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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)

   Abstract 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 switches 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. Diamagnetic mechanism of critical current non-reciprocity in multilayered superconductors

   https://doi.org/10.1038/s41467-023-36786-5  

   Sundaresh, Ananthesh; Väyrynen, Jukka I.; Lyanda-Geller, Yuli; Rokhinson, Leonid P. (December 2023, Nature Communications)

   Abstract The suggestion that non-reciprocal critical current (NRC) may be an intrinsic property of non-centrosymmetric superconductors has generated renewed theoretical and experimental interest motivated by an analogy with the non-reciprocal resistivity due to the magnetochiral effect in uniform materials with broken spatial and time-reversal symmetry. Theoretically it has been understood that terms linear in the Cooper pair momentum do not contribute to NRC, although the role of higher-order terms remains unclear. In this work we show that critical current non-reciprocity is a generic property of multilayered superconductor structures in the presence of magnetic field-generated diamagnetic currents. In the regime of an intermediate coupling between the layers, the Josephson vortices are predicted to form at high fields and currents. Experimentally, we report the observation of NRC in nanowires fabricated from InAs/Al heterostructures. The effect is independent of the crystallographic orientation of the wire, ruling out an intrinsic origin of NRC. Non-monotonic NRC evolution with magnetic field is consistent with the generation of diamagnetic currents and formation of the Josephson vortices. This extrinsic NRC mechanism can be used to design novel devices for superconducting circuits. 

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3. Nodal band-off-diagonal superconductivity in twisted graphene superlattices

   https://doi.org/10.1038/s41467-023-42471-4  

   Christos, Maine; Sachdev, Subir; Scheurer, Mathias S. (December 2023, Nature Communications)

   Abstract The superconducting state and mechanism are among the least understood phenomena in twisted graphene systems. Recent tunneling experiments indicate a transition between nodal and gapped pairing with electron filling, which is not naturally understood within current theory. We demonstrate that the coexistence of superconductivity and flavor polarization leads to pairing channels that are guaranteed by symmetry to be entirely band-off-diagonal, with a variety of consequences: most notably, the pairing invariant under all symmetries can have Bogoliubov Fermi surfaces in the superconducting state with protected nodal lines, or may be fully gapped, depending on parameters, and the band-off-diagonal chiralp-wave state exhibits transitions between gapped and nodal regions upon varying the doping. We demonstrate that band-off-diagonal pairing can be the leading state when only phonons are considered, and is also uniquely favored by fluctuations of a time-reversal-symmetric intervalley coherent order motivated by recent experiments. Consequently, band-off-diagonal superconductivity allows for the reconciliation of several key experimental observations in graphene moiré systems. 

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4. Electronic structure of topological defects in the pair density wave superconductor

   https://doi.org/10.1103/PhysRevB.110.214508  

   Rosales, Marcus; Fradkin, Eduardo (December 2024, Physical Review B)

   Pair density waves (PDWs) are a inhomogeneous superconducting states whose Cooper pairs possess a finite momentum resulting in a oscillatory gap in space, even in the absence of an external magnetic field. There is growing evidence for the existence of PDW superconducting order in many strongly correlated materials, particularly in the cuprate superconductors and in several other different types of systems. A feature of the PDW state is that inherently it has a CDW as a composite order associated with it. Here we study the structure of the electronic topological defects of the PDW, paying special attention to the half-vortex and its electronic structure that can be detected in STM experiments. We discuss tell-tale signatures of the defects in violations of inversion symmetry, in the excitation spectrum and their spectral functions in the presence of topological defects. We discuss the “Fermi surface” topology of Bogoliubov quasiparticle of the PDWphases, and we briefly discuss the role of quasiparticle interference. 

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5. General duality and magnet-free passive phononic Chern insulators

   https://doi.org/10.1038/s41467-023-36420-4  

   Zhang, Qicheng; He, Li; Mele, Eugene J.; Zhen, Bo; Johnson, A. T. Charlie (February 2023, Nature Communications)

   Abstract Integrated phononics plays an important role in both fundamental physics and technology. Despite great efforts, it remains a challenge to break time-reversal symmetry to achieve topological phases and non-reciprocal devices. Piezomagnetic materials offer an intriguing opportunity as they break time-reversal symmetry intrinsically, without the need for an external magnetic field or an active driving field. Moreover, they are antiferromagnetic, and possibly compatible with superconducting components. Here, we develop a theoretical framework that combines linear elasticity with Maxwell’s equations via piezoelectricity and/or piezomagnetism beyond the commonly adopted quasi-static approximation. Our theory predicts and numerically demonstrates phononic Chern insulators based on piezomagnetism. We further show that the topological phase and chiral edge states in this system can be controlled by the charge doping. Our results exploit a general duality relation between piezoelectric and piezomagnetic systems, which can potentially be generalized to other composite metamaterial systems. 

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