Dynamical response of dissipative helical edge states

Doru Sticlet (1) , Jérôme Cayssol (1)

1 LOMA - Laboratoire Ondes et Matière d'Aquitaine

Quantum spin Hall insulators are characterized by topologically protected counterpropagating edge states. Here we study the dynamical response of these helical edge states under a time-dependent flux biasing, in the presence of a heat bath. It is shown that the relaxation time of the edge carriers can be determined from a measurement of the dissipative response of topological insulator disks. The effects of various perturbations, including Zeeman coupling and disorder, are also discussed. Introduction. The hallmark of two-dimensional (2D) quan-tum spin Hall (QSH) topological insulators (TIs) consists in the existence of dissipationless conducting edge states in the absence of any time-reversal breaking perturbations [1]. Due to spin-orbit coupling and a particular bulk band structure, the edge carriers' spin is tied to their momentum [2,3]. These helical edge states have been reported experimentally in HgTe/CdTe [4] and InAs/GaSb [5] quantum wells. So far, most of the studies have covered the equilibrium or ground-state physics of helical edge states, while less is known about their dynamics and the associated relaxation mechanisms. Only recently, the problem of dissipation has gained attention in the context of topological insulators (TI) [6] and topological superconductors [7]. Recently, it has been proposed that the Floquet type of TIs can be engineered by applying a proper external drive on semimetals or trivial band insulators [8]. Floquet bands have already been reported in time-resolved photoemission experiments on three-dimensional TIs [9], and their topolog-ical nature is under active debate. Relaxation phenomena are crucial to establish such nonequilibrium steady states of matter, and ensure the balance between the energy injected by the drive and the energy dissipated towards microscopic degrees of freedom of the environment. Meanwhile, experimental progress has been achieved in extracting typical relaxation times of carriers in coherent con-ductors such as normal-superconducting (NS) rings [10,11]. In such experiments, a small coherent system, characterized by a flux-dependent spectrum, is coupled to a multimode superconducting resonator. The dissipative and nondissipative magnetic susceptibility of unconnected samples is obtained by measuring the energy shifts and quality factors of the resonances as a function of frequency, temperature, and dc magnetic flux. In this Rapid Communication, we suggest that these techniques could be applied to extract the typical relaxation times of helical edge carriers circulating around disks of two-dimensional (2D) TIs. In view of these experimental advances, this Rapid Com-munication addresses the dynamical response of the generic helical edge state of a 2D TI coupled to a thermal bath and threaded by a time-dependent flux (t), which is the superposition of a dc flux φ and a small alternating flux at

Mots clés: Electronic transport in nanoscale materials and structures; Electronic transport in mesoscopic systems; Quantum wires

Domaines: Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]

Doru Sticlet, Jérôme Cayssol. Dynamical response of dissipative helical edge states. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2014, 90 (20), pp.201303 (1-5). ⟨10.1103/PhysRevB.90.201303⟩. ⟨hal-01094367⟩