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Register a new userFractional Topological Superconductivity and Parafermion Corner States
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Added by
Katharina Laubscher
Publication date
2019
fields
Physics
and research's language is
English
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We consider a system of weakly coupled Rashba nanowires in the strong spin-orbit interaction (SOI) regime. The nanowires are arranged into two tunnel-coupled layers proximitized by a top and bottom superconductor such that the superconducting phase difference between them is $pi$. We show that in such a system strong electron-electron interactions can stabilize a helical topological superconducting phase hosting Kramers partners of $mathbb{Z}_{2m}$ parafermion edge modes, where $m$ is an odd integer determined by the position of the chemical potential. Furthermore, upon turning on a weak in-plane magnetic field, the system is driven into a second-order topological superconducting phase hosting zero-energy $mathbb{Z}_{2m}$ parafermion bound states localized at two opposite corners of a rectangular sample. As a special case, zero-energy Majorana corner states emerge in the non-interacting limit $m=1$, where the chemical potential is tuned to the SOI energy of the single nanowires.
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We consider a setup consisting of two coupled sheets of bilayer graphene in the regime of strong spin-orbit interaction, where electrostatic confinement is used to create an array of effective quantum wires. We show that for suitable interwire couplings the system supports a topological insulator phase exhibiting Kramers partners of gapless helical edge states, while the additional presence of a small in-plane magnetic field and weak proximity-induced superconductivity leads to the emergence of zero-energy Majorana corner states at all four corners of a rectangular sample, indicating the transition to a second-order topological superconducting phase. The presence of strong electron-electron interactions is shown to promote the above phases to their exotic fractional counterparts. In particular, we find that the system supports a fractional topological insulator phase exhibiting fractionally charged gapless edge states and a fractional second-order topological superconducting phase exhibiting zero-energy $mathbb{Z}_{2m}$ parafermion corner states, where $m$ is an odd integer determined by the position of the chemical potential.
Recently, a new type of second-order topological insulator has been theoretically proposed by introducing an in-plane Zeeman field into the Kane-Mele model in the two-dimensional honeycomb lattice. A pair of topological corner states arise at the corners with obtuse angles of an isolated diamond-shaped flake. To probe the corner states, we study their transport properties by attaching two leads to the system. Dressed by incoming electrons, the dynamic corner state is very different from its static counterpart. Resonant tunneling through the dressed corner state can occur by tuning the in-plane Zeeman field. At the resonance, the pair of spatially well separated and highly localized corner states can form a dimer state, whose wavefunction extends almost the entire bulk of the diamond-shaped flake. By varying the Zeeman field strength, multiple resonant tunneling events are mediated by the same dimer state. This re-entrance effect can be understood by a simple model. These findings extend our understanding of dynamic aspects of the second-order topological corner states.
The concept of topological phases has been generalized to higher-order topological insulators and superconductors with novel boundary states on corners or hinges. Meanwhile, recent experimental advances in controlling dissipation (such as gain and loss) open new possibilities in studying non-Hermitian topological phases. Here, we show that higher-order topological corner states can emerge by simply introducing staggered on-site gain/loss to a Hermitian system in trivial phases. For such a non-Hermitian system, we establish a general bulk-corner correspondence by developing a biorthogonal nested-Wilson-loop and edge-polarization theory, which can be applied to a wide class of non-Hermitian systems with higher-order topological orders. The theory gives rise to topological invariants characterizing the non-Hermitian topological multipole moments (i.e., corner states) that are protected by reflection or chiral symmetry. Such gain/loss induced higher-order topological corner states can be experimentally realized using photons in coupled cavities or cold atoms in optical lattices.
We report the theoretical discovery and characterization of higher-order Floquet topological phases dynamically generated in a periodically driven system with mirror symmetries. We demonstrate numerically and analytically that these phases support lower-dimensional Floquet bound states, such as corner Floquet bound states at the intersection of edges of a two-dimensional system, protected by the nonequilibrium higher-order topology induced by the periodic drive. We characterize higher-order Floquet topologies of the bulk Floquet Hamiltonian using mirror-graded Floquet topological invariants. This allows for the characterization of a new class of higher-order anomalous Floquet topological phase, where the corners of the open system host Floquet bound states with the same as well as with double the period of the drive. Moreover, we show that bulk vortex structures can be dynamically generated by a drive that is spatially inhomogeneous. We show these bulk vortices can host multiple Floquet bound states. This stirring drive protocol leverages a connection between higher-order topologies and previously studied fractionally charged, bulk topological defects. Our work establishes Floquet engineering of higher-order topological phases and bulk defects beyond equilibrium classification and offers a versatile tool for dynamical generation and control of topologically protected Floquet corner and bulk bound states.
Topologically protected gapless edge states are phases of quantum matter which behave as massless Dirac fermions, immunizing against disorders and continuous perturbations. Recently, a new class of topological insulators (TIs) with topological corner states have been theoretically predicted in electric systems, and experimentally realized in two-dimensional (2D) mechanical and electromagnetic systems, electrical circuits, optical and sonic crystals, and elastic phononic plates. Here, we demonstrate a pseudospin-valley-coupled phononic TI, which simultaneously exhibits gapped edge states and topological corner states. Pseudospin-orbit coupling edge states and valley-polarized edge state are respectively induced by the lattice deformation and the symmetry breaking. When both of them coexist, these topological edge states will be greatly gapped and the topological corner state emerges. Under direct field measurements, the robust edge propagation behaving as an elastic waveguide and the topological corner mode working as a robust localized resonance are experimentally confirmed. The pseudospin-valley coupling in our phononic TIs can be well-controlled which provides a reconfigurable platform for the multiple edge and corner states, and exhibits well applications in the topological elastic energy recovery and the highly sensitive sensing.
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