitude with $\textit{P}$ and changes sign at $P_{cr}$. Thus, the CSS and the corresponding two-dimensional magnetic order collapse at $P_{cr}$ where the energy gap $Δ$ of the bulk material starts to close abruptly, revealing the connection between the CSS and the semiconducting bulk state in FeSi.

cond-mat.str-el↗

arXiv2024

Cores of partitions in rectangles

For a positive integer $t \geq 2$, the $t$-core of a partition plays an important role in modular representation theory and combinatorics. We initiate the study of $t$-cores of partitions contained in an $r \times s$ rectangle. Our main results are as follows. We first give a simple formula for the number of partitions in the rectangle that are themselves $t$-cores and compute its asymptotics for large $r,s$. We then prove that the number of partitions inside the rectangle whose $t$-cores are a fixed partition $ρ$ is given by a product of binomial coefficients. Finally, we use this formula to compute the distribution of the $t$-core of a uniformly random partition inside the rectangle extending our previous work on all partitions of a fixed integer $n$ (Ann. Appl. Prob. 2023). In particular, we show that in the limit as $r,s \to \infty$ maintaining a fixed aspect ratio, we again obtain a Gamma distribution with the same shape parameter $α= (t-1)/2$ and rate parameter $β$ that depends on the aspect ratio.

math.CO↗

arXiv2023

The size of $t$-cores and hook lengths of random cells in random partitions

Fix $t \geq 2$. We first give an asymptotic formula for certain sums of the number of $t$-cores. We then use this result to compute the distribution of the size of the $t$-core of a uniformly random partition of an integer $n$. We show that this converges weakly to a gamma distribution after dividing by $\sqrt{n}$. As a consequence, we find that the size of the $t$-core is of the order of $\sqrt{n}$ in expectation. We then apply this result to show that the probability that $t$ divides the hook length of a uniformly random cell in a uniformly random partition equals $1/t$ in the limit. Finally, we extend this result to all modulo classes of $t$ using abacus representations for cores and quotients.

math.PR↗

arXiv2022

Euler characteristics of tautological bundles over Quot schemes of curves

We compute the Euler characteristics of tautological vector bundles and their exterior powers over the Quot schemes of curves. We give closed-form expressions over punctual Quot schemes in all genera. For higher rank quotients of a trivial vector bundle, we obtain answers in genus zero. We also study the Euler characteristics of the symmetric powers of the tautological bundles, for rank zero quotients.

math.AG↗

arXiv2022

Driving chemical reactions with polariton condensates

When molecular transitions strongly couple to photon modes, they form hybrid light-matter modes called polaritons. Collective vibrational strong coupling is a promising avenue for control of chemistry, but this can be deterred by the large number of quasi-degenerate dark modes. The macroscopic occupation of a single polariton mode by excitations, as observed in Bose-Einstein condensation, offers promise for overcoming this issue. Here we theoretically investigate the effect of vibrational polariton condensation on the kinetics of electron transfer processes. Compared with excitation with infrared laser sources, the condensate changes the reaction yield significantly due to additional channels with reduced activation barriers resulting from the large accumulation of energy in the lower polariton, and the many modes available for energy redistribution during the reaction. Our results offer tantalizing opportunities to use condensates for driving chemical reactions, kinetically bypassing usual constraints of fast intramolecular vibrational redistribution in condensed phase.

physics.chem-ph↗

arXiv2021

The virtual intersection theory of isotropic Quot Schemes

Isotropic Quot schemes parameterize rank $r$ isotropic subsheaves of a vector bundle equipped with symplectic or symmetric quadratic form. We define a virtual fundamental class for isotropic Quot schemes over smooth projective curves. Using torus localization, we prescribe a way to calculate top intersection numbers of tautological classes, and obtain explicit formulas when $r=2$. These include and generalize the Vafa-Intriligator formula. In this setting, we compare the Quot scheme invariants with the invariants obtained via the stable map compactification.

math.AG↗

arXiv2020

Word Segmentation from Unconstrained Handwritten Bangla Document Images using Distance Transform

Segmentation of handwritten document images into text lines and words is one of the most significant and challenging tasks in the development of a complete Optical Character Recognition (OCR) system. This paper addresses the automatic segmentation of text words directly from unconstrained Bangla handwritten document images. The popular Distance transform (DT) algorithm is applied for locating the outer boundary of the word images. This technique is free from generating the over-segmented words. A simple post-processing procedure is applied to isolate the under-segmented word images, if any. The proposed technique is tested on 50 random images taken from CMATERdb1.1.1 database. Satisfactory result is achieved with a segmentation accuracy of 91.88% which confirms the robustness of the proposed methodology.

cs.CV↗