Session Y2: Spin and Valley Pseudo-Spin Transport in Strongly Spin-Orbit Coupled Systems

Theory of classical and quantum transport in monolayers of MoS$_{2}$

From the family of new van der Waals materials, the class of layered transition metal dichalcogenides has emerged as a particularly interesting system due to the inherent spin and valley degrees of freedom. In this talk we focus on the interplay between these degrees of freedom and the different types of disorder in monolayers of molybdenum disulphide. Within the semiclassical Drude-Boltzmann formalism, treating the screening of impurities with the random phase approximation, we demonstrate that different scattering mechanisms such as charged impurity scattering, intervalley scattering, and phonons provide different signatures in electronic transport. This allows us to conclude, for example, that in CVD-grown monolayers of MoS$_{2}$, intervalley scattering dominates over other mechanisms at low temperatures [1].~ Interestingly, charged impurities generate spatial inhomogeneity in the carrier density that results in a classical disorder-induced magnetoresistance that can be observed at room temperature [2].~ However, at lower temperatures, in this regime of strong intervalley scattering, we predict that the quantum phase-coherent corrections to the conductivity results in a one-parameter crossover from weak localization to weak anti-localization as a function of magnetic field, where this crossover is determined only by the spin lifetime.~ ~By comparing with available experimental data [3], we show that this combined framework allows for a novel way to measure the spin-relaxation in monolayers of MoS$_{2}$. We find that the spin scattering arises from the Dyakonov-Perel spin-orbit scattering mechanism with a conduction band spin-splitting of about 4 meV, consistent with calculations using density functional theory. REFERENCES: [1] ``\textit{Transport Properties of Monolayer MoS}$_{2}$\textit{ Grown by Chemical Vapor Deposition}'', H. Schmidt, S. Wang, L. Chu, M. Toh, R. Kumar, W. Zhao, A. H. Castro Neto, J. Martin, S. Adam, B. \"{O}zyilmaz, and G. Eda, \textit{Nano Lett.} \textbf{14}, 1909 (2014); [2] ``\textit{Disorder induced magnetoresistance in a two dimensional electron system}'', J. Ping, I. Yudhistira, N. Ramakrishnan, S. Cho, S. Adam, M. S. Fuhrer, \textit{Phys. Rev. Lett.} \textbf{113}, 047206 (2014); [3] ``\textit{Quantum transport and observation of Dyakonov-Perel spin-orbit scattering in monolayer MoS}$_{2}$'', H. Schmidt, I. Yudhistira, L. Chu, A. H. Castro Neto, B. \"{O}zyilmaz, S. Adam, G. Eda, arXiv:1503.00428, (2015).   

Optical imaging of the valley Hall effect in MoS$_2$ transistors

The newly emerged two-dimensional (2D) transition metal dichalcogenides (TMDs) with nonequivalent K and K' valleys have provided an ideal laboratory for exploring the valley degree of freedom of electrons, as well as their potential applications for information processing. Valley Hall effect (VHE), in which a transverse valley current is formed under a longitudinal electrical bias in the absence of a magnetic field, has been predicted in 2D TMDs with broken inversion symmetry. The effect has recently been demonstrated in monolayer MoS$_2$ through a photo-induced anomalous Hall effect, which uses circularly polarized light to preferentially excite electrons into a specific valley. In this talk, we will present our recent results on the development of Kerr rotation microscopy to image the VHE. The valley polarizations of opposite sign accumulated on two opposing edges of MoS$_2$ transistors from the VHE are measured directly. We will also discuss the possibility of electrical control of the VHE in bilayer MoS$_2$, which possesses inversion symmetry. An application of a vertical electric field breaks the inversion symmetry and consequently yields the VHE.   

Breaking time reversal symmetry, quantum anomalous Hall state and dissipationless chiral conduction in topological insulators

Breaking time reversal symmetry (TRS) in a topological insulator (TI) with ferromagnetic perturbation can lead to many exotic quantum phenomena exhibited by Dirac surface states including the quantum anomalous Hall (QAH) effect and dissipationless quantized Hall transport. The realization of the QAH effect in realistic materials requires ferromagnetic insulating materials and topologically non-trivial electronic band structures. In a TI, the ferromagnetic order and TRS breaking is achievable by conventional way, through doping with a magnetic element, or by ferromagnetic proximity coupling. Our experimental studies by both approaches will be discussed. In doped TI van Vleck ferromagnetism was observed. The proximity induced magnetism at the interface was stable, beyond the expected temperature range. We shall describe in a hard ferromagnetic TI system a robust QAH state and dissipationless edge current flow is achieved,$^{\mathrm{1,2}}$ a major step towards dissipationless electronic applications with no external fields, making such devices more amenable for metrology and spintronics applications. Our study of the gate and temperature dependences of local and nonlocal magnetoresistance, may elucidate the causes of the dissipative edge channels and the need for very low temperature to observe QAH. In close collaboration with: CuiZu Chang,$^{\mathrm{2,3}}$ Ferhat Katmis, $^{\mathrm{1.2,3}}$ Peng Wei. $^{\mathrm{1,2,3\thinspace }}$; From Nuclear Eng. Dept. MIT, M. Li, J. Li; From Penn State U, W-W. Zhao, D. Y. Kim, C-x. Liu, J. K. Jain, M. H. W. Chan; From Oakridge National Lab, V. Lauter; From Northeastern U., B. A. Assaf, M. E. Jamer, D. Heiman; From Argonne Lab, J. W. Freeland; From Ruhr-Universitaet Bochum (Germany), F. S. Nogueira, I. Eremin; From Saha Institute of Nuclear Physics (India), B. Satpati. References: \begin{enumerate} \item P. Wei et al., Phys. Rev. Lett. 110, 186807 (2013) \item C-Z Chang et al., Nat. Matl 13, 473 (2015), Phys. Rev. Lett. 115, 057206 (2015) \end{enumerate}