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We have proposed an arbitrary vector beam (VB) generation scheme in a thin disk-shaped quantum dot (QD) medium considering phonon interaction. The QD biexciton system exhibits interplay between first and third-order nonlinear susceptibility between two orthogonal circular polarisation transitions. Three QD transitions are coupled with one applied weak and two strong control orbital angular momentum (OAM) carrying fields. Therefore, the applied field experiences absorption, and a new field with the desired OAM is generated via four-wave mixing (FWM). These two orthogonal field superpositions produce VB at the QD medium end. We have also demonstrated the polarization rotation of a VB by changing only the relative control field phase. Additionally, we have analyzed the effect of temperature on the VB generation., Comment: 10 pages, 5 figures

The LnSbTe (Ln = Lanthanides) family, like isostructural ZrSiS type compounds, has emerged as a fertile playground for exploring the interaction of electronic correlations and magnetic ordering with the nodal line band topology. Here, we report a detailed electronic band structure investigation of TbSbTe, corroborated by electrical transport, thermodynamic, and magnetic studies. Temperature-dependent magnetic susceptibility and thermodynamic transport studies indicate the onset of antiferromagnetic ordering below TN = 5.1 K. The electronic band structure study, carried out with high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements aided with density functional theory based first-principles calculations reveals presence of nodal lines in the GammaX high symmetry direction, forming a diamond-shaped nodal plane around Gamma high symmetry point. A strongly photon energy dependent nodal feature located at the X point of the surface Brillouin zone, indicating an extended nodal line along X R direction, is also observed. This study elucidates the intricate interplay among symmetry-protected band characteristics, the influence of spin orbit coupling, magnetism, and topological properties., Comment: 21 pages, 4 figures

In this paper, we present a probabilistic extension of the Fubini polynomials and numbers associated with a random variable satisfying some appropriate moment conditions. We obtain the exponential generating function and an integral representation for it. The higher order Fubini polynomials and recurrence relations are also derived. A probabilistic generalization of a series transformation formula and some interesting examples are discussed. A connection between the probabilistic Fubini polynomials and Bernoulli, Poisson, and geometric random variables are also established. Finally, a determinant expression formula is presented.

We propose two-mode two-photon microlaser using a single semiconductor quantum dot grown inside a two-mode microcavity. We explore both incoherent and coherent pumping at low temperatures to achieve suitable conditions for two-mode two-photon lasing. The two-mode two-photon stimulated emission is strongly suppressed but the single-photon stimulated emission is enhanced by exciton-phonon interactions. In coherently pumped quantum dot one can achieve large two-mode two-photon lasing where single-photon lasing is almost absent. We also discuss generation of steady state two-mode entangled state using two-photon resonant pumping., Comment: 12 pages, 13 figures

We report on the magnetic and electrical properties of a (Mn$_3$Sn)$_2$ triangular network kagome structured high quality Ho substituted ErMn$_6$Sn$_6$ single-crystal sample by magneto-transport measurements. Er$_{0.5}$Ho$_{0.5}$Mn$_6$Sn$_6$ orders antiferromagnetically at N\'{e}el temperature $T_\mathrm{N} \sim$ 350 K followed by a ferrimagnetic (FiM) transition at $T_\mathrm{C} \sim$ 114 K and spin-orientation transition at $T_\mathrm{t} \sim$ 20 K. The field-manifestations of these magnetic phases in the \textit{ab}-basal plane and along the \textit{c}-axis are illustrated through temperature-field \textit{T-H} phase diagrams. In \textit{H}$\parallel$\textit{c}, narrow hysteresis between spin reorientation and field-induced FiM phases below $T_\mathrm{t}$, enhanced/strengthened FiM phase below $T_\mathrm{C}$ and stemming of FiM phase out of strongly coexisting AFM and FiM phases below $T_\mathrm{N}$ through a non-meta-magnetic transition are confirmed to arise from strong R-Mn sublattices interaction. In contrast, \textit{H}$\parallel$\textit{ab}-plane, between $T_\mathrm{N}$ and $T_\mathrm{C}$, individually contributing R-Mn sublattices with weak antiferromagnetic interactions undergo a field-induced spin-flop quasi-metamagnetic transition to FiM state. The temperature dependent electrical resistivity suggests metallic nature with Fermi liquid behavior at low temperatures. Essentially, the current study stimulates interest to investigate the magnetic and electrical properties of mixed rare-earth layered kagome magnetic metals for possible novel and exotic behavior., Comment: 9 pages, 6 figures

