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Register a new userNon-Abelian Bloch oscillations in higher-order topological insulators
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Bloch oscillations (BOs) are a fundamental phenomenon by which a wave packet undergoes a periodic motion in a lattice when subjected to an external force. Observed in a wide range of synthetic lattice systems, BOs are intrinsically related to the geometric and topological properties of the underlying band structure. This has established BOs as a prominent tool for the detection of Berry phase effects, including those described by non-Abelian gauge fields. In this work, we unveil a unique topological effect that manifests in the BOs of higher-order topological insulators through the interplay of non-Abelian Berry curvature and quantized Wilson loops. It is characterized by an oscillating Hall drift that is synchronized with a topologically-protected inter-band beating and a multiplied Bloch period. We elucidate that the origin of this synchronization mechanism relies on the periodic quantum dynamics of Wannier centers. Our work paves the way to the experimental detection of non-Abelian topological properties in synthetic matter through the measurement of Berry phases and center-of-mass displacements.
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Conventional topological insulators support boundary states that have one dimension lower than the bulk system that hosts them, and these states are topologically protected due to quantized bulk dipole moments. Recently, higher-order topological insulators have been proposed as a way of realizing topological states that are two or more dimensions lower than the bulk, due to the quantization of bulk quadrupole or octupole moments. However, all these proposals as well as experimental realizations have been restricted to real-space dimensions. Here we construct photonic higher-order topological insulators (PHOTI) in synthetic dimensions. We show the emergence of a quadrupole PHOTI supporting topologically protected corner modes in an array of modulated photonic molecules with a synthetic frequency dimension, where each photonic molecule comprises two coupled rings. By changing the phase difference of the modulation between adjacently coupled photonic molecules, we predict a dynamical topological phase transition in the PHOTI. Furthermore, we show that the concept of synthetic dimensions can be exploited to realize even higher-order multipole moments such as a 4th order hexadecapole (16-pole) insulator, supporting 0D corner modes in a 4D hypercubic synthetic lattice that cannot be realized in real-space lattices.
Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries. Here, we extend the notion of three-dimensional topological insulators to systems that host no gapless surface states, but exhibit topologically protected gapless hinge states. Their topological character is protected by spatio-temporal symmetries, of which we present two cases: (1) Chiral higher-order topological insulators protected by the combination of time-reversal and a four-fold rotation symmetry. Their hinge states are chiral modes and the bulk topology is $mathbb{Z}_2$-classified. (2) Helical higher-order topological insulators protected by time-reversal and mirror symmetries. Their hinge states come in Kramers pairs and the bulk topology is $mathbb{Z}$-classified. We provide the topological invariants for both cases. Furthermore we show that SnTe as well as surface-modified Bi$_2$TeI, BiSe, and BiTe are helical higher-order topological insulators and propose a realistic experimental setup to detect the hinge states.
We study disorder effects in a two-dimensional system with chiral symmetry and find that disorder can induce a quadrupole topological insulating phase (a higher-order topological phase with quadrupole moments) from a topologically trivial phase. Their topological properties manifest in a topological invariant defined based on effective boundary Hamiltonians, the quadrupole moment, and zero-energy corner modes. We find gapped and gapless topological phases and a Griffiths regime. In the gapless topological phase, all the states are localized, while in the Griffiths regime, the states at zero energy become multifractal. We further apply the self-consistent Born approximation to show that the induced topological phase arises from disorder renormalized masses. We finally introduce a practical experimental scheme with topoelectrical circuits where the predicted topological phenomena can be observed by impedance measurements. Our work opens the door to studying higher-order topological Anderson insulators and their localization properties.
Non-Bloch topological invariants preserve the bulk-boundary correspondence in non-Hermitian topological systems, and are a key concept in the contemporary study of non-Hermitian topology. Here we report the dynamic detection of non-Bloch topological invariants in single-photon quantum walks, revealed through the biorthogonal chiral displacement, and crosschecked with the dynamic spin textures in the generalized quasimomentum-time domain following a quantum quench. Both detection schemes are robust against symmetry-preserving disorders, and yield consistent results with theoretical predictions. Our experiments are performed far away from any boundaries, and therefore underline non-Bloch topological invariants as intrinsic properties of the system that persist in the thermodynamic limit. Our work sheds new light on the experimental investigation of non-Hermitian topology.
Pursuing topological phase and matter in a variety of systems is one central issue in current physical sciences and engineering. Motivated by the recent experimental observation of corner states in acoustic and photonic structures, we theoretically study the dipolar-coupled gyration motion of magnetic solitons on the two-dimensional breathing kagome lattice. We calculate the phase diagram and predict both the Tamm-Shockley edge modes and the second-order corner states when the ratio between alternate lattice constants is greater than a critical value. We show that the emerging corner states are topologically robust against both structure defects and moderate disorders. Micromagnetic simulations are implemented to verify the theoretical predictions with an excellent agreement. Our results pave the way for investigating higher-order topological insulators based on magnetic solitons.
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