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Register a new userTransition of a 2D spin mode to a helical state by lateral confinement
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Added by
Patrick Altmann Mr.
Publication date
2015
fields
Physics
and research's language is
English
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Spin-orbit interaction (SOI) leads to spin precession about a momentum-dependent spin-orbit field. In a diffusive two-dimensional (2D) electron gas, the spin orientation at a given spatial position depends on which trajectory the electron travels to that position. In the transition to a 1D system with increasing lateral confinement, the spin orientation becomes more and more independent on the trajectory. It is predicted that a long-lived helical spin mode emerges. Here we visualize this transition experimentally in a GaAs quantum-well structure with isotropic SOI. Spatially resolved measurements show the formation of a helical mode already for non-quantized and non-ballistic channels. We find a spin-lifetime enhancement that is in excellent agreement with theoretical predictions. Lateral confinement of a 2D electron gas provides an easy-to-implement technique for achieving high spin lifetimes in the presence of strong SOI for a wide range of material systems.
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The presence of edges locally breaks the inversion symmetry of heterostructures and gives rise to lateral (edge) spin-orbit coupling (SOC), which, under some conditions, can lead to the formation of helical edge states. If the edge SOC is strong enough, the helical edge states can penetrate the band-gap and be energetically isolated from the bulk-like states. As a result backward scattering is suppressed, dissipationless helical edge channels protected against time-inversion symmetric perturbations emerge, and the system behaves as a 2D topological insulator (TI). However, unlike in previous works on TIs, the mechanism proposed here for the creation of protected helical edge states relies on the strong edge SOC rather than on band inversion.
We study the electronic transport across an electrostatically-gated lateral junction in a HgTe quantum well, a canonical 2D topological insulator, with and without applied magnetic field. We control carrier density inside and outside a junction region independently and hence tune the number and nature of 1D edge modes propagating in each of those regions. Outside the 2D gap, magnetic field drives the system to the quantum Hall regime, and chiral states propagate at the edge. In this regime, we observe fractional plateaus which reflect the equilibration between 1D chiral modes across the junction. As carrier density approaches zero in the central region and at moderate fields, we observe oscillations in resistance that we attribute to Fabry-Perot interference in the helical states, enabled by the broken time reversal symmetry. At higher fields, those oscillations disappear, in agreement with the expected absence of helical states when band inversion is lifted.
The interaction of a magnetic insulator with the helical electronic edge of a two-dimensional topological insulator has been shown to lead to many interesting phenomena. One of these is that for a suitable orientation of the magnetic anisotropy axis, the exchange coupling to an easy-plane magnet has no effect on DC electrical transport through a helical edge, despite the fact that it opens a gap in the spectrum of the helical edge [Meng {em et al.}, Phys. Rev. B {bf 90}, 205403 (2014)]. Here, we theoretically consider such a magnet embedded in an interferometer, consisting of a pair of helical edge states connected by two tunneling contacts, at which electrons can tunnel between the two edges. Using a scattering matrix approach, we show that the presence of the magnet in one of the interferometer arms gives rise to AC currents in response to an applied DC voltage. On the other hand, the DC Aharonov-Bohm effect is absent at zero temperature and small DC voltages, and only appears if the applied voltage or the temperature exceeds the magnet-induced excitation gap.
Chiral and helical Majorana edge modes are two archetypal gapless excitations of two-dimensional topological superconductors. They belong to superconductors from two different Altland-Zirnbauer symmetry classes characterized by $mathbb{Z}$ and $mathbb{Z}_2$ topological invariant respectively. It seems improbable to tune a pair of co-propagating chiral edge modes to counter-propagate without symmetry breaking. Here we show that such a direct topological transition is in fact possible, provided the system possesses an additional symmetry $mathcal{O}$ which changes the bulk topological invariant to $mathbb{Z}oplus mathbb{Z}$ type. A simple model describing the proximity structure of a Chern insulator and a $p_x$-wave superconductor is proposed and solved analytically to illustrate the transition between two topologically nontrivial phases. The weak pairing phase has two chiral Majorana edge modes, while the strong pairing phase is characterized by $mathcal{O}$-graded Chern number and hosts a pair of counter-propagating Majorana fermions. The bulk topological invariants and edge theory are worked out in detail. Implications of these results to topological quantum computing based on Majorana fermions are discussed.
Bulk chromium triiodide (CrI$_3$) has long been known as a layered van der Waals ferromagnet. However, its monolayer form was only recently isolated and confirmed to be a truly two-dimensional (2D) ferromagnet, providing a new platform for investigating light-matter interactions and magneto-optical phenomena in the atomically thin limit. Here, we report spontaneous circularly polarized photoluminescence in monolayer CrI$_3$ under linearly polarized excitation, with helicity determined by the monolayer magnetization direction. In contrast, the bilayer CrI$_3$ photoluminescence exhibits vanishing circular polarization, supporting the recently uncovered anomalous antiferromagnetic interlayer coupling in CrI$_3$ bilayers. Distinct from the Wannier-Mott excitons that dominate the optical response in well-known 2D van der Waals semiconductors, our absorption and layer-dependent photoluminescence measurements reveal the importance of ligand-field and charge-transfer transitions to the optoelectronic response of atomically thin CrI$_3$. We attribute the photoluminescence to a parity-forbidden d-d transition characteristic of Cr$^{3+}$ complexes, which displays broad linewidth due to strong vibronic coupling and thickness-independent peak energy due to its localized molecular orbital nature.
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