Microscopic theory for the light-induced anomalous Hall effect in graphene

Abstract

We employ a quantum Liouville equation with relaxation to model the recently observed anomalous Hall effect in graphene irradiated by an ultrafast pulse of circularly polarized light. In the weak-field regime, we demonstrate that the Hall effect originates from an asymmetric population of photocarriers in the Dirac bands. By contrast, in the strong-field regime, the system is driven into a non-equilibrium steady state that is well-described by topologically non-trivial Floquet-Bloch bands. Here, the anomalous Hall current originates from the combination of a population imbalance in these dressed bands together with a smaller anomalous velocity contribution arising from their Berry curvature. This robust and general finding enables the simulation of electrical transport from light-induced Floquet-Bloch bands in an experimentally relevant parameter regime and creates a pathway to designing ultrafast quantum devices with Floquet-engineered transport properties.Optical control of functional materials has emerged as an important research front bridging condensed matter physics [1] and ultrafast spectroscopy [2]. Many noteworthy phenomena have been discovered in opticallydriven quantum solids, including light-induced superconductivity [3, 4], various types of photo-initiated insulatormetal transitions [5][6][7][8], light control of microscopic interactions like electron-phonon coupling [9][10][11], and theoretically predicted Floquet-topological phases of matter [12][13][14][15][16]. Floquet-topological phases in particular have stimulated much interest but direct evidence of electronphoton Floquet-dressed states in solids is scarce to this date [17,18], in contrast to the field of artificial lattices [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].Recently a light-induced anomalous Hall effect was observed in graphene using ultrafast transport techniques [36]. A key challenge for the interpretation of the reported effects lies in the competition between Floquet engineering of Hamiltonians versus the role of electronic population effects. For the case of laser-driven graphene, the latter are particularly important as the pump laser is generically resonant with electronic excitations. Here we provide a theoretical framework within which this class of experiments [36] can be interpreted.A graphene lattice subjected to circular driving has been studied theoretically in a variety of frameworks [12-15, 22, 37-43]. We focus here on the low-frequency driving regime and find that the driven-dissipative dynamics together with the applied bias field plays a crucial role in understanding the transport properties of the Floquetengineered state. Our real-time simulations contain both the population imbalance of excited photocarriers in the Dirac cone of graphene as well as the Floquet-topological Berry curvature of photon-dressed bands. We find that population effects play an important role under the lowfrequency driving used in the experiments in both weak and strong driving limits. In the weak-driving regime,...

Light-induced anomalous Hall effect in massless Dirac fermion systems and topological insulators with dissipation

“…Motivated by this theoretical prediction, McIver et al recently observed the light-induced anomalous Hall effect in graphene under the presence of a circular laser field [27]. Soon after, we have theoretically investigated the microscopic origin of the observed light-induced anomalous Hall effect by the quantum Liouville equation with phenomenological dissipation [28]. As a result, we clarified that the imbalance of photocarrier distribution of topological Floquet states in the Brillouin zone predominantly causes the light-induced anomalous Hall current with a small contribution from the emergent Berry curvature of the Floquet states.…”

“…Here, T 1 denotes the longitudinal relaxation time, which is responsible for the population decay, while T 2 denotes the transverse relaxation time, which is responsible for decoherence. According to [28], the relaxation times, T 1 and T 2 , are set to 100 fs and 20 fs, respectively. Here, we choose the longitudinal relaxation time…”

“…However, despite the great interest in the subject, population effects with dissipation have only recently been discussed more seriously in the context of Floquet and topological engineering in open [35,36] and closed [37][38][39] nonequilibrium many-body systems. Dissipation and population effects are definitely important in explaining the recent experiments on the light-induced Hall effect [27,28], and here we will provide an in-depth discussion of them. In this work, we first discuss appropriate treatment of phenomenological relaxation for dissipative light-driven condensed matter systems, taking care of electronic decoherence and thermalization via electron-electron and electron-phonon scattering.…”

Floquet analysis of excitations in materials

“…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.…”

“…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. In this context it is important to note that dissipative systems, where the energy can redistributed to a heat bath, can help to stabilize the Floquet phase [13,76,79]. In the next section, instead, we will explore the possibility to achieve establishing Floquet dressed states without the continued transfer of energy into the system.…”