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In this thesis, our main focus is on the $HHH$ and $VVHH$ couplings which are loosely bound. The $HHH$ coupling will determine the shape the Higgs potential and $VVHH$ couplings will tell us how the gauge bosons are coupled to the Higgs fields. We consider a few processes of Higgs boson production and decay to study these couplings. We calculate one-loop QCD and electroweak correction for these processes. In this thesis, we discuss spinor helicity formalism, which has been used in computing Feynman amplitudes for QCD and electroweak correction to these processes. We discuss one-loop Feynman integrals and one-loop electroweak renormalization and Catani-Seymour dipole subtraction scheme in this thesis. We compute all possible self-energy contributions at one-loop for electroweak renormalization. In this thesis, in the first work, we consider the process $b\bar{b}\rightarrow W^+W^-H$. Due to the non-negligible coupling of the Higgs boson with the bottom quarks, there is a dependence on the $WWHH$ coupling in this process. We find that the corrections to the final state with the longitudinally polarized $W$ bosons are large. In the second work, we study one-loop electroweak correction to $H\rightarrow \nu_e\bar{\nu_e}\nu_\mu\bar{\nu_\mu}$. We discuss $\gamma^5$-anomaly, complex mass scheme and input parameter schemes which are relevant for one-loop electroweak correction. The corrections depend on the $HHH$ and $ZZHH$ couplings. We investigate this dependence in $\kappa$-framework. In the third work, we study one-loop electroweak correction to the $H\rightarrow e^+e^-\mu^+\mu^-$ process. The corrections depend on $HHH$ and $ZZHH$ couplings. We observe the same behavior in the relative change of the decay width for this process as the process $H\rightarrow \nu_e\bar{\nu_e}\nu_\mu\bar{\nu_\mu}$ when we vary $HHH$ and $ZZHH$ couplings., Comment: PhD thesis

Despite the discovery of the Higgs boson, the Higgs sector of the standard model is still not fully established. In particular, the self couplings of the Higgs boson, and its couplings with gauge bosons, are still to be fully determined. We consider electroweak corrections to the process $H\rightarrow \nu_e\bar{\nu}_e\nu_\mu\bar{\nu}_\mu$. The corrections depend on the $HHH$ and $ZZHH$ couplings. We investigate this dependence in $\kappa$-framework. We find that the width depends on $HHH$ coupling significantly. The dependence on $ZZHH$ coupling is only marginal. We also discuss the dependence on $ZZWW$ coupling.

Topological insulators (TIs) with symmetry-protected surface states, offer exciting opportunities for next-generation photonic and optoelectronic device applications. The heterojunctions of TIs and semiconductors (e.g. Si, Ge) have been observed to excellent photo-responsive characteristics. However, the realization of high-frequency operations in these heterojunctions can be hindered by unwanted 1/f (or Flicker) noise and phase noise. Therefore, an in-depth understanding of 1/f noise figures becomes paramount for the effective utilization of such materials.Here we report optoelectronic response and 1/f noise characteristics of a p-n diode fabricated using topological insulator, Bi2Se3 and silicon for potential photo-detector. Through meticulous temperature-dependent current-voltage (I-V) and capacitance-voltage (C-V) measurements, we ascertain crucial parameters like barrier height, ideality factor, and reverse saturation current of the photodetector. The low-frequency 1/f conductance noise spectra suggest a significant presence of trap states influencing the optoelectronic transport properties. The forward noise characteristics exhibit typical 1/f features, having a uni-slope across four decades of frequency, suggesting a homogeneous distribution of barrier height. The spectral and photocurrent-dependent responses show the power law behavior of noise level on photon flux. The hybrid heterojunction demonstrates excellent photo-response and reasonably low noise level, promising signatures for the room-temperature visible photodetector applications., Comment: 9 pages, 6 figures, research article

High-spin states in the transitional $^{217}$Ac nucleus are established up to 3.8 MeV excitation energy and $I^{\pi} =$ 41/2$^+$ with the addition of around 20 new transitions. The structure of the yrast and near-yrast states below the 29/2$^+$ isomer is revisited. The inconsistencies in the level schemes reported earlier are resolved. The level structure above the 29/2$^+$ isomer is established for the first time. Large-basis shell-model calculations with the KHPE interaction are performed to compare the experimentally observed level energies with the theoretical predictions. A comparison with the systematics of the N = 128 isotones suggests that the yrast structures result from a weak coupling of the odd proton to the even-even 216Ra core, which is consistent with the shell-model configurations. Furthermore, alpha decay of the 29/2$^+$ isomer is revisited and the decay scheme established from this work is discussed in the framework of the shell model., Comment: 11 pages, 9 figures

Optically confined colloidal particles, when placed in close proximity, form a dissipatively coupled system through hydrodynamic interactions. Here, we demonstrate that these interactions can be harnessed to design systems with non-trivial and highly tunable non-equilibrium characteristics, directly quantifiable from experimental data. Furthermore, we clarify that such interactions do not modify the underlying potential energy function, nor do they violate the energy balance at the level of individual trajectories, as was believed earlier. Moreover, they offer new opportunities for tailored control and design of mesoscale systems with emergent and targeted nonequilibrium properties., Comment: 13 pages, 6 figures (supplementary informations included)

A graph $G = (V, E)$ is word-representable, if there exists a word w over the alphabet V such that for letters ${x, y} \in V$ , $x$ and $y$ alternate in $w$ if and only if $xy \in E$. In this paper, we prove that any non-empty word-representable graph can be represented by a word containing no non-trivial squares. This result provides a positive answer to the open problem present in the book Words and graphs written by Sergey Kitaev, and Vadim Lozin. Also, we prove that for a word-representable graph $G$, if the representation number of $G$ is $k$, then every $k$-uniform word representing the graph $G$ is also square-free. Moreover, we prove that every minimal-length word representing a graph is square-free. Then, we count the number of possible square-free word-representations of a complete graph. At last, using the infinite square-free string generated from the Thue-Morse sequence, we prove that infinitely many square-free words represent a non-complete connected word-representable graph., Comment: 12 pages

Active fluctuations are known to play a significant role in the intracellular transport of passive objects. However, the effect of viscoelasticity of the environment in shaping such processes is relatively less understood. Here, with a minimal experiment using a driven colloid in a viscoelastic bath, we show that viscoelasticity significantly increases the mean injected power to the passive object ($\sim 50\%$ compared to a viscous medium), for the same strength of the external driving. Additionally, we observe a notable reduction in negative work fluctuations across a wide range of driving amplitudes. These findings collectively suggest an enhanced directionality in driven processes within a viscoelastic bath, which we attribute to the emergence of interactions between the colloid and the viscoelastic medium., Comment: 30 pages, 9 figures (Accepted for publication in New Journal of Physics)

We report a strong nonlinear optical response of 2D MoSe$_2$ nanoflakes (NFs) through spatial self-phase modulation (SSPM) and cross-phase modulation (XPM) induced by nonlocal coherent light-matter interactions. The coherent interaction of light and MoSe$_2$ NFs creates the SSPM of laser beams, forming concentric diffraction rings. The nonlinear refractive index ($n_2$) and the third-order broadband nonlinear optical susceptibility ($\chi^{(3)}$) of MoSe$_2$ NFs are determined from the self diffraction pattern at different exciting wavelengths of 405, 532, and 671 nm with varying the laser intensity. The evolution and deformation of diffraction ring patterns are observed and analyzed by the `wind-chime' model and thermal effect. By taking advantage of the reverse saturated absorption of 2D SnS$_2$ NFs compared to MoSe$_2$, an all-optical diode has been designed with MoSe$_2$/SnS$_2$ hybrid structure to demonstrate the nonreciprocal light propagation. Also a few other optical devices based on MoSe$_2$ and other semiconducting materials such as Bi$_2$Se$_3$, CuPc, and graphene have been investigated. The all-optical logic gates and all-optical information conversion have been demonstrated through the XPM technique using two laser beams. The proposed optical scheme based on MoSe$_2$ NFs has been demonstrated as a potential candidate for all-optical nonlinear photonic devices such as all-optical diodes and all-optical switches., Comment: 20 pages, 6 figures, accepted in advanced optical materials

We have investigated the nature of ferromagnetic order and phase transitions in two dimensional (2D) van der Waals (vdW) layered material, Fe$_4$GeTe$_2$ through measurements of magnetization, magneto-caloric Effect (MCE), and heat capacity. Fe$_4$GeTe$_2$ hosts a complex magnetic phase with two distinct transitions: paramagnetic to ferromagnetic at around $T_\text{C}$ $\sim$ 266 K and another spin reorientation transition (SRT) at around $T_\text{SRT}$ $\sim $ 100 K. The magnetization measurements shows a prominent thermal hysteresis in proximity to $T_\text{SRT}$ at $H\parallel c$, which implies the first-order nature of SRT. Reasonable MCE has been observed around both transition temperatures ( at around $T_\text{C}$, -$\Delta$S$_M^\text{max}$ = 1.95 and 1.99 J.Kg$^{-1}$K$^{-1}$ and at around $T_\text{SRT}$, -$\Delta$S$_M^\text{max}$= 3.9 and 2.4 J.Kg$^{-1}$K$^{-1}$ along $H\parallel ab$ and $H\parallel c$ respectively) at 50 kOe magnetic field change. The above results reveal higher MCE value at $T_\text{SRT}$ compared to the values of MCE at $T_\text{C}$. The scaling analysis of MCE at $T_\text{C}$, shows that the rescaled $\Delta$S$_M (T, H)$ follow a universal curve confirming the second-order character of the ferromagnetic transition. The same scaling analysis of MCE breaks down at $T_\text{SRT}$ suggesting that SRT is not a second order phase transition. The exponent $n$ from field dependence of magnetic entropy change presents a maximum of $|n|>2$ confirming the first-order nature of SRT., Comment: 12 pages, 10 figures + appendix