Robustness of quantized transport through edge states of finite length: Imaging current density in Floquet topological versus quantum spin and anomalous Hall insulators

Abstract

The theoretical analysis of topological insulators (TIs) has been traditionally focused on infinite homogeneous crystals with band gap in the bulk and nontrivial topology of their wave functions, or infinite wires whose boundaries host surface or edge metallic states. Such infinite-length edge states exhibit quantized conductance which is insensitive to edge disorder, as long as it does not break the underlying symmetry or introduce energy scale larger than the bulk gap. However, experimental devices contain finite-size topological region attached to normal metal (NM) leads, which poses a question about how precise is quantization of longitudinal conductance and how electrons transition from topologically trivial NM leads into the edge states. This particularly pressing issue for recently conjectured two-dimensional (2D) Floquet TI where electrons flow from time-independent NM leads into time-dependent edge states, the very recent experimental realization [J. W. McIver et al., Nat. Phys. 16, 38 (2020)] of Floquet TI using graphene irradiated by circularly polarized light did not exhibit either quantized longitudinal or Hall conductance. Here, we employ a charge-conserving solution for Floquet-nonequilibrium Green functions of irradiated graphene nanoribbon to compute longitudinal two-terminal conductance, as well as spatial profiles of local current density as electrons propagate from NM leads into the Floquet TI. For comparison, we also compute conductance of graphene-based realization of 2D quantum Hall, quantum anomalous Hall, and quantum spin Hall insulators. Although zero-temperature conductance within the gap of these three conventional time-independent 2D TIs of finite length exhibits small oscillations due to reflections at the NM-lead/2D-TI interface, it remains very close to perfectly quantized plateau at 2e 2 /h and completely insensitive to edge disorder. This is due to the fact that inside conventional TIs there is only edge local current density which circumvents any disorder. In contrast, in the case of Floquet TI both bulk and edge local current densities contribute equally to total current, which leads to longitudinal conductance below the expected quantized plateau that is further reduced by edge vacancies. We propose two experimental schemes to detect coexistence of bulk and edge current densities within Floquet TI: (i) drilling a nanopore in the interior of irradiated region of graphene will induce backscattering of bulk current density, thereby reducing longitudinal conductance by ∼28%; (ii) imaging of magnetic field produced by local current density using diamond nitrogen-vacancy centers.

Have mysterious topological valley currents been observed in graphene superlattices?

“…In 2021, some of the authors of [1] published a new manuscript in Nature entitled 'Long-range nontopological edge currents in charge-neutral graphene' [24], in which they argue the potential predominant role of 'edge (current) accumulation' in analysing nonlocal transport signals in absence or presence of external magnetic field, and finally conclude that 'The observation here of long-range edge currents not protected by topology, but nevertheless robust and coexisting with the bulk conduction, calls for careful re-examination of some of the reported nonlocal transport phenomena. ' A direct imaging of the formation of valley-polarized edge currents, while concurrently measuring the same nonlocal resistance as observed earlier in [1,5,7], could actually provide the sought-after smoking gun for conclusive determination of the nonlocal transport mechanism, as also discussed in other context of topological physics [12] or hydrodynamics flow in Dirac materials [25].…”

“…The original theoretical interpretation [10] of the experiments published in [1] essentially introduces a new type of topological effect in condensed matter, rather different from those for which the Nobel Prize in Physics was awarded in 2016 [11]. In this new picture, topological valley currents, which would carry the nonlocal signal observed in [1] in the center of the gap, are produced by Fermi sea states just beneath the gap, and not by gapless edge states [12] at the Fermi energy. This is unlike all other known cases [11] where 'unexpected topologically protected edge states recur again and again in connection with topological state of matter' (quote taken from [11]).…”

Spin-Polarized Tunable Photocurrents

“…Similar systems were considered before with a few differences: ref studied laser-illuminated transition metal dichalcogenide without the spin–orbit coupling considered here, and refs and studied germanene and silicene in the high-frequency regime while here we focus on frequencies smaller than the bandwidth. Other studies using Floquet theory focused on the topological states induced by light, − rather than the modification of native topological states considered here. A noteworthy exception is the recent report on the effects of laser illumination on graphene in the the quantum-Hall regime .…”

Quantum Hall edge states under periodic driving: a Floquet induced chirality switch

“…In the non-interacting limit this is equivalent to the Keldysh formalism [49,52]. This has been used for a variety of systems including laser illuminated graphene [41,53]. The time-average current, Ī = 1 T T 0 dt I(t), is calculated according to…”