Three-dimensional Topological Materials Research Articles

Axion electrodynamics in topological materials

One of the intriguing properties characteristic to three-dimensional topological materials is the topological magnetoelectric phenomena arising from a topological term called the θ term. Such magnetoelectric phenomena are often termed the axion electrodynamics since the θ term has exactly the same form as the action describing the coupling between a hypothetical elementary particle, axion, and a photon. The axion was proposed about 40 years ago to solve the so-called strong CP problem in quantum chromodynamics and is now considered a candidate for dark matter. In this Tutorial, we overview theoretical and experimental studies on the axion electrodynamics in three-dimensional topological materials. Starting from the topological magnetoelectric effect in three-dimensional time-reversal invariant topological insulators, we describe the basic properties of static and dynamical axion insulators whose realizations require magnetic orderings. We also discuss the electromagnetic responses of Weyl semimetals with a focus on the chiral anomaly. We extend the concept of the axion electrodynamics in condensed matter to topological superconductors, whose responses to external fields can be described by a gravitational topological term analogous to the θ term.

Observation of a Charge-2 Photonic Weyl Point in the Infrared.

Weyl points are robust point degeneracies in the band structure of a periodic material, which act as monopoles of Berry curvature. They have been at the forefront of research in three-dimensional topological materials as they are associated with novel behavior both in the bulk and on the surface. Here, we present the experimental observation of a charge-2 photonic Weyl point in a low-index-contrast photonic crystal fabricated by two-photon polymerization. The reflection spectrum obtained via Fourier-transform infrared spectroscopy closely matches simulations and shows two bands with quadratic dispersion around a point degeneracy.

Dissipation-induced topological transitions in continuous Weyl materials

Many topologically non-trivial systems have been recently realized using electromagnetic, acoustic, and other classical wave-based platforms. As the simplest class of three-dimensional topological systems, Weyl semimetals have attracted significant attention in this context. However, the robustness of the topological Weyl state in the presence of dissipation, which is common to most classical realizations, has not been studied in detail. In this paper, we demonstrate that the symmetry properties of the Weyl material play a crucial role in the annihilation of topological charges in the presence of losses. We consider the specific example of a continuous plasma medium and compare two possible realizations of a Weyl-point dispersion based on breaking time-reversal symmetry (reciprocity) or breaking inversion symmetry. We theoretically show that the topological state is fundamentally more robust against losses in the nonreciprocal realization. Our findings elucidate the impact of dissipation on three-dimensional topological materials and metamaterials.

Strain-Engineered Nonlinear Hall Effect in HgTe

As paradigmatic phenomena, Hall effects have inspired tremendous studies of symmetry and topology in condensed matter physics. Intriguingly, a second-order nonlinear Hall effect was recently proposed in noncentrosymmetric materials even in the presence of time-reversal symmetry. This effect originates from the Berry curvature dipole of electronic band structures and was predicted in Dirac and Weyl materials such as transition metal dichalcogenides and Weyl semimetals. Although it has been experimentally verified in some transition metal dichalcogenides, no obvious observation of such effects has been reported in Weyl semimetals. Taking advantage of the ideal Weyl phase with no coexisting trivial bands at the Fermi level, we use strained HgTe as a concrete example to show that the ideal Weyl semimetal is a promising platform for demonstrating the nonlinear Hall effect. Based on numerical calculations of the Berry curvature dipole, it was found that the magnitude of nonlinear Hall effect can be simply engineered by in-plane strain. Our work provides a versatile platform with high tunability, which could greatly facilitate the study of nonlinear Hall effect in three-dimensional topological materials.

Discovery of log-periodic oscillations in ultraquantum topological materials.

Quantum oscillations are usually the manifestation of the underlying physical nature in condensed matter systems. Here, we report a new type of log-periodic quantum oscillations in ultraquantum three-dimensional topological materials. Beyond the quantum limit (QL), we observe the log-periodic oscillations involving up to five oscillating cycles (five peaks and five dips) on the magnetoresistance of high-quality single-crystal ZrTe5, virtually showing the clearest feature of discrete scale invariance (DSI). Further, theoretical analyses show that