arXiv subjects

Bastian Höckendorf

Publications and source records attributed to Bastian Höckendorf.

9 recordsLinked to original sources

arXiv2021

Immutable quantized transport in Floquet chains

We show how quantized transport can be realized in Floquet chains through encapsulation of a chiral or helical shift. The resulting transport is immutable rather than topological in the sense that it neither requires a band gap nor is affected by arbitrarily strong perturbations. Transport is still characterized by topological quantities but encapsulation of the shift prevents topological phase transitions. To explore immutable transport we introduce the concept of a shiftbox, explain the relevant topological quantities both for momentum-space dispersions and real-space transport, and study model systems of Floquet chains with strictly quantized chiral and helical transport. Natural platforms for the experimental investigation of these scenarios are photonic Floquet chains constructed in waveguide arrays, as well as topolectrical or mechanical systems.

cond-mat.mes-hall↗

arXiv2021

Controlling the direction of topological transport in a non-Hermitian time-reversal symmetric Floquet ladder

We propose a one-dimensional Floquet ladder that possesses two distinct topological transport channels with opposite directionality. The transport channels occur due to a $\mathbb Z_2$ non-Hermitian Floquet topological phase that is protected by time-reversal symmetry. The signatures of this phase are two pairs of Kramers degenerate Floquet quasienergy bands that are separated by an imaginary gap. We discuss how the Floquet ladder can be implemented in a photonic waveguide lattice and show that the direction of transport in the resulting waveguide structure can be externally controlled by focusing two light beams into adjacent waveguides. The relative phase between the two light beams selects which of the two transport channels is predominantly populated, while the angles of incidence of the two light beams determine which of the transport channels is suppressed by non-Hermitian losses. We identify the optimal lattice parameters for the external control of transport and demonstrate the robustness of this mechanism against disorder.

cond-mat.mes-hall↗

arXiv2020

Real and imaginary edge states in stacked Floquet honeycomb lattices

We present a non-Hermitian Floquet model with topological edge states in real and imaginary band gaps. The model utilizes two stacked honeycomb lattices which can be related via four different types of non-Hermitian time-reversal symmetry. Implementing the correct time-reversal symmetry provides us with either two counterpropagating edge states in a real gap, or a single edge state in an imaginary gap. The counterpropagating edge states allow for either helical or chiral transport along the lattice perimeter. In stark contrast, we find that the edge state in the imaginary gap does not propagate. Instead, it remains spatially localized while its amplitude continuously increases. Our model is well-suited for realizing these edge states in photonic waveguide lattices.

cond-mat.mes-hall↗

arXiv2020

Cutting off the non-Hermitian boundary from an anomalous Floquet topological insulator

In two-dimensional anomalous Floquet insulators, non-Hermitian boundary state engineering can be used to completely separate chiral boundary states from bulk bands in the quasienergy spectrum. The topological properties of such spectrally separated boundary states are no longer restricted by the strict bulk-boundary correspondence of Hermitian systems. We show that this additional topological freedom enables one to faithfully transfer the topological properties of a boundary attached to a Floquet insulator to a non-Hermitian Floquet chain obtained by physically cutting off the boundary from the bulk. We implement this scenario for a simple model of an anomalous Floquet insulator with Hermitian and non-Hermitian boundaries, and discuss the relevance of our construction for the experimental realization of non-Hermitian topological phases that connect dimensions one and two.

cond-mat.mes-hall↗

arXiv2020

Topological origin of quantized transport in non-Hermitian Floquet chains

We show that non-Hermiticity enables topological phases with unidirectional transport in one-dimensional Floquet chains. The topological signatures of these phases are non-contractible loops in the spectrum of the Floquet propagator that are separated by an imaginary gap. Such loops occur exclusively in non-Hermitian Floquet systems. We define the corresponding topological invariant as the winding number of the Floquet propagator relative to the imaginary gap. To relate topology to transport, we introduce the concept of regularized dynamics of non-Hermitian chains. We establish that, under the conditions of regularized dynamics, transport is quantized in so far as the charge transferred over one period equals the topological winding number. We illustrate these theoretical findings with the example of a Floquet chain that features a topological phase transition and acts as a charge pump in the non-trivial topological phase. We finally discuss whether these findings justify the notion that non-Hermitian Floquet chains support topological transport.