We investigate the feasibility of minimum absorption and minimum broadening of pulse propagation in an inhomogeneously broadened semiconductor quantum dot medium. The phonon interaction is inevitable in studying any semiconductor quantum dot system. We have used the polaron transformation technique to deal with quantum dot phonon interaction in solving system dynamics. We demonstrate that a short pulse can propagate inside the medium with minimal absorption and broadening in pulse shape. The stable pulse area becomes slightly higher than the prediction of the pulse area theorem and is also dependent on the environment temperature. The change in the final pulse shape is explained very well by numerically solving the propagation equation supported by the susceptibility of the medium. Our system also exhibits the pulse breakup phenomena for higher input pulse areas. Therefore, the considered scheme can have important applications in quantum communication, quantum information, and mode-locking with the advantage of scalability and controllability., Comment: 11 pages, 11 figures

The sol-gel prepared (1-x) Na0.5Bi0.5TiO3- (x) CaMnO3 (x=0, 0.03, 0.06, 0.12) compositions show a Rhombohedral (R3c) phase for x=0.06 while a mixed Rhombohedral (R3c) and orthorhombic (Pnma) phases for the x=0.12. The lattice volume consistently decreased with an increase in the CaMnO3 content. The phase transition temperature (Tc) decreased with an increase in the CaMnO3 compositions. The room temperature dielectric constant increased, and loss decreased for the x=0.03 composition due to a decrease in the oxygen vacancy and Bi loss confirmed by the valence state study (XPS). All the compositions show a variation of the room temperature dielectric property with an application of magnetic field confirming a magnetodielectric coupling. The x=0.06 composition shows the highest negative magnetodielectric constant (MD%) of 3.69 at 100kHz at an applied field of 5 kG.

Kagome-lattice magnets $R$Mn$_6$Sn$_6$ recently emerged as a new platform to exploit the interplay between magnetism and topological electronic states. Some of the most exciting features of this family are the dramatic dependence of the easy magnetization direction on the rare-earth specie and the kagome geometry of the Mn planes that in principle can generate flat bands and Dirac points; gapping of the Dirac points by spin-orbit coupling has been suggested recently to be responsible for the observed anomalous Hall response in the member TbMn$_6$Sn$_6$. In this paper, we address both issues with ab initio calculations. We have discovered the significant role played by higher-order crystal-field parameters and rare-earth magnetic anisotropy constants in these systems. We demonstrate that the microscopic origin of rare-earth anisotropy can also be quantified and understood at various levels: ab initio, phenomenological, and analytical. In particular, using a simple and physically transparent analytical model, we explain, with full quantitative agreement, the evolution of anisotropy across the series. We analyze the topological properties of Mn-dominated bands and demonstrate how they emerge from the multiorbital planar kagome model. We further show that the most pronounced quasi-2D dispersion are too far removed from the Fermi level, and therefore cannot explain the observed quasi-2D anomalous Hall effect. By employing ab initio many-body approaches, we demonstrate that the exchange-correlation effects for itinerant Mn-$d$ electrons do not significantly alter the obtained electronic and magnetic structure. Therefore, we conclude that, contrary to previous claims, the most pronounced 2D kagome-derived topological band features bear little relevance to transport in $R$Mn$_6$Sn$_6$, albeit they may possibly be brought to focus by electron or hole doping., Comment: 14+11 pages, 10+7 figures

The enhancement of interfacial Dzyaloshinskii-Moriya Interaction (DMI) in magnetic multilayers results in the stabilization of topological spin textures like chiral domain walls and skyrmions. Here we report on the evaluation of interface-driven magnetic interactions in a uniquely designed multilayer where each magnetic layer of two AFM coupled sublattices of 3d and 4f moments is sandwiched between the layers of \beta-tungsten and holmium whose spin Hall angles are large but opposite in sign. The atomic and magnetic periodicity of these multilayers is established by polarized neutron reflectivity measurements and the presence of a labyrinth domain spin texture of zero remanence with x-ray photoelectron microscopy. Measurements of the Hall resistivity (\rho_{xy}(T, H)) together with static magnetization (M(T,H)) over a broad range of temperature (T) and magnetic field (H) indicate impending compensation between 3d and 4f sublattices at T>350 K. These multilayers are characterized by a small (0.04 %) but positive magnetoresistance indicative of interface enhance scattering and a large (40 n\Omega.m) and negative anomalous \rho_{xy}(T,H) which results from a parallel alignment of 4f moments with the external magnetic field. No distinct scaling is seen between \rho_{xy}(T,H), \rho_{xx}(T, H) and M(T,H) at temperatures above 200K where the magnetization develops out-of-plane anisotropy. The field scans of \rho_{xy} at T>200K show a distinct cusp in the vicinity of magnetic saturation. These Hall data have been analyzed in the framework of a model where a distinct topological contribution to \rho_{xy} rides over the anomalous Hall resistivities of the 3d and 4f magnetic sublattices. It is suggested that this apparent topological effect results from an interfacial DMI and dominates \rho_{xy}(T,H) in the temperature regime where the 3d and 4f lattices are nearly compensated., Comment: 7 figures

