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The topology of two-dimensional materials traditionally manifests itself through the quantization of the Hall conductance, which is revealed in transport measurements 1–3 .Recently, it was predicted that topology can also give rise to a characteristic spectroscopic response on subjecting a Chern insulator to a circular drive: comparing the frequency-integrated depletion rates associated with drives of opposite orientation leads to a quantized response dictated by the topological Chern number of the populated Bloch band 4,5 .Here we experimentally demonstrate this intriguing topological effect using ultracold fermionic atoms in topological Floquet bands. In addition, our depletion-rate measurements also provide an experimental estimation of the Wannier-spread functional, a fundamental geometric property of Bloch bands related to the quantum metric 6,7 .Our results establish topological spectroscopic responses as a versatile probe, which could be applied to access the geometry and topology of many-body quantum systems, such as fractional Chern insulators 8 ., SCOPUS: le.j, info:eu-repo/semantics/published

Coastal erosion has become a worldwide concern, typically in the densely populated Asian mega-river deltas. Severe coastal erosion in the southern Red River Delta (RRD) has been intensively studied. Coastal morphological change in the northern RRD was examined in detail through DEM (Digital Elevation Model) analysis based on time series of bathymetrical maps (1965–2004) and Landsat images (1975–2015) in this study. The results show that the northern RRD is featured by rapid coastal accretion in the past few decades, although suspended sediment flux has dropped by roughly 60% after the completeness of Hoa Binh Dam (HBD) in 1988 and relative sea level rose at 1.9 mm yr−1. However, accretion at the outer part of subtidal shoals and platforms was observed to slow down quickly or even turned into erosion in the last two decades. The resuspended sediments from the erosion zone can be transported landward to replenish the inner coastal zone, keeping the latter accretion in the near future to compensate for the sediment discharge decrease from the river. However, this lag effect should be terminated soon if other adverse effects go worse, e.g., damming rivers, sea-level rising, strengthening storms, land reclamation and other poor-designed coastal engineering. Coastal planners and managers should pay full attention to these changes.

The dissipative response of a quantum system upon periodic driving can be exploited as a probe of its topological properties. Here we explore the implications of such phenomena in two-dimensional gases subjected to a uniform magnetic field. It is shown that a filled Landau level exhibits a quantized circular dichroism, which can be traced back to its underlying nontrivial topology. Based on selection rules, we find that this quantized effect can be suitably described in terms of Rabi oscillations, whose frequencies satisfy simple quantization laws. We discuss how quantized dissipative responses can be probed locally, both in the bulk and at the boundaries of the system. This work suggests alternative forms of topological probes based on circular dichroism., SCOPUS: ar.j, info:eu-repo/semantics/published

We reveal an intriguing manifestation of topology, which appears in the depletion rate of topological states of matter in response to an external drive. This phenomenon is presented by analyzing the response of a generic two-dimensional (2D) Chern insulator subjected to a circular time-periodic perturbation. Because of the system's chiral nature, the depletion rate is shown to depend on the orientation of the circular shake; taking the difference between the rates obtained from two opposite orientations of the drive, and integrating over a proper drive-frequency range, provides a direct measure of the topological Chern number (n) of the populated band: This "differential integrated rate" is directly related to the strength of the driving field through the quantized coefficient η0 = ν/ℏ2, where h = 2π ℏ is Planck's constant. Contrary to the integer quantum Hall effect, this quantized response is found to be nonlinear with respect to the strength of the driving field, and it explicitly involves interband transitions. We investigate the possibility of probing this phenomenon in ultracold gases and highlight the crucial role played by edge states in this effect. We extend our results to 3D lattices, establishing a link between depletion rates and the nonlinear photogalvanic effect predicted for Weyl semimetals. The quantized circular dichroism revealed in this work designates depletion rate measurements as a universal probe for topological order in quantum matter., SCOPUS: ar.j, info:eu-repo/semantics/published

Topological band structures can be designed by subjecting lattice systems to time-periodic modulations, as was proposed for irradiated graphene, and recently demonstrated in two-dimensional (2D) ultracold gases and photonic crystals. However, changing the topological nature of Floquet Bloch bands from trivial to non-trivial, by progressively launching the time-modulation, is necessarily accompanied with gap-closing processes: this has important consequences for the loading of particles into a target Floquet band with non-trivial topology, and hence, on the subsequent measurements. In this work, we analyse how such loading sequences can be optimized in view of probing the topology of 2D Floquet bands through transport measurements. In particular, we demonstrate the robustness of center-of-mass responses, as compared to current responses, which present important irregularities due to an interplay between the micro-motion of the drive and inter-band interference effects. The results presented in this work illustrate how probing the center-of-mass displacement of atomic clouds offers a reliable method to detect the topology of Floquet bands, after realistic loading sequences., SCOPUS: ar.j, info:eu-repo/semantics/published