cond-mat.mes-hall↗

arXiv2019

Non-Hermitian Boundary State Engineering in Anomalous Floquet Topological Insulators

In Hermitian topological systems, the bulk-boundary correspondence strictly constraints boundary transport to values determined by the topological properties of the bulk. We demonstrate that this constraint can be lifted in non-Hermitian Floquet insulators. Provided that the insulator supports an anomalous topological phase, non-Hermiticity allows us to modify the boundary states independently of the bulk, without sacrificing their topological nature. We explore the ensuing possibilities for a Floquet topological insulator with non-Hermitian time-reversal symmetry, where the helical transport via counterpropagating boundary states can be tailored in ways that overcome the constraints imposed by Hermiticity. Non-Hermitian boundary state engineering specifically enables the enhancement of boundary transport relative to bulk motion, helical transport with a preferred direction, and chiral transport in the same direction on opposite boundaries. We explain the experimental relevance of our findings for the example of photonic waveguide lattices.

cond-mat.mes-hall↗

arXiv2019

Universal driving protocol for symmetry-protected Floquet topological phases

Universal driving protocol for symmetry-protected Floquet topological phasesWe propose a universal driving protocol for the realization of symmetry-protected topological phases in $2+1$ dimensional Floquet systems. Our proposal is based on the theoretical analysis of the possible symmetries of a square lattice model with pairwise nearest-neighbor coupling terms. Among the eight possible symmetry operators we identify the two relevant choices for topological phases with either time-reversal, chiral, or particle-hole symmetry. From the corresponding symmetry conditions on the protocol parameters, we obtain the universal driving protocol where each of the symmetries can be realized or broken individually. We provide specific parameter values for the different cases, and demonstrate the existence of symmetry-protected copropagating and counterpropagating topological boundary states. The driving protocol especially allows us to switch between bosonic and fermionic time-reversal symmetry, and thus between a trivial and non-trivial symmetry-protected topological phase, through continuous variation of a parameter.

cond-mat.str-el↗

arXiv2018

Fermionic time-reversal symmetry in a photonic topological insulator

Much of the recent enthusiasm directed towards topological insulators as a new state of matter is motivated by their hallmark feature of protected chiral edge states. In fermionic systems, Kramers degeneracy gives rise to these entities in the presence of time-reversal symmetry (TRS). In contrast, bosonic systems obeying TRS are generally assumed to be fundamentally precluded from supporting edge states. In this work, we dispel this perception and experimentally demonstrate counter-propagating chiral states at the edge of a time-reversal-symmetric photonic waveguide structure. The pivotal step in our approach is encoding the effective spin of the propagating states as a degree of freedom of the underlying waveguide lattice, such that our photonic topological insulator is characterised by a $\mathbb{Z}_2$-type invariant. Our findings allow for fermionic properties to be harnessed in bosonic systems, thereby opening new avenues for topological physics in photonics as well as acoustics, mechanics and even matter waves.

physics.optics↗

arXiv2018

Topological invariants for Floquet-Bloch systems with chiral, time-reversal, or particle-hole symmetry

We introduce $\mathbb Z_2$-valued bulk invariants for symmetry-protected topological phases in $2+1$ dimensional driven quantum systems. These invariants adapt the $W_3$-invariant, expressed as a sum over degeneracy points of the propagator, to the respective symmetry class of the Floquet-Bloch Hamiltonian. The bulk-boundary correspondence that holds for each invariant relates a non-zero value of the bulk invariant to the existence of symmetry-protected topological boundary states. To demonstrate this correspondence we apply our invariants to a chiral Harper, time-reversal Kane-Mele, and particle-hole symmetric graphene model with periodic driving, where they successfully predict the appearance of boundary states that exist despite the trivial topological character of the Floquet bands. Especially for particle-hole symmetry, combination of the $W_3$ and the $\mathbb Z_2$-invariants allows us to distinguish between weak and strong topological phases.

cond-mat.mes-hall↗