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Register a new userA fractional corner anomaly reveals higher-order topology
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Added by
Christopher W Peterson
Publication date
2020
fields
Physics
and research's language is
English
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Spectral measurements of boundary localized in-gap modes are commonly used to identify topological insulators via the bulk-boundary correspondence. This can be extended to high-order topological insulators for which the most striking feature is in-gap modes at boundaries of higher co-dimension, e.g. the corners of a 2D material. Unfortunately, this spectroscopic approach is not always viable since the energies of the topological modes are not protected and they can often overlap the bulk bands, leading to potential misidentification. Since the topology of a material is a collective product of all its eigenmodes, any conclusive indicator of topology must instead be a feature of its bulk band structure, and should not rely on specific eigen-energies. For many topological crystalline insulators the key topological feature is fractional charge density arising from the filled bulk bands, but measurements of charge distributions have not been accessible to date. In this work, we experimentally measure boundary-localized fractional charge density of two distinct 2D rotationally-symmetric metamaterials, finding 1/4 and 1/3 fractionalization. We then introduce a new topological indicator based on collective phenomenology that allows unambiguous identification of higher-order topology, even in the absence of in-gap states. Finally, we demonstrate the higher-order bulk-boundary correspondence associated with this fractional feature by using boundary deformations to spectrally isolate localized corner modes where they were previously unobservable.
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The recent discoveries of higher-order topological insulators (HOTIs) have shifted the paradigm of topological materials, which was previously limited to topological states at boundaries of materials, to those at boundaries of boundaries, such as corners . So far, all HOTI realisations have assumed static equilibrium described by time-invariant Hamiltonians, without considering time-variant or nonequilibrium properties. On the other hand, there is growing interest in nonequilibrium systems in which time-periodic driving, known as Floquet engineering, can induce unconventional phenomena including Floquet topological phases and time crystals. Recent theories have attemped to combine Floquet engineering and HOTIs, but there has thus far been no experimental realisation. Here we report on the experimental demonstration of a two-dimensional (2D) Floquet HOTI in a three-dimensional (3D) acoustic lattice, with modulation along z axis serving as an effective time-dependent drive. Direct acoustic measurements reveal Floquet corner states that have time-periodic evolution, whose period can be even longer than the underlying drive, a feature previously predicted for time crystals. The Floquet corner states can exist alongside chiral edge states under topological protection, unlike previous static HOTIs. These results demonstrate the unique space-time dynamic features of Floquet higher-order topology.
Photonic crystals have provided a controllable platform to examine excitingly new topological states in open systems. In this work, we reveal photonic topological corner states in a photonic graphene with mirror-symmetrically patterned gain and loss. Such a nontrivial Wannier-type higher-order topological phase is achieved through solely tuning on-site gain/loss strengths, which leads to annihilation of the two valley Dirac cones at a time-reversal-symmetric point, as the gain and loss change the effective tunneling between adjacent sites. We find that the symmetry-protected photonic corner modes exhibit purely imaginary energies and the role of the Wannier center as the topological invariant is illustrated. For experimental considerations, we also examine the topological interface states near a domain wall. Our work introduces an interesting platform for non-Hermiticity-induced photonic higher-order topological insulators, which, with current experimental technologies, can be readily accessed.
Generally, the topological corner state in two-dimensional second-order topological insulator (2D SOTI) is equivalent to the well-known domain wall state, originated from the mass-inversion between two adjacent edges with phase shift of pi. In this work, go beyond this conventional physical picture, we report a fractional mass-kink induced 2D SOTI in monolayer FeSe with canted checkerboard antiferromagnetic (AFM) order by analytic model and first-principles calculations. The canted spin associated in-plane Zeeman field can gap out the quantum spin Hall edge state of FeSe, forming a fractional mass-kink with phase shift of pi/2 at the rectangular corner, and generating an in-gap topological corner state with fractional charge of e/4. Moreover, the topological corner state is robust to local perturbation, existing in both naturally and non-naturally cleaved corners, regardless of the edge orientation. Our results not only demonstrate a material system to realize the unique 2D AFM SOTI, but also pave a new way to design the higher-order topological states from fractional mass-kink with arbitrary phase shift, which are expected to draw immediate experimental attention.
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.
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