Topological spin and valley pumping in silicene

Scientific Reports, Aug 2016

We propose to realize adiabatic topological spin and valley pumping by using silicene, subject to the modulation of an in-plane ac electric field with amplitude Ey and a vertical electric field consisting of an electrostatic component and an ac component with amplitudes and . By tuning and , topological valley pumping or spin-valley pumping can be achieved. The low-noise valley and spin currents generated can be useful in valleytronic and spintronic applications. Our work also demonstrates that bulk topological spin or valley pumping is a general characteristic effect of two-dimensional topological insulators, irrelevant to the edge state physics.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://www.nature.com/articles/srep31325.pdf

Topological spin and valley pumping in silicene

Abstract We propose to realize adiabatic topological spin and valley pumping by using silicene, subject to the modulation of an in-plane ac electric field with amplitude Ey and a vertical electric field consisting of an electrostatic component and an ac component with amplitudes and . By tuning and , topological valley pumping or spin-valley pumping can be achieved. The low-noise valley and spin currents generated can be useful in valleytronic and spintronic applications. Our work also demonstrates that bulk topological spin or valley pumping is a general characteristic effect of two-dimensional topological insulators, irrelevant to the edge state physics. Introduction Topological transport phenomena are generally protected by certain topological invariants, and exhibit universal properties that are immune to impurity scattering and insensitive to material details. Since the discovery of the integer quantum Hall (IQH) effect in two-dimensional (2D) electron systems1 in 1980, the first example of the topological transport phenomena, the fascinating characteristics of topological transport continue to be the primary focus of more and more research activities. Laughlin interpreted the precise integer quantization of the Hall conductivity in units of e2/h in the IQH effect in terms of an adiabatic quantum charge pump2. Thouless, Kohmoto, Nightingale, and Nijs established a relation between the quantized Hall conductivity and a topological invariant3, namely, the TKNN number or the Chern number. Thouless and Niu further related the amount of charge pumped in a charge pump to the Chern number4. In recent years, the quantum spin Hall (QSH) effect, a spin analogue of the IQH effect, was proposed theoretically5,6, and realized experimentally in HgTe quantum wells7 and InAs/GaSb bilayers8. A QSH system, also called a 2D topological insulator (TI)9,10, is insulating in the bulk with a pair of gapless helical edge states11 at the sample boundary. In the ideal case, where the electron spin is conserved, a QSH system can be viewed as two independent IQH systems without Landau levels12, so that the topological properties of the system can be described by the opposite Chern numbers of the two spin species. In general, when the electron spin is not conserved, unconventional topological invariants, either the Z2 index13 or spin Chern numbers14,15,16, are needed to describe the QSH systems. The time-reversal symmetry is considered to be a prerequisite for the QSH effect, which protects both the Z2 index and gapless nature of the edge states. However, based upon the spin Chern numbers, it was shown that the bulk topological properties remain intact even when the time-reversal symmetry is broken. This finding evokes the interest to pursue direct investigation and utilization of the robust topological properties of the TIs, besides using their symmetry-protected gapless edge states, which are more fragile in realistic environments. Recently, Chen et al. proposed that a spin Chern pumping effect from the bulk of the 2D TI, a HgTe quantum well, can be realized by using time-dependent dual gate voltages and an in-plane ac electric field17, which paves a way for direct investigation and utilization of the bulk topological properties of the TIs. The work of Chen et al. is a generalization of the earlier proposals of topological spin pumps18,19,20,21,22, based upon 1D abstract models, to a realistic 2D TI material. The spin Chern pump is a full spin analogue to the Thouless charge pump, in the sense that it is driven by topological invariants alone, without relying on any symmetries. For example, it has been shown that magnetic impurities breaking both spin conservation and time-reversal symmetry only modify the amount of spin pumped per cycle in a perturbative manner17,22, being essentially distinct from the QSH effect. Wan and Fischer suggested to realize a topological valley resonance effect in graphene by using the time-dependent lattice vibration of optical phonon modes, which can pump out a noiseless and quantized valley current flowing into graphene leads23. This topological valley resonance effect is intimately related to the spin or valley Chern pumping, as it is solely attributable to the valley Chern numbers, independent of the time-reversal symmetry23. Silicene, the cousin of graphene, is a monolayer of silicon atoms instead of carbon atoms on a 2D honeycomb lattice. Recently, this material has been experimentally synthesized24,25,26 and theoretically explored27,28,29,30. Similar to graphene, the energy spectrum of silicene has two Dirac valleys, around the K and K′ points sited at opposite corners of the hexagonal Brillouin zone. Silicene has a much larger spin-orbit gap than graphene, favoring the QSH effect. As another prominent property distinguishing it from graphene, silicene has a buckled lattice structure, which allows us to control the Dirac masses at K and K′ points independently, by applying an exter (...truncated)


This is a preview of a remote PDF: https://www.nature.com/articles/srep31325.pdf

Wei Luo, L. Sheng, B. G. Wang, D. Y. Xing. Topological spin and valley pumping in silicene, Scientific Reports, 2016, Issue: 6, DOI: 10.1038/srep31325