arXiv subjects

S. Kushwaha

Publications and source records attributed to S. Kushwaha.

4 recordsLinked to original sources

arXiv2021

Best Approximations by $\mathcal{F}_{p^l}$-Continued Fractions

In this article, for a certain subset $\mathcal{X}$ of the extended set of rational numbers, we introduce the notion of {\it best $\mathcal{X}$-approximations} of a real number. The notion of best $\mathcal{X}$-approximation is analogous to that of best rational approximation. We explore these approximations with the help of $\mathcal{F}_{p^l}$-continued fractions, where $p$ is a prime and $l\in\mathbb{N}$, we show that the convergents of the $\mathcal{F}_{p^l}$-continued fraction expansion of a real number $x$ satisfying certain maximal conditions are exactly the best $\mathcal{F}_{p^l}$-approximations of $x$.

math.NT↗

arXiv2021

Farey-subgraphs and Continued Fractions

In this note, we study a family of subgraphs of the Farey graph, denoted as $\mathcal{F}_N$ for every $N\in\mathbb{N}.$ We show that $\mathcal{F}_N$ is connected if and only if $N$ is either equal to one or a prime power. We introduce a class of continued fractions referred to as $\mathcal{F}_N$-continued fractions for each $N>1.$ We establish a relation between $\mathcal{F}_N$-continued fractions and certain paths from infinity in the graph $\mathcal{F}_N.$ We discuss existence and uniqueness of $\mathcal{F}_N$-continued fraction expansions of real numbers.

math.NT↗

arXiv2016

Time-Reversal-Breaking Weyl Fermions in Magnetic Heusler Alloys

Weyl fermions have recently been observed in several time-reversal-invariant semimetals and photonics materials with broken inversion symmetry. These systems are expected to have exotic transport properties such as the chiral anomaly. However, most discovered Weyl materials possess a substantial number of Weyl nodes close to the Fermi level that give rise to complicated transport properties. Here we predict, for the first time, a new family of Weyl systems defined by broken time-reversal symmetry, namely, Co-based magnetic Heusler materials XCo2Z (X = IVB or VB; Z = IVA or IIIA). To search for Weyl fermions in the centrosymmetric magnetic systems, we recall an easy and practical inversion invariant, which has been calculated to be -1, guaranteeing the existence of an odd number of pairs of Weyl fermions. These materials exhibit, when alloyed, only two Weyl nodes at the Fermi level - the minimum number possible in a condensed matter system. The Weyl nodes are protected by the rotational symmetry along the magnetic axis and separated by a large distance (of order 2$π$) in the Brillouin zone. The corresponding Fermi arcs have been calculated as well. This discovery provides a realistic and promising platform for manipulating and studying the magnetic Weyl physics in experiments.

cond-mat.mtrl-sci↗

arXiv2016

MoTe2: A Type-II Weyl Topological Metal

Based on the ab initio calculations, we show that MoTe2, in its low-temperature orthorhombic structure characterized by an X-ray diffraction study at 100 K, realizes 4 type-II Weyl points between the N-th and N+1-th bands, where N is the total number of valence electrons per unit cell. Other WPs and nodal lines between different other bands also appear close to the Fermi level due to a complex topological band structure. We predict a series of strain-driven topological phase transitions in this compound, opening a wide range of possible experimental realizations of different topological semimetal phases. Crucially, with no strain, the number of observable surface Fermi arcs in this material is 2 - the smallest number of arcs consistent with time-reversal symmetry.

cond-mat.mtrl-sci↗