We theoretically investigate a periodically driven semimetal based on square lattice. The possibility of engineering both Floquet Topological Insulator featuring edge states and higher order topological insulating phase, accommodating corner modes has been demonstrated starting from the Hamiltonian picture. phase transition takes place in bulk quasi-energy spectrum with variation drive amplitude where Chern number changes sign $+1$ to $-1$. This can be attributed broken time-reversal...

We theoretically investigate the Floquet generation of a second-order topological superconducting (SOTSC) phase hosting Majorana corner modes (MCMs), considering quantum spin Hall insulator with proximity-induced $s$-wave pairing in it. Our dynamical prescription consists periodic kick time-reversal symmetry breaking in-plane magnetic field and fourfold rotational mass term bulk while these MCMs are preserved by antiunitary particle-hole symmetry. The first driving protocol always leads to...

After exploring much on two-dimensional higher-order topological superconductors (HOTSCs) hosting Majorana corner modes (MCMs) only, we propose a simple fermionic model based three-dimensional insulator proximized with $s$-wave superconductor to realize hinge (MHMs) followed by MCMs under the application of appropriate Wilson-Dirac perturbations. We interestingly find that second-order superconductor, MHMs, appears above threshold value first type perturbation while third-order...

After extensive investigation on the Floquet second-order topological insulator (FSOTI) in two dimension (2D), here we propose driving schemes to systematically engineer hierarchy of first-order insulator, FSOTI, and third-order three (3D). Our protocols allow these phases showcase regular $0$, anomalous $\pi$, hybrid $0$-$\pi$-modes a unified phase diagram, obtained for both 2D 3D systems, while staring from lower order or non-topological phases. Both step drive mass kick exhibit analogous...

Being motivated by intriguing phenomena, such as the breakdown of conventional bulk boundary correspondence and emergence skin modes in context non-Hermitian (NH) topological insulators, we here propose a NH second-order superconductor (SOTSC) model that hosts Majorana zero (MZMs). Employing non-Bloch form Hamiltonian, topologically characterize above biorthogonal nested polarization resolve apparent correspondence. Unlike Hermitian SOTSC, note MZMs inhabit only one corner out four...

We theoretically investigate a practically realizable Floquet topological superconductor model based on one-dimensional Rashba nanowire and proximity-induced $s$-wave superconductivity in the presence of Zeeman field. The driven system hosts regular 0-Majorana end modes anomalous $\ensuremath{\pi}$-Majorana (MEMs). By tuning chemical potential frequency drive, we illustrate generation multiple MEMs our theoretical setup. utilize chiral symmetry operator to topologically characterize these...

We put forth a theoretical framework for engineering two-dimensional (2D) second-order topological superconductor (SOTSC) by utilizing heterostructure: incorporating noncollinear magnetic textures between an $s$-wave and 2D quantum spin Hall insulator. It stabilizes the higher order superconducting phase, resulting in Majorana corner modes (MCMs) at four corners of domain. The calculated nonzero quadrupole moment characterizes bulk topology. Subsequently, through unitary transformation,...

We report on a realistic and rather general scheme where noncollinear magnetic textures proximitized with the most common $s$-wave superconductor can appear as alternative to $p$-wave superconductor---the prime proposal realize two-dimensional (2D) Kitaev model for topological superconductors (TSCs) hosting Majorana flat edge mode (MFEM). A minimal Hamiltonian suitable magnet/superconductor heterostructures reveals robust MFEM within gap of Shiba bands due emergence an effective...

We theoretically investigate the Floquet generation of second-order topological superconducting (SOTSC) phase in high-temperature platform both two dimension (2D) and three (3D). Starting from a $d$-wave pairing gap, we periodically kick mass term to engineer dynamical SOTSC within specific range strength drive. Under such breaking time-reversal symmetry (TRS), show emergence weak phase, harboring eight corner modes, i.e., zero-energy Majorana per corner, with vanishing quadrupole moment. On...

We propose a three-step periodic drive protocol to engineer two-dimensional (2D) Floquet quadrupole superconductors and three-dimensional (3D) octupole hosting zero-dimensional Majorana corner modes (MCMs), based on unconventional $d$-wave superconductivity. Remarkably, the driven system conceives four phases with only zero MCMs, no anomalous $\ensuremath{\pi}$ both regular MCMs. To circumvent subtle issue of characterizing MCMs separately, we employ periodized evolution operator architect...

We consider a non-Hermitian (NH) analog of second-order topological insulator, protected by chiral symmetry, in the presence next-nearest-neighbor hopping elements to theoretically investigate interplay beyond first-nearest-neighbor amplitudes and order away from Hermiticity. In addition four zero-energy corner modes present model, we uncover that second-nearest-neighbor introduces another phase with 16 modes. Importantly, NH effects are manifested altering Hermitian boundaries for both...

