Light-induced anomalous Hall effect in graphene

Abstract

Many striking non-equilibrium phenomena have been discovered or predicted in opticallydriven quantum solids 1 , ranging from light-induced superconductivity 2,3 to Floquetengineered topological phases 4-8 . These effects are expected to lead to dramatic changes in electrical transport, but can only be comprehensively characterized or functionalized with a direct interface to electrical devices that operate at ultrafast speeds 1-8 . Here, we make use of laser-triggered photoconductive switches 9 to measure the ultrafast transport properties of monolayer graphene, driven by a mid-infrared femtosecond pulse of circularly polarized light. The goal of this experiment is to probe the transport signatures of a predicted light-induced topological band structure in graphene 4,5 , similar to the one originally proposed by Haldane 10 . We report the observation of an anomalous Hall effect in the absence of an applied magnetic field. We also extract quantitative properties of the non-equilibrium state. The dependence of the effect on a gate potential used to tune the Fermi level reveals multiple features that reflect the effective band structure expected from Floquet theory. This includes a ∼60 meV wide conductance plateau centered at the Dirac point, where a gap of approximately equal magnitude is expected to open. We also find that when the Fermi level lies within this plateau, the estimated anomalous Hall conductance saturates around ∼1.8±0.4 e 2 /h.Optical driving has been proposed as a means to engineer topological properties in topologically trivial systems 4-8 . One proposal for such a 'Floquet topological insulator' is based on breaking time-reversal symmetry in graphene through a coherent interaction with circularly polarized light 4 . In this theory, the light field drives electrons in circular trajectories through the band structure (Fig. 1a). Close to the Dirac point, these states are predicted to acquire a non-adiabatic Berry phase every optical cycle, which is equal and opposite for the upper and lower band. This time-averaged extra phase accumulation amounts to an energy * These authors contributed equally to this work

Floquet analysis of excitations in materials

“…The proposals for Floquet phases presented thus far all use external radiation to realize the dressed electronic structure. However, as shown in the experiment reported in [75] and pointed out in many theoretical works [13,77,78], the continued application of a laser to solids results in heating and eventually damage of the sample. Therefore, in experiments a delicate balance needs to be struck between the time necessary to establish the Floquet phase and the maximum time the material can sustain the radiation.…”

“…The challenge in observing this current in a pump-probe setup is that it has to be detected at very fast timescales, because one needs to use ultrafast pump pulses to avoid damaging the material. In [75], an ultrafast transport measurement setup based on optical switches is presented that achieves the detection of a current with a resolution of 1ps. With this setup the authors succeed in obtaining the light-induced Hall conductivity in graphene.…”

“…In equilibrium materials, the origin of an anomalous Hall current can be unambiguously related to the Berry curvature structure, however in driven systems a careful analysis of the excitation process is required to relate an observed Hall current to the topological nature of the Floquet bands. Using the concept of Floquet fidelity, a measure of how well a given dynamical system is described by its corresponding Floquet states, the authors of [76] show that for the strong pump pulse intensities used in the experiment of [75], Floquet states are well established throughout the Brillouin zone (BZ) as shown in figure 3(d). The observed Hall current, however, is found to result not purely from the topology of the Floquet states, but is partly due to an imbalance in the population of excited states created by the pump.…”

Perspective on topological states of non-Hermitian lattices

“…Unlike conventional phases of matter, the new topological phases [1][2][3][4][5][6][7] cannot be described by a local order parameter [8][9][10]. Now, the frontiers in this field keep expanding at a rapid pace in ever more interesting directions, like the search for gapless but topological phases such as Weyl semimetals [11,12] and topological states in Floquet systems [13][14][15].…”

Floquet boundary states in AB -stacked graphite

“…20 Experiments have successfully confirmed the possibility of creating and tuning hybrid electron-photon states, 15,21 also called Floquet-Bloch states, and also the generation of a laserinduced Hall effect in graphene. 22 The name Floquet here is used because the prevalent theory for this type of driven systems: the Floquet theory, [23][24][25][26] from which the spectrum, effective Hamiltonians, 27,28 a map of the topological invariants 29,30 and transport properties [31][32][33] can be computed. Most of the attention has been devoted to illuminating two-dimensional materials, including graphene, 10,[34][35][36] germanene, 37 silicene, 38 and MoS2.…”