With intricate lattice structures, kagome materials are an excellent platform to study various fascinating topological quantum states. In particular, kagome materials, revealing large responses to external stimuli such as pressure or magnetic field, are subject to special investigation. Here, we study the kagome-net HoMn$_6$Sn$_6$ magnet that undergoes paramagnetic to ferrimagnetic transition (below 376 K) and reveals spin-reorientation transition below 200 K. In this compound, we observe the topological Hall effect and substantial contribution of anomalous Hall effect above 100 K. We unveil the pressure effects on magnetic ordering at a low magnetic field from the pressure tunable magnetization measurement. By utilizing high-resolution angle-resolved photoemission spectroscopy, Dirac-like dispersion at the high-symmetry point K is revealed in the vicinity of the Fermi level, which is well supported by the first-principles calculations, suggesting a possible Chern-gapped Dirac cone in this compound. Our investigation will pave the way to understand the magneto-transport and electronic properties of various rare-earth-based kagome magnets.

Recently, kagome materials have become an engrossing platform to study the interplay among symmetry, magnetism, topology, and electron correlation. The latest works on RMn6Sn6 (R = rare earth metal) compounds have illustrated that this family could be intriguing to investigate various physical phenomena due to large spin-orbit coupling and strong magnetic ordering. However, combined transport and spectroscopic studies in RMn6Sn6 materials are still limited. Here, we report magnetic, magneto-transport, and angle-resolved photoemission spectroscopy measurements of a kagome magnet ErMn6Sn6 that undergoes antiferromagnetic (TN = 345 K) to ferrimagnetic (TC = 68 K) phase transitions in the presence of field. We observe large anomalous and topological Hall effects serving as transport signatures of the nontrivial Berry curvature. The isothermal magnetization exhibits strong anisotropic nature and the topological Hall effect of the compound depends on the critical field of metamagnetic transition. Our spectroscopic results complemented by theoretical calculations show the multi-orbital kagome fermiology. This work provides new insight into the tunability and interplay of topology and magnetism in a kagome magnet., Comment: 18 pages, 18 figures; Supplementary Information included, To be published in PRB

The linear exponential distribution is a generalization of the exponential and Rayleigh distributions. This distribution is one of the best models to fit data with increasing failure rate (IFR). But it does not provide a reasonable fit for modeling data with decreasing failure rate (DFR) and bathtub shaped failure rate (BTFR). To overcome this drawback, we propose a new record-based transmuted generalized linear exponential (RTGLE) distribution by using the technique of Balakrishnan and He (2021). The family of RTGLE distributions is more flexible to fit the data sets with IFR, DFR, and BTFR, and also generalizes several well-known models as well as some new record-based transmuted models. This paper aims to study the statistical properties of RTGLE distribution, like, the shape of the probability density function and hazard function, quantile function and its applications, moments and its generating function, order and record statistics, Renyi entropy. The maximum likelihood estimators, least squares and weighted least squares estimators, Anderson-Darling estimators, Cramer-von Mises estimators of the unknown parameters are constructed and their biases and mean squared errors are reported via Monte Carlo simulation study. Finally, the real data set based on failure time illustrates the goodness of fit and applicability of the proposed distribution; hence, suitable recommendations are forwarded., Comment: 29 pages, 5 figures, 9 tables

The standard classic special relativistic transformation of the electromagnetic (EM) field under proper Lorentz transformations is revisited. As to the pure Lorentz-boosts, popular treatments on EM transformation contemplate ideal geometries generating special static charge and steady current distributions and in conjunction, invoke parallel and perpendicular (to the boost-velocity) components of the fields so engendered; the outcomes subsequently being suitably generalized. We demonstrate ab initio, the EM field transformation under arbitrary oblique uniform relative boost velocities from a broader, rigorous yet remarkably lucid perspective, exploiting the antisymmetry of the EM-field tensor and symmetry of the general Lorentz-boost transformation preemptively eliminating the labor of performing complicated matrix multiplications. Gratifyingly, this instructive exercise manifestly encompasses time varying fields and yields the transformation relations in a coordinate-free form. Further, the EM field transformation under proper, instantaneous 3D rotations is demonstrated to transform as a passive rotation of the coordinate axes, where the electric and magnetic fields transform independently as purely electric and magnetic fields, respectively. The present didactical exercise, amenable to be incorporated in graduate courses on relativistic electrodynamics, should serve as an excellent illustration on how powerful symmetry arguments simplify the otherwise tedious calculations while endowing complete generality to the connections obtained.