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Register a new userTopological dynamics of gyroscopic and Floquet lattices from Newtons laws
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Despite intense interest in realizing topological phases across a variety of electronic, photonic and mechanical platforms, the detailed microscopic origin of topological behavior often remains elusive. To bridge this conceptual gap, we show how hallmarks of topological modes - boundary localization and chirality - emerge from Newtons laws in mechanical topological systems. We first construct a gyroscopic lattice with analytically solvable edge modes, and show how the Lorentz and spring restoring forces conspire to support very robust dangling bond boundary modes. The chirality and locality of these modes intuitively emerges from microscopic balancing of restoring forces and cyclotron tendencies. Next, we introduce the highlight of this work, a very experimentally realistic mechanical non-equilibrium (Floquet) Chern lattice driven by AC electromagnets. Through appropriate synchronization of the AC driving protocol, the Floquet lattice is pushed around by a rotating potential analogous to an object washed ashore by water waves. Besides hosting dangling bond chiral modes analogous to the gyroscopic boundary modes, our Floquet Chern lattice also supports peculiar half-period chiral modes with no static analog. With key parameters controlled electronically, our setup has the advantage of being dynamically tunable for applications involving arbitrary Floquet modulations. The physical intuition gleaned from our two prototypical topological systems are applicable not just to arbitrarily complicated mechanical systems, but also photonic and electrical topological setups.
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Networks of interacting gyroscopes have proven to be versatile structures for understanding and harnessing finite-frequency topological excitations. Spinning components give rise to band gaps and topologically protected wave transport along the systems boundaries, whether the gyroscopes are arranged in a lattice or in an amorphous configuration. Here, we examine the irrelevance of periodic order for generating topological gaps. Starting from the symplectic dynamics of our model metamaterial, we present a general method for predicting whether a gap exists and for approximating the Chern number using only local features of a network, bypassing the costly diagonalization of the systems dynamical matrix. We then study how strong disorder interacts with band topology in gyroscopic metamaterials and find that amorphous gyroscopic Chern insulators exhibit similar critical behavior to periodic lattices. Our experiments and simulations additionally reveal a topological Anderson insulation transition, wherein disorder drives a trivial phase into a topological one.
We study quantum noise in a nonequilibrium, periodically driven, open system attached to static leads. Using a Floquet Greens function formalism we show, both analytically and numerically, that local voltage noise spectra can detect the rich structure of Floquet topological phases unambiguously. Remarkably, both regular and anomalous Floquet topological bound states can be detected, and distinguished, via peak structures of noise spectra at the edge around zero-, half-, and full-drive-frequency. We also show that the topological features of local noise are robust against moderate disorder. Thus, local noise measurements are sensitive detectors of Floquet topological phases.
This article reviews experimental work on the ultrafast electron dynamics in the topological surface state (TSS) of three-dimensional (3D) topological insulators (TIs) observed with time- and angle-resolved two-photon photoemission (2PPE). The focus is laid on the generation of ultrafast photocurrents and the time-resolved observation of their decay. 2PPE not only allow to unambiguously relate the photocurrents to the spin-polarized electronic surface states. Probing of the asymmetric momentum distribution of the electrons carrying the current makes it possible to study the microscopic scattering processes that governs the unusual electron transport in the time domain. Ultrashort mid-infrared pump pulses permit not only a direct optical excitation of the TSS in Sb$_2$Te$_3$ but also lead to a strong asymmetry of the TSS population in momentum space. Two-dimensional band mapping of the TSS shows that this asymmetry is in fact representative for a macroscopic photocurrent while the helicity-dependence of the photocurrent is found to be small. The time-resolved observation of the photocurrent decay reveals a huge mean free path of the electrons in the TSS.
We develop a theory of topological transitions in a Floquet topological insulator, using graphene irradiated by circularly polarized light as a concrete realization. We demonstrate that a hallmark signature of such transitions in a static system, i.e. metallic bulk transport with conductivity of order $e^2/h$, is substantially suppressed at some Floquet topological transitions in the clean system. We determine the conditions for this suppression analytically and confirm our results in numerical simulations. Remarkably, introducing disorder dramatically enhances this transport by several orders of magnitude.
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.
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