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Register a new userStrain-engineering of Berry curvature dipole and valley magnetization in monolayer MoS$_2$
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The Berry curvature dipole is a physical quantity that is expected to allow various quantum geometrical phenomena in a range of solid-state systems. Monolayer transition metal dichalcogenides provide an exceptional platform to modulate and investigate the Berry curvature dipole through strain. Here we theoretically demonstrate and experimentally verify for monolayer MoS$_rm{2}$ the generation of valley orbital magnetization as a response to an in-plane electric field due to the Berry curvature dipole. The measured valley orbital magnetization shows excellent agreement with the calculated Berry curvature dipole which can be controlled by the magnitude and direction of strain. Our results show that the Berry curvature dipole acts as an effective magnetic field in current-carrying systems, providing a novel route to generate magnetization.
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The electronic topology is generally related to the Berry curvature, which can induce the anomalous Hall effect in time-reversal symmetry breaking systems. Intrinsic monolayer transition metal dichalcogenides possesses two nonequivalent K and K valleys, having Berry curvatures with opposite signs, and thus vanishing anomalous Hall effect in this system. Here we report the experimental realization of asymmetrical distribution of Berry curvature in a single valley in monolayer WSe2 through applying uniaxial strain to break C3v symmetry. As a result, although the Berry curvature itself is still opposite in K and K valleys, the two valleys would contribute equally to nonzero Berry curvature dipole. Upon applying electric field, the emergent Berry curvature dipole would lead to an out-of-plane orbital magnetization, which further induces an anomalous Hall effect with a linear response to E^2, known as nonlinear Hall effect. We show the strain modulated transport properties of nonlinear Hall effect in monolayer WSe2 with moderate hole-doping by gating. The second-harmonic Hall signals show quadratic dependence on electric field, and the corresponding orbital magnetization per current density can reach as large as 60. In contrast to the conventional Rashba-Edelstein effect with in-plane spin polarization, such current-induced orbital magnetization is along the out-of-plane direction, thus promising for high-efficient electrical switching of perpendicular magnetization.
Ideal monolayers of common semiconducting transition metal dichalcogenides (TMDCs) such as MoS$_2$, WS$_2$, MoSe$_2$, and WSe$_2$ possess many similar electronic properties. As it is the case for all semiconductors, however, the physical response of these systems is strongly determined by defects in a way specific to each individual compound. Here we investigate the ability of exfoliated monolayers of these TMDCs to support high-quality, well-balanced ambipolar conduction, which has been demonstrated for WS$_2$, MoSe$_2$, and WSe$_2$, but not for MoS$_2$. Using ionic-liquid gated transistors we show that, contrary to WS$_2$, MoSe$_2$, and WSe$_2$, hole transport in exfoliated MoS$_2$ monolayers is systematically anomalous, exhibiting a maximum in conductivity at negative gate voltage (V$_G$) followed by a suppression of up to 100 times upon further increasing V$_G$. To understand the origin of this difference we have performed a series of experiments including the comparison of hole transport in MoS$_2$ monolayers and thicker multilayers, in exfoliated and CVD-grown monolayers, as well as gate-dependent optical measurements (Raman and photoluminescence) and scanning tunneling imaging and spectroscopy. In agreement with existing {it ab-initio} calculations, the results of all these experiments are consistently explained in terms of defects associated to chalcogen vacancies that only in MoS$_2$ monolayers -- but not in thicker MoS$_2$ multilayers nor in monolayers of the other common semiconducting TMDCs -- create in-gap states near the top of the valence band that act as strong hole traps. Our results demonstrate the importance of studying systematically how defects determine the properties of 2D semiconducting materials and of developing methods to control them.
The optical susceptibility is a local, minimally-invasive and spin-selective probe of the ground state of a two-dimensional electron gas. We apply this probe to a gated monolayer of MoS$_2$. We demonstrate that the electrons are spin polarized. Of the four available bands, only two are occupied. These two bands have the same spin but different valley quantum numbers. We argue that strong Coulomb interactions are a key aspect of this spontaneous symmetry breaking. The Bohr radius is so small that even electrons located far apart in phase space interact, facilitating exchange couplings to align the spins.
A Kekule bond texture in graphene modifies the electronic band structure by folding the Brillouin zone and bringing the two inequivalent Dirac points to the center. This can result, in the opening of a gap (Kek-O) or the locking of the valley degree of freedom with the direction of motion (Kek-Y). We analyze the effects of uniaxial strain on the band structure of Kekule-distorted graphene for both textures. Using a tight-binding approach, we introduce strain by considering the hopping renormalization and corresponding geometrical modifications of the Brillouin zone. We numerically evaluate the dispersion relation and present analytical expressions for the low-energy limit. Our results indicate the emergence of a Zeeman-like term due to the coupling of the pseudospin with the pseudomagnetic strain potential which separates the valleys by moving them in opposite directions away from the center of the Brillouin zone. For the Kek-O phase, this results in a competition between the Kekule parameter that opens a gap and the magnitude of strain which closes it. While for the Kek-Y phase, in a superposition of two shifted Dirac cones. As the Dirac cones are much closer in the supperlattice reciprocal space that in pristine graphene, we propose strain as a control parameter for intervalley scattering.
The valley dependent optical selection rules in recently discovered monolayer group-VI transition metal dichalcogenides (TMDs) make possible optical control of valley polarization, a crucial step towards valleytronic applications. However, in presence of Landaul level(LL) quantization such selection rules are taken over by selection rules between the LLs, which are not necessarily valley contrasting. Using MoS$_{2}$ as an example we show that the spatial inversion-symmetry breaking results in unusual valley dependent inter-LL selection rules, which directly locks polarization to valley. We find a systematic valley splitting for all Landau levels (LLs) in the quantum Hall regime, whose magnitude is linearly proportional to the magnetic field and in comparable with the LL spacing. Consequently, unique plateau structures are found in the optical Hall conductivity, which can be measured by the magneto-optical Faraday rotations.
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