In recent years, there has been a surge of interest in exploring higher-order topology and their semimetallic counterparts, particularly the context Dirac, Weyl, nodal line semimetals, termed Dirac semimetals (HODSM), Weyl (HONLSM). The HODSM phase exhibits hinge Fermi arcs (FAs) with quantized topological invariant. Conversely, HONLSM is hybrid-order manifesting both drumhead-like surface states FAs as signature first- second-order topology, also possesses invariants. this work, we...

We propose a practically feasible time-periodic sinusoidal drive protocol in onsite mass term to generate the two-dimensional~(2D) Floquet second-order topological superconductor, hosting both regular $0$- and anomalous $\pi$-Majorana corner modes~(MCMs) while starting from static 2D insulator/$d$-wave superconductor heterostructure setup. theoretically study local density spectra time dynamics of MCMs presence such drive. The dynamical are topologically characterized by employing average...

We theoretically explore the Floquet generation of Majorana end modes~(MEMs) (both regular $0$- and anomalous $\pi$-modes) implementing a periodic sinusoidal modulation in chemical potential an experimentally feasible setup based on one-dimensional chain magnetic impurity atoms having spin spiral configuration (out-of-plane N\'eel-type) fabricated surface most common bulk $s$-wave superconductor. obtain rich phase diagram parameter space, highlighting possibility generating multiple...

Condensed matter systems are continuously subjected to dissipation, which often has adverse effects on quantum phenomena. We focus the impact of dissipation a superconducting Rashba nanowire. reveal that system can still host Majorana zero-modes (MZMs) with finite lifetime in presence dissipation. Most interestingly, also generate two kinds dissipative boundary states: four robust (RZMs) and MZMs, regime where non-dissipative is topologically trivial. The MZMs appear via bulk gap closing...

In recent years, there has been a surge of interest in exploring higher-order topology and their semi-metallic counterparts, particularly the context Dirac Weyl semimetals, termed as semimetal (HODSM) (HOWSM). The HODSM phase exhibits hinge Fermi arcs (FAs) with quantized topological invariant. Conversely, HOWSM is hybrid-order manifesting both surface FAs signature first- second-order also possesses invariants. this work, we investigate tight binding model for multi-HODSM (mHODSM) hosting...

The presence of random disorder in a metallic system accounts for the localization extended states general. On contrary, can induce topological phases hosting boundary out non-topological system, giving birth to Anderson insulator phase. In this context, we theoretically investigate generation an equilibrium higher-order phase potential time-periodic dynamical background. particular, time-dependent drive and concomitantly render Floquet insulator~(FHOTAI) phase, while clean, undriven is...

Periodically driven systems offer a perfect breeding ground for out-of-equilibrium engineering of topological boundary states at zero energy ($0$-mode), as well finite ($\pi$-mode), with the latter having no static analog. The Floquet operator and effective Hamiltonian, which encapsulate stroboscopic features system, capture both spectral localization properties $0$- $\pi$-modes but sometimes fail to provide complete characterization, especially when coexist. In this work, we utilize...

Condensed matter systems are continuously subjected to dissipation, which often has adverse effects on quantum phenomena. We focus the impact of dissipation a superconducting Rashba nanowire. reveal that system can still host Majorana zero-modes (MZMs) with finite lifetime in presence dissipation. Most interestingly, also generate two kinds dissipative boundary states: four robust (RZMs) and MZMs, regime where non-dissipative is topologically trivial. The MZMs appear via bulk gap closing...

We consider non-Hermitian (NH) analog of a second-order topological insulator, protected by chiral symmetry, in the presence second-nearest neighbor hopping elements to theoretically investigate interplay between long-range and order away from Hermiticity. In addition four zero-energy corner modes present first nearest model, we uncover that second introduces another phase with sixteen modes. Importantly, NH effects are manifested altering Hermitian boundaries for both models. While...

Periodically driven systems offer a perfect breeding ground for out-of-equilibrium engineering of topological boundary states at zero energy (0 mode), as well finite (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>π</a:mi></a:math> with the latter having no static analog. The Floquet operator and effective Hamiltonian, which encapsulate stroboscopic features system, capture both spectral localization properties 0 <b:math...

We theoretically investigate a practically realizable Floquet topological superconductor model, based on one-dimensional Rashba nanowire and proximity induced $s$-wave superconductivity in the presence of Zeeman field. The driven system hosts regular $0$- anomalous $π$-Majorana end modes~(MEMs). By tuning chemical potential frequency drive, we illustrate generation multiple MEMs our theoretical set up. utilize chiral symmetry operator to topologically characterize these via dynamical winding...

We report on a realistic and rather general scheme where noncollinear magnetic textures proximitized with the most common $s$-wave superconductor can appear as alternative to $p$-wave superconductor{--}the prime proposal realize two-dimensional (2D) Kitaev model for topological superconductors (TSCs) hosting Majorana flat edge mode (MFEM). A minimal Hamiltonian suitable magnet/superconductor heterostructures reveals robust MFEM within gap of Shiba bands due emergence an effective...