Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems

By Mark Rudner, N. Lindner, Erez Berg, Michael Levin. 2012

894 citations recorded by the source corpus.

Recently, several authors have investigated topological phenomena in periodically-driven systems of non-interacting particles. These phenomena are identified through analogies between the Floquet spectra of driven systems and the band structures of static Hamiltonians. Intriguingly, these works have revealed that the topological characterization of driven systems is richer than that of static systems. In particular, in driven systems in two dimensions (2D), robust chiral edge states can appear even though the Chern numbers of all the bulk Floquet bands are zero. Here we elucidate the crucial distinctions between static and driven 2D systems, and construct a new topological invariant that yields the correct edge state structure in the driven case. We provide formulations in both the time and frequency domains, which afford additional insight into the origins of the "anomalous" spectra which arise in driven systems. Possible realizations of these phenomena in solid state and cold atomic systems are discussed.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/c16e8f8e3ca746a92066b0600ecf238b964dd9c5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Electrical and Electronic Engineering

Citations in the corpus

Chiral floquet phases of many-body localized bosons (2016, background): “This can be seen by noting that the winding number W 1⁄4 1⁄2i=ð2πÞ R dkTrðU†∂kUÞ is a topological invariant quantized to be an integer [29].”
Experimental observation of optical Weyl points and Fermi arc-like surface states (2016, background): “[34] Mark S Rudner, Netanel H Lindner, Erez Berg, and Michael Levin.”
Colloquium: Nonthermal pathways to ultrafast control in quantum materials (2021, background): “An additional topological invariant named the winding number can also arise in the low-frequency limit (Kitagawa et al., 2010; Rudner et al., 2013), which is defined over time rather than momentum space, and thus realizable only in periodically driven systems.”
Topological Phases of Non-Hermitian Systems (2018, background): “A good illustration is the anomalous edge states [64], which exist in spite of a trivial Uðk; TÞ 1⁄4 1.”
Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points (2017, background): “– The bulkboundary correspondence, which determines the existence of edge/surface states from bulk topological invariants, is a leitmotif ubiquitous in the field of topological insulators [45–47] and their more recent archetypes [48].”
Topological bands for ultracold atoms (2018, neutral): “number of anomalous edge states requires one to know not just the stroboscopic evolution defined by the Floquet operator, but also the full time-evolution operator at intermediate times, from which an additional invariant can be constructed (Rudner et al., 2013).”
Topological photonics (2018, methodology): “aforementioned “anomalous” regime of the topological phase diagram, where chiral edge modes are uniquely determined by the nontrivial winding number (Kitagawa et al., 2010a; Nathan and Rudner, 2015; Rudner et al., 2013).”
Periodically Driven Quantum Systems: Effective Hamiltonians and Engineered Gauge Fields (2014, background): “[54,58], which features topological Floquet edge states, corresponds to the case N 1⁄4 5.”