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1. Ferroelectric nonlinear anomalous Hall effect in few-layer WTe2

   https://doi.org/10.1038/s41524-019-0257-1  

   Wang, Hua ; Qian, Xiaofeng ( December 2019 , npj Computational Materials)

   Under broken time reversal symmetry such as in the presence of external magnetic field or internal magnetization, a transverse voltage can be established in materials perpendicular to both longitudinal current and applied magnetic field, known as classical Hall effect. However, this symmetry constraint can be relaxed in the nonlinear regime, thereby enabling nonlinear anomalous Hall current in time-reversal invariant materials – an underexplored realm with exciting new opportunities beyond classical linear Hall effect. Here, using group theory and first-principles theory, we demonstrate a remarkable ferroelectric nonlinear anomalous Hall effect in time-reversal invariant few-layer WTe₂where nonlinear anomalous Hall current switchesmore »in odd-layer WTe₂except 1T′ monolayer while remaining invariant in even-layer WTe₂upon ferroelectric transition. This even-odd oscillation of ferroelectric nonlinear anomalous Hall effect was found to originate from the absence and presence of Berry curvature dipole reversal and shift dipole reversal due to distinct ferroelectric transformation in even and odd-layer WTe₂. Our work not only treats Berry curvature dipole and shift dipole on an equal footing to account for intraband and interband contributions to nonlinear anomalous Hall effect, but also establishes Berry curvature dipole and shift dipole as new order parameters for noncentrosymmetric materials. The present findings suggest that ferroelectric metals and Weyl semimetals may offer unprecedented opportunities for the development of nonlinear quantum electronics.

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2. Electrically and magnetically switchable nonlinear photocurrent in РТ-symmetric magnetic topological quantum materials

   https://doi.org/10.1038/s41524-020-00462-9  

   Wang, Hua ; Qian, Xiaofeng ( December 2020 , npj Computational Materials)

   Nonlinear photocurrent in time-reversal invariant noncentrosymmetric systems such as ferroelectric semimetals sparked tremendous interest of utilizing nonlinear optics to characterize condensed matter with exotic phases. Here we provide a microscopic theory of two types of second-order nonlinear direct photocurrents, magnetic shift photocurrent (MSC) and magnetic injection photocurrent (MIC), as the counterparts of normal shift current (NSC) and normal injection current (NIC) in time-reversal symmetry and inversion symmetry broken systems. We show that MSC is mainly governed by shift vector and interband Berry curvature, and MIC is dominated by absorption strength and asymmetry of the group velocity difference at time-reversedmore »±kpoints. Taking$${\cal{P}}{\cal{T}}$$$PT$-symmetric magnetic topological quantum material bilayer antiferromagnetic (AFM) MnBi₂Te₄as an example, we predict the presence of large MIC in the terahertz (THz) frequency regime which can be switched between two AFM states with time-reversed spin orderings upon magnetic transition. In addition, external electric field breaks$${\cal{P}}{\cal{T}}$$$PT$symmetry and enables large NSC response in bilayer AFM MnBi₂Te₄, which can be switched by external electric field. Remarkably, both MIC and NSC are highly tunable under varying electric field due to the field-induced large Rashba and Zeeman splitting, resulting in large nonlinear photocurrent response down to a few THz regime, suggesting bilayer AFM-zMnBi₂Te₄as a tunable platform with rich THz and magneto-optoelectronic applications. Our results reveal that nonlinear photocurrent responses governed by NSC, NIC, MSC, and MIC provide a powerful tool for deciphering magnetic structures and interactions which could be particularly fruitful for probing and understanding magnetic topological quantum materials.

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3. Observation of backscattering induced by magnetism in a topological edge state

   https://doi.org/10.1073/pnas.2005071117  

   Jäck, Berthold ; Xie, Yonglong ; Andrei Bernevig, B. ; Yazdani, Ali ( June 2020 , Proceedings of the National Academy of Sciences)

   The boundary modes of topological insulators are protected by the symmetries of the nontrivial bulk electronic states. Unless these symmetries are broken, they can give rise to novel phenomena, such as the quantum spin Hall effect in one-dimensional (1D) topological edge states, where quasiparticle backscattering is suppressed by time-reversal symmetry (TRS). Here, we investigate the properties of the 1D topological edge state of bismuth in the absence of TRS, where backscattering is predicted to occur. Using spectroscopic imaging and spin-polarized measurements with a scanning tunneling microscope, we compared quasiparticle interference (QPI) occurring in the edge state of a pristine bismuthmore »bilayer with that occurring in the edge state of a bilayer, which is terminated by ferromagnetic iron clusters that break TRS. Our experiments on the decorated bilayer edge reveal an additional QPI branch, which can be associated with spin-flip scattering across the Brioullin zone center between time-reversal band partners. The observed QPI characteristics exactly match with theoretical expectations for a topological edge state, having one Kramer’s pair of bands. Together, our results provide further evidence for the nontrivial nature of bismuth and in particular, demonstrate backscattering inside a helical topological edge state induced by broken TRS through local magnetism.

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4. Kondo physics in antiferromagnetic Weyl semimetal Mn _3+x Sn _1−x films

   https://doi.org/10.1126/sciadv.abc1977  

   Khadka, Durga ; Thapaliya, T. R. ; Hurtado Parra, Sebastian ; Han, Xingyue ; Wen, Jiajia ; Need, Ryan F. ; Khanal, Pravin ; Wang, Weigang ; Zang, Jiadong ; Kikkawa, James M. ; et al ( August 2020 , Science Advances)

   Topology and strong electron correlations are crucial ingredients in emerging quantum materials, yet their intersection in experimental systems has been relatively limited to date. Strongly correlated Weyl semimetals, particularly when magnetism is incorporated, offer a unique and fertile platform to explore emergent phenomena in novel topological matter and topological spintronics. The antiferromagnetic Weyl semimetal Mn 3 Sn exhibits many exotic physical properties such as a large spontaneous Hall effect and has recently attracted intense interest. In this work, we report synthesis of epitaxial Mn 3+ x Sn 1− x films with greatly extended compositional range in comparison with that ofmore »bulk samples. As Sn atoms are replaced by magnetic Mn atoms, the Kondo effect, which is a celebrated example of strong correlations, emerges, develops coherence, and induces a hybridization energy gap. The magnetic doping and gap opening lead to rich extraordinary properties, as exemplified by the prominent DC Hall effects and resonance-enhanced terahertz Faraday rotation.« less
5. Evidence for one-dimensional chiral edge states in a magnetic Weyl semimetal Co3Sn2S2

   https://doi.org/10.1038/s41467-021-24561-3  

   Howard, Sean ; Jiao, Lin ; Wang, Zhenyu ; Morali, Noam ; Batabyal, Rajib ; Kumar-Nag, Pranab ; Avraham, Nurit ; Beidenkopf, Haim ; Vir, Praveen ; Liu, Enke ; et al ( July 2021 , Nature Communications)

   The physical realization of Chern insulators is of fundamental and practical interest, as they are predicted to host the quantum anomalous Hall (QAH) effect and topologically protected chiral edge states which can carry dissipationless current. Current realizations of the QAH state often require complex heterostructures and sub-Kelvin temperatures, making the discovery of intrinsic, high temperature QAH systems of significant interest. In this work we show that time-reversal symmetry breaking Weyl semimetals, being essentially stacks of Chern insulators with inter-layer coupling, may provide a new platform for the higher temperature realization of robust chiral edge states. We present combined scanningmore »tunneling spectroscopy and theoretical investigations of the magnetic Weyl semimetal, Co₃Sn₂S₂. Using modeling and numerical simulations we find that depending on the strength of the interlayer coupling, chiral edge states can be localized on partially exposed kagome planes on the surfaces of a Weyl semimetal. Correspondingly, our dI/dVmaps on the kagome Co₃Sn terraces show topological states confined to the edges which display linear dispersion. This work provides a new paradigm for realizing chiral edge modes and provides a pathway for the realization of higher temperature QAH effect in magnetic Weyl systems in the two-dimensional limit.

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