arXiv subjects

Sarath Sasi

Publications and source records attributed to Sarath Sasi.

7 recordsLinked to original sources

arXiv2026

Magnetically tunable symmetry-enforced nodal lines producing huge anomalous Hall conductivity in altermagnetic $α$-MnTe

Altermagnetic $α$-MnTe exhibits huge anomalous Hall conductivity (AHC) up to room-temperature together with weak ferromagnetism arising from spin and orbital polarizations. We clarify the origin of the large value of the AHC by identifying two sets of distinct symmetry-enforced nodal lines in the valence bands with Mn character, located at $k_z=0$ and $k_z=\fracπ{c}$, protected by mirror symmetry $M_z$ and glide symmetry $G_z = \{M_z\,|\,0,0,\tfrac{c}{2}\}$, respectively. Both nodal lines are energy-dependent with an approximate C$_6$ symmetry, which is reduced to an exact C$_2$ symmetry due to the presence of the Néel vector. The highest valence band exhibits a Mexican-hat dispersion, whereas the second-highest valence band exhibits an inverted Mexican-hat dispersion, with nodal lines at the crossing between the two bands. Within first-principles accuracy, we demonstrate that these nodal lines give rise to the large AHC observed experimentally and exhibit a strong interplay with the weak ferromagnetism. We further show that even a small spin canting strongly modifies the nodal lines and the AHC, making them both magnetically tunable. By disentangling the altermagnetic and ferromagnetic contributions to the AHC, the altermagnetic contribution dominates at small canting angles, while the ferromagnetic contribution becomes sizeable for larger values. Using linear dichroism in angle-resolved photoemission spectroscopy, we show a signature of the nodal line at the border of the Brillouin zone.

cond-mat.mtrl-sci↗

arXiv2026

Electron-phonon-dominated charge-density-wave fluctuations in TiSe$_2$ accessed by ultrafast nonequilibrium dynamics

The complex phase diagram of 1T-TiSe2 consists of a charge density wave (CDW) below 200 K, and CDW fluctuations of still unknown origin at higher temperatures. Here, we use time-resolved extreme ultraviolet momentum microscopy and density functional perturbation theory to uncover the formation mechanism of CDW fluctuations and their spectral features at 295 K. We investigated the transient dynamics of fluctuations upon nonresonant ultrafast photoexcitation, and directly correlate it with the CDW soft-phonon hardening. Surprisingly, our results show that the coherent amplitude mode modulating ultrafast CDW recovery persists above TCDW, and reveal that CDW fluctuations are dominated by the electron-phonon interaction rather than excitonic correlations as commonly believed. Our findings on these microscopic CDW fluctuations clarify the complex interplay between electronic and lattice degrees of freedom at elevated temperatures and, therefore, could be useful in understanding the nature of the CDW phase transition in 1T-TiSe2 and similar quantum materials.

cond-mat.str-el↗

arXiv2025

Principal eigenvalues and asymptotic behavior for the weighted $p$-Laplacian with Robin boundary conditions on exterior domains

The spectral theory of the p-Laplacian is well developed for classical Dirichlet and Neumann boundary conditions, but the transitional Robin regime on exterior domains remains largely unexplored. This paper studies a weighted p-Laplacian eigenvalue problem with Robin boundary conditions on the exterior of the unit ball in Euclidean space of dimension N, with N greater than p. The weight function belongs to a critical Lorentz class and decays at infinity. Under natural assumptions on the weight, we prove the existence, uniqueness, simplicity, and isolation of a positive principal eigenvalue and establish local first-order regularity of the associated eigenfunction. We analyze the dependence of the principal eigenvalue on the Robin parameter and recover the Neumann and Dirichlet limits as the parameter approaches zero and infinity, respectively. The far-field behavior of the eigenfunction exhibits a universal algebraic decay rate that is independent of the Robin parameter, while the near-boundary structure displays an explicit scaling with respect to the parameter. We further investigate the gradient behavior of the eigenfunction, showing the existence of a unique critical radius and providing quantitative bounds on both the critical radius and the boundary value in terms of the Robin parameter. The main contribution of this work is the derivation of unified gradient estimates that connect the near-boundary and far-field regions through a characteristic length scale determined by the Robin parameter, yielding a global description of how boundary effects penetrate into the exterior domain.

math.AP↗

arXiv2024

On a shape derivative formula for the Robin $p$-Laplace eigenvalue

We obtain shape derivative formulae for the first eigenvalue of the Robin $p$-Laplace operator. This result is used to study the variation of the first eigenvalue with respect to perturbations of the domain. In particular, we prove that for large values of the boundary parameter, the first eigenvalue is monotonic with respect to domain inclusion for smooth domains.

math.AP↗

arXiv2024

Optimal harvesting for a logistic model with grazing

We consider semi-linear elliptic equations of the following form: \begin{equation*} \left\{ \begin{aligned} -Δu &= λ[u-\dfrac{u^2}{K}-c \dfrac{u^2}{1+u^2}-h(x) u]=:λf_h(u), \quad && x \in Ω, \frac{\partial u}{\partial η}&+qu = 0, \quad && x\in\partialΩ, \end{aligned} \right. \end{equation*} where, $h\in U=\{h\in L^2(Ω): 0\leq h(x)\leq H\}.$ We prove the existence and uniqueness of the positive solution for large $λ.$ Further, we establish the existence of an optimal control $h\in U$ that maximizes the functional $J(h)=\int_Ωh(x)u_h(x)~\rm{d}x-\int_Ω(B_1+B_2 h(x))h(x)~\rm{d}x$ over $U$, where $u_h$ is the unique positive solution of the above problem associated with $h$, $B_1>0$ is the cost per unit effort when the level of effort is low and $B_2>0$ represents the rate at which the cost rises as more labor is employed. Finally, we provide a unique optimality system.

math.AP↗

arXiv2016

On the strict monotonicity of the first eigenvalue of the $p$-Laplacian on annuli

Let $B_1$ be a ball in $\mathbb{R}^N$ centred at the origin and $B_0$ be a smaller ball compactly contained in $B_1$. For $p\in(1, \infty)$, using the shape derivative method, we show that the first eigenvalue of the $p$-Laplacian in annulus $B_1\setminus \overline{B_0}$ strictly decreases as the inner ball moves towards the boundary of the outer ball. The analogous results for the limit cases as $p \to 1$ and $p \to \infty$ are also discussed. Using our main result, further we prove the nonradiality of the eigenfunctions associated with the points on the first nontrivial curve of the Fučik spectrum of the $p$-Laplacian on bounded radial domains.

math.AP↗

arXiv2015

On the structure of the second eigenfunctions of the p-Laplacian on a ball

In this paper, we prove that the second eigenfunctions of the $p$-Laplacian, $p>1$, are not radial on the unit ball in $\mathbb{R}^N,$ for any $N\ge 2.$ Our proof relies on the variational characterization of the second eigenvalue and a variant of the deformation lemma. We also construct an infinite sequence of eigenpairs $\{τ_n,Ψ_n\}$ such that $Ψ_n$ is nonradial and has exactly $2n$ nodal domains. A few related open problems are also stated.

math.AP↗