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Register a new userFloquet generation of Second Order Topological Superconductor
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We theoretically investigate the Floquet generation of second-order topological superconducting (SOTSC) phase, hosting Majorana corner modes (MCMs), considering a quantum spin Hall insulator (QSHI) with proximity induced superconducting $s$-wave pairing in it. Our dynamical prescription consists of the periodic kick in time-reversal symmetry breaking in-plane magnetic field and four-fold rotational symmetry breaking mass term while these Floquet MCMs are preserved by anti-unitary particle-hole symmetry. The first driving protocol always leads to four zero energy MCMs (i.e. one Majorana per corner) as a sign of a {it{strong}} SOTSC phase. Interestingly, the second protocol can result in a {it{weak}} SOTSC phase, harbouring eight zero energy MCMs (two Majorana states per corner), in addition to the {it{strong}} SOTSC phase. We characterize the topological nature of these phases by Floquet quadrupolar moment and Floquet Wannier spectrum. We believe that relying on the recent experimental advancement in the driven systems and proximity induced superconductivity, our schemes may be possible to test in the future.
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We theoretically investigate the Floquet generation of second-order topological superconducting (SOTSC) phase in the high-temperature platform both in two-dimension (2D) and three-dimension (3D). Starting from a $d$-wave superconducting pairing gap, we periodically kick the mass term to engineer the dynamical SOTSC phase within a specific range of the strength of the drive. Under such dynamical breaking of time-reversal symmetry (TRS), we show the emergence of the textit{weak} SOTSC phase, harboring eight corner modes ie two zero-energy Majorana per corner, with vanishing Floquet quadrupole moment. On the other hand, our study interestingly indicates that upon the introduction of an explicit TRS breaking Zeeman field, the textit{weak} SOTSC phase can be transformed into textit{strong} SOTSC phase, hosting one zero-energy Majorana mode per corner, with quantized quadrupole moment. We also compute the Floquet Wannier spectra that further establishes the textit{weak} and textit{strong} nature of these phases. We numerically verify our protocol computing the exact Floquet operator in open boundary condition and then analytically validate our findings with the low energy effective theory (in the high-frequency limit). The above protocol is applicable for 3D as well where we find one dimensional (1D) hinge mode in the SOTSC phase. We then show that these corner modes are robust against moderate disorder and the topological invariants continue to exhibit quantized nature until disorder becomes substantially strong. The existence of zero-energy Majorana modes in these higher-order phases is guaranteed by the anti-unitary spectral symmetry.
Two-dimensional second-order topological superconductors (SOTSCs) have gapped bulk and edge states, with zero-energy Majorana bound states localized at corners. Motivated by recent advances in Majorana nanowire experiments, we propose to realize a tunable SOTSC as a two-dimensional nanowire array. We show that the coupling between the Majorana modes of adjacent wires can be controlled by phase-biasing the device, allowing to access a variety of topological phases. We characterize the system using scattering theory, which provides access to its transport properties and its topological invariants. The setup is robust against disorder, both in the nanowires themselves and in the Josephson junctions formed between adjacent wires. Further, we identify a parameter regime in which an initially trivial system is rendered topological upon adding disorder, providing an example of a second-order topological Anderson phase.
We propose a versatile framework to dynamically generate Floquet higher-order topological insulators by multi-step driving of topologically trivial Hamiltonians. Two analytically solvable examples are used to illustrate this procedure to yield Floquet quadrupole and octupole insulators with zero- and/or $pi$-corner modes protected by mirror symmetries. Furthermore, we introduce dynamical topological invariants from the full unitary return map and show its phase bands contain Weyl singularities whose topological charges form dynamical multipole moments in the Brillouin zone. Combining them with the topological index of Floquet Hamiltonian gives a pair of $mathbb{Z}_2$ invariant $ u_0$ and $ u_pi$ which fully characterize the higher-order topology and predict the appearance of zero- and $pi$-corner modes. Our work establishes a systematic route to construct and characterize Floquet higher-order topological phases.
We demonstrate, both theoretically and experimentally, the concept of non-linear second-order topological insulators, a class of bulk insulators with quantized Wannier centers and a bulk polarization directly controlled by the level of non-linearity. We show that one-dimensional edge states and zero-dimensional corner states can be induced in a trivial crystal insulator made of evanescently coupled resonators with linear and nonlinear coupling coefficients, simply by tuning the excitation intensity. This allows global external control over topological phase transitions and switching to a phase with non-zero bulk polarization, without requiring any structural or geometrical changes. We further show how these non-linear effects enable dynamic tuning of the spectral properties and localization of the topological edge and corner states. Such self-induced second-order topological insulators, which can be found and implemented in a wide variety of physical platforms ranging from electronics to microwaves, acoustics, and optics, hold exciting promises for reconfigurable topological energy confinement, power harvesting, data storage, and spatial management of high-intensity fields.
We show that a two-dimensional semiconductor with Rashba spin-orbit coupling could be driven into the second-order topological superconducting phase when a mixed-pairing state is introduced. The superconducting order we consider involves only even-parity components and meanwhile breaks time-reversal symmetry. As a result, each corner of a square-shaped Rashba semiconductor would host one single Majorana zero mode in the second-order nontrivial phase. Starting from edge physics, we are able to determine the phase boundaries accurately. A simple criterion for the second-order phase is further established, which concerns the relative position between Fermi surfaces and nodal points of the superconducting order parameter. In the end, we propose two setups that may bring this mixed-pairing state into the Rashba semiconductor, followed by a brief discussion on the experimental feasibility of the two platforms.
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