Abstract
We study valley polarization, spin, and valley Hall conductivity in doped monolayer MoS2 considering dopant introduced magnetic exchange field using low energy effective Hamiltonian. We found that dopant introduced magnetic exchange field breaks the time inversion symmetry and decouples the energetically degenerated valleys into nondegenerate. Moreover, the calculated result reveals that, at low temperature, in insulating regime, anomalous Hall conductivity in a single valley and the total valley Hall conductivity are quantized, whereas the total spin Hall conductivity vanishes identically. We also found that the strength of the spin-orbit coupling together with the exchange field determines the valley polarization, which in turn controls valley and spin Hall conductivity in doped monolayer MoS2 system. The spin Hall and valley Hall conductivity is dissipationless in the absence of any external magnetic field. Therefore, our results are crucial to generate low power electronics devices.
Highlights
The charge and spin degrees of freedom (DOF) of electrons are at heart of modern electronics as they form the basis of a wide range of applications, such as transistors, photodetectors, and magnetic memory devices
The use of valley indexes for a potential information carrier was first suggested in the studies of conventional semiconductors such as AlAs and Si [2].On the other hand, the presence of a valley-dependent orbital magnetic moment in graphene with gap suggests that currents flow perpendicular to applied electric field even in the absence of a magnetic field, named the ‘valley Hall effect.’
For particular limits hex = λso=0 and hex = 2λso total spin Hall conductivity in (36) vanishes whereas the total valley Hall conductivity is simplified to −(4q2/ h)((Δ2m + a2t2kF2)/atkF)1/2, which indicates that the interplay between spin-orbit coupling and dopant introduced magnetic exchange field is crucial for existence of spin and valley
Summary
The charge and spin degrees of freedom (DOF) of electrons are at heart of modern electronics as they form the basis of a wide range of applications, such as transistors, photodetectors, and magnetic memory devices. Among various material candidates for valleytronics, spatial inversion symmetry broken two-dimensional (2D) honeycomb lattice systems such as graphene and monolayer MoS2 are predicted to be the most useful. These systems have two valleys called K and K’. To graphene in monolayer MoS2 the inversion symmetry is explicitly broken [2], which can give rise to the valley Hall effect where carriers in different valleys flow to opposite transverse edges when an in-plane electric field is applied [4, 5]. We present the numerical results showing effect of the spin-orbit coupling and dopant introduced exchange field on energy band structure of two prominent valleys (K+ and K−) and total valley and spin Hall conductivity.
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