Switching Spin and Charge between Edge States in Topological Insulator Constrictions

Abstract

We show how the coupling between opposite edge states, which overlap in a constriction made of the topological insulator mercury telluride (HgTe), can be employed both for steering the charge flow into different edge modes and for controlled spin switching. Unlike in a conventional spin transistor, the switching does not rely on a tunable Rashba spin-orbit interaction, but on the energy dependence of the edge state wavefunctions. Based on this mechanism, and supported by extensive numerical transport calculations, we present two different ways to control spin-and charge-currents, depending on the local gating of the constriction, resulting in a high fidelity spin transistor.PACS numbers: 85.75.Hh, 85.35.Ds Since the prediction of a new topological state of matter in graphene [1], materials exhibiting peculiar surface states and acting as topological insulators have attracted wide attention [2]. Shortly after the theoretical proposal for a mercury telluride (HgTe)-based two-dimensional topological insulator [3], the observation of the quantum spin Hall effect [4] and non-local edge transport [5] brought compelling experimental evidence for quantized conductance due to edges states. The transport along the HgTe boundaries can be conveniently explained by an edge channel picture [6]: Two states with opposite spin orientation propagate along opposite device edges in the same direction and thus lead to a quantized conductance of 2e 2 /h. Due to the spatial separation of the spin-states the spin-orbit coupling is suspended, and the system geometry can be employed for spin selection [5].Spin-selectivity is also a crucial element of the DattaDas spin transistor proposal [7], where charge flow is controlled electrically through the gate-dependent Rashba spin orbit interaction [8] (SOI) in a conventional twodimensional semiconductor heterostructure placed in between ferromagnetic contacts. Its realization, however, turns out to be difficult owing to spin relaxation in the semiconductor heterostructure and interfacial effects such as the conductivity mismatch [9] between the different materials. HgTe-based topological insulators appear to be promising candidates for spin processing devices since they also can be gated and exhibit considerable SOI but, on the contrary, are composed of a single material class only. Moreover, the one-dimensional (1d) nature of their edge states suppresses orbital effects present in bulk conductors, leading to high spin polarizations and to a much better (spin) switching quality.To our knowledge there have been only a few proposals for spin-transistors based on two-dimensional topological insulators. Two of them rely on spin switching with a magnetic field at a pn-junction [10] or in an AharonovBohm interferometer [11]. Recently it has further been suggested, also within a phenomenological model, that separate gating of the two branches of an AharonovBohm interferometer allows for manipulating charge-and spin-transport [12]. By contrast, our present proposal relies on an electrical operati...

Proposal for an on-demand source of polarized electrons into the edges of a topological insulator

“…Due to TRS, only three processes at a QPC are allowed, namely: (1) a spin-preserving forward scattering, (2) a spin-and edgeflipping forward scattering and (3) a spin-preserving edge-flipping backscattering. The relevant Hamiltonians at the QPC were already investigated in previous works [35][36][37] [for clarity we recall them in App. A].…”

Noise and current correlations in tunnel junctions of quantum spin Hall edge states

“…Lateral gates V T and V B can be also implemented. In HgTe/CdTe quantum wells, a 100 − 200 nm wide constriction leads to a tunneling amplitude magnitude |Γ p | ∼ 0.25 − 2.5 meV, 28,29 well below the bulk gap. Using the value of the Fermi velocity v F 0.5 × 10 6 m/s, 11 a lengthscale ξ 0 = v F /|Γ p | ∼ 0.1 − 1 µm is obtained.…”

“…14, 16 The value of the spin-flipping magnitude |Γ f | is typically smaller than |Γ p | by a factor 3 to 4 only. 28,29,35,37,39 Then, within the suitable voltage bias configurations discussed above, the two partition noises P p and P f can be tuned with varying the charge and spin gate voltages V p and V f in the meV regime. Similarly, in the DQPC setup the individual PQC reflection is controlled by the constrictions, and a distance of about 1µm between the two QPCs leads to a pattern for P p and P f that has a typical period of a few meV.…”

“…In the central region of the setup, the two edge states are coupled by electron tunneling. The tunneling Hamiltonian that preserves time-reversal symmetry consists of two terms [29][30][31][32][33][34][35] , H tun =Ĥ p tun +Ĥ f tun , wherê…”

“…[24][25][26][27] For the helical states, a constriction in the QSH bar causes a local wavefunction overlap 28,29 that is known to yield two types of tunneling processes. [29][30][31][32][33][34][35][36][37][38][39] The first type is the customary spin-preserving (p) process, where an electron tunnels across the junction maintaining its spin orientation, and thereby reversing its group velocity. The second type is less conventional and is a spin-flipping (f ) process, where a tunneling electron reverses its spin orientation maintaining its group velocity: it mainly originates from the interplay between bulk-inversion asymmetry and wavefunction overlap, even in absence of magnetic coupling.…”