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A recent scientific debate has arisen: Which processes underlie the actual ground of the valley Hall effect (VHE) in two-dimensional materials? The original VHE emerges in samples with ballistic transport of electrons due to the anomalous velocity terms resulting from the Berry phase effect. In disordered samples though, alternative mechanisms associated with electron scattering off impurities have been suggested: (i) asymmetric electron scattering, called skew scattering, and (ii) a shift of the electron wave packet in real space, called a side jump. It has been claimed that the side jump not only contributes to the VHE but fully offsets the anomalous terms regardless of the drag force for fundamental reasons and, thus, the side-jump together with skew scattering become the dominant mechanisms. However, this claim is based on equilibrium theories without any external valley-selective optical pumping, which makes the results fundamentally interesting but incomplete and impracticable. We develop in this paper a microscopic theory of the photoinduced VHE using the Keldysh nonequilibrium diagrammatic technique and find that the asymmetric skew scattering mechanism is dominant in the vicinity of the interband absorption edge. This allows us to explain the operation of optical transistors based on the VHE.
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The quantum valley Hall effect (QVHE) has been observed in a variety of experimental setups, both quantum and classical. While extremely promising for applications, one should be reminded that QVHE is not an exact topological phenomenon and that, so far, it has been fully understood only qualitatively in certain extreme limits. Here we present a technique to relate QVHE systems with exact quantum spin-Hall insulators that accept real-space representations, without taking any extreme limit. Since the bulk-boundary correspondence is well understood for the latter, we are able to formulate precise quantitative statements about the QVHE regime and its robustness against disorder. We further investigate the effect using a novel experimental platform based on magnetically coupled spinners. Visual renderings, quantitative data and various tests of the domain-wall modes are supplied, hence giving an unprecedented insight into the effect.
Gapped graphene has been proposed to be a good platform to observe the valley Hall effect, a transport phenomenon involving the flow of electrons that are characterized by different valley indices. In the present work, we show that this phenomenon is better described as an instance of the orbital Hall effect, where the ambiguous valley indices are replaced by a physical quantity, the orbital magnetic moment, which can be defined uniformly over the entire Brillouin zone. This description removes the arbitrariness in the choice of arbitrary cut-off for the valley-restricted integrals in the valley Hall conductivity, as the conductivity in the orbital Hall effect is now defined as the Brillouin zone integral of a new quantity, called the orbital Berry curvature. This reformulation in terms of OHE provides the direct explanation to the accumulated opposite orbital moments at the edges of the sample, observed in previous Kerr rotation measurements.
We study the electronic structures and topological properties of $(M+N)$-layer twisted graphene systems. We consider the generic situation that $N$-layer graphene is placed on top of the other $M$-layer graphene, and is twisted with respect to each other by an angle $theta$. In such twisted multilayer graphene (TMG) systems, we find that there exists two low-energy flat bands for each valley emerging from the interface between the $M$ layers and the $N$ layers. These two low-energy bands in the TMG system possess valley Chern numbers that are dependent on both the number of layers and the stacking chiralities. In particular, when the stacking chiralities of the $M$ layers and $N$ layers are opposite, the total Chern number of the two low-energy bands for each valley equals to $pm(M+N-2)$ (per spin). If the stacking chiralities of the $M$ layers and the $N$ layers are the same, then the total Chern number of the two low-energy bands for each valley is $pm(M-N)$ (per spin). The valley Chern numbers of the low-energy bands are associated with large, valley-contrasting orbital magnetizations, suggesting the possible existence of orbital ferromagnetism and anomalous Hall effect once the valley degeneracy is lifted either externally by a weak magnetic field or internally by Coulomb interaction through spontaneous symmetry breaking.
Graphene subject to high levels of shear strain leads to strong pseudo-magnetic fields resulting in the emergence of Landau levels. Here we show that, with modest levels of strain, graphene can also sustain a classical valley hall effect (VHE) that can be detected in nonlocal transport measurements. We provide a theory of the strain-induced VHE starting from the quantum Boltzmann equation. This allows us to show that, averaging over short-range impurity configurations destroys quantum coherence between valleys, leaving the elastic scattering time and inter-valley scattering rate as the only parameters characterizing the transport theory. Using the theory, we compute the nonlocal resistance of a Hall bar device in the diffusive regime. Our theory is also relevant for the study of moderate strain effects in the (nonlocal) transport properties of other two-dimensional materials and van der Walls heterostructures.
2D materials with valley-related multiple Hall effect are both fundamentally intriguing and practically appealing to explore novel phenomena and applications, but have been largely overlooked up to date. Here, using first-principles calculations, we present that valley related multiple Hall effect can exist in single-layer VSi2P4. We identify single-layer VSi2P4 as a ferromagnetic semiconductor with out-of-plane magnetization and valley physics. Arising from the joint effect of inversion symmetry breaking and time reversal symmetry breaking, the exotic spontaneous valley polarization occurs in single-layer VSi2P4, thus facilitating the observation of anomalous valley Hall effect. Moreover, under external strain, band inversion can occur at only one of the valleys of single-layer VSi2P4, enabling the long-sought valley-polarized quantum anomalous Hall effect, and meanwhile the anomalous valley Hall effect is well preserved.. Our work not only enriches the research on valley-related multiple Hall effect, but also opens a new avenue for exploring valley-polarized quantum anomalous Hall effect.
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