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For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their wavefunctions. A key challenge is to identify and implement experiments that probe or control these quantum properties. In this review, we describe recent progress in this direction, focusing on nonlinear electromagnetic responses that arise directly from quantum geometry and topology. We give an overview of the field by discussing new theoretical ideas, groundbreaking experiments, and the novel materials that drive them. We conclude by discussing how these techniques can be combined with new device architectures to uncover, probe, and ultimately control novel quantum phases with emergent topological and correlated properties.
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Multiferroics are those materials with more than one ferroic order, and magnetoelectricity refers to the mutual coupling between magnetism and electricity. The discipline of multiferroicity has never been so highly active as that in the first decade of the twenty-first century, and it has become one of the hottest disciplines of condensed matter physics and materials science. A series of milestones and steady progress in the past decade have enabled our understanding of multiferroic physics substantially comprehensive and profound, which is further pushing forward the research frontier of this exciting area. The availability of more multiferroic materials and improved magnetoelectric performance are approaching to make the applications within reach. While seminal review articles covering the major progress before 2010 are available, an updated review addressing the new achievements since that time becomes imperative. In this review, following a concise outline of the basic knowledge of multiferroicity and magnetoelectricity, we summarize the important research activities on multiferroics, especially magnetoelectricity and related physics in the last six years. We consider not only single-phase multiferroics but also multiferroic heterostructures. We address the physical mechanisms regarding magnetoelectric coupling so that the backbone of this divergent discipline can be highlighted. A series of issues on lattice symmetry, magnetic ordering, ferroelectricity generation, electromagnon excitations, multiferroic domain structure and domain wall dynamics, and interfacial coupling in multiferroic heterostructures, will be revisited in an updated framework of physics. In addition, several emergent phenomena and related physics, including magnetic skyrmions and generic topological structures associated with magnetoelectricity will be discussed.
While recent advances in band theory and sample growth have expanded the series of extremely large magnetoresistance (XMR) semimetals in transition metal dipnictides $TmPn_2$ ($Tm$ = Ta, Nb; $Pn$ = P, As, Sb), the experimental study on their electronic structure and the origin of XMR is still absent. Here, using angle-resolved photoemission spectroscopy combined with first-principles calculations and magnetotransport measurements, we performed a comprehensive investigation on MoAs$_2$, which is isostructural to the $TmPn_2$ family and also exhibits quadratic XMR. We resolve a clear band structure well agreeing with the predictions. Intriguingly, the unambiguously observed Fermi surfaces (FSs) are dominated by an open-orbit topology extending along both the [100] and [001] directions in the three-dimensional Brillouin zone. We further reveal the trivial topological nature of MoAs$_2$ by bulk parity analysis. Based on these results, we examine the proposed XMR mechanisms in other semimetals, and conclusively ascribe the origin of quadratic XMR in MoAs$_2$ to the carriers motion on the FSs with dominant open-orbit topology, innovating in the understanding of quadratic XMR in semimetals.
Dirac states hosted by Sb/Bi square nets are known to exist in the layered antiferromagnetic AMnX$_2$ (A = Ca/Sr/Ba/Eu/Yb, X=Sb/Bi) material family the space group to be P4/nmm or I4/mmm. In this paper, we present a comprehensive study of quantum transport behaviors, angle-resolved photoemission spectroscopy (ARPES) and first-principles calculations on SrZnSb2, a nonmagnetic analogue to AMnX2, which crystallizes in the pnma space group with distorted square nets. From the quantum oscillation measurements up to 35 T, three major frequencies including F$_1$ = 103 T, F$_2$ = 127 T and F$_3$ = 160 T, are identified. The effective masses of the quasiparticles associated with these frequencies are extracted, namely, m*$_1$ = 0.1 m$_e$, m*$_2$ = 0.1 m$_e$ and m*$_3$ = 0.09m$_e$, where m$_e$ is the free electron mass. From the three-band Lifshitz-Kosevich fit, the Berry phases accumulated along the cyclotron orbit of the quasiparticles are 0.06$pi$, 1.2$pi$ and 0.74$pi$ for F$_1$, F$_2$ and F$_3$, respectively. Combined with the ARPES data and the first-principles calculations, we reveal that F2 and F3 are associated with the two nontrivial Fermi pockets at the Brillouin zone edge while F1 is associated with the trivial Fermi pocket at the zone center. In addition, the first-principles calculations further suggest the existence of Dirac nodal line in the band structure of SrZnSb$_2$.
The nature of Fermi surface defines the physical properties of conductors and many physical phenomena can be traced to its shape. Although the recent discovery of a current-dependent nonlinear magnetoresistance in spin-polarized non-magnetic materials has attracted considerable attention in spintronics, correlations between this phenomenon and the underlying fermiology remain unexplored. Here, we report the observation of nonlinear magnetoresistance at room temperature in a semimetal WTe2, with an interesting temperature-driven inversion. Theoretical calculations reproduce the nonlinear transport measurements and allow us to attribute the inversion to temperature-induced changes in Fermi surface convexity. We also report a large anisotropy of nonlinear magnetoresistance in WTe2, due to its low symmetry of Fermi surfaces. The good agreement between experiments and theoretical modeling reveals the critical role of Fermi surface topology and convexity on the nonlinear magneto-response. These results lay a new path to explore ramifications of distinct fermiology for nonlinear transport in condensed-matter.
TaAs as one of the experimentally discovered topological Weyl semimetal has attracted intense interests recently. The ambient TaAs has two types of Weyl nodes which are not on the same energy level. As an effective way to tune lattice parameters and electronic interactions, high pressure is becoming a significant tool to explore new materials as well as their exotic states. Therefore, it is highly interesting to investigate the behaviors of topological Weyl fermions and possible structural phase transitions in TaAs under pressure. Here, with a combination of ab initio calculations and crystal structure prediction techniques, a new hexagonal P-6m2 phase is predicted in TaAs at pressure around 14 GPa. Surprisingly, this new phase is a topological semimetal with only single set of Weyl nodes exactly on the same energy level. The phase transition pressure from the experimental measurements, including electrical transport measurements and Raman spectroscopy, agrees with our theoretical prediction reasonably. Moreover, the P-6m2 phase seems to be quenched recoverable to ambient pressure, which increases the possibilities of further study on the exotic behaviors of single set of Weyl fermions, such as the interplay between surface states and other properties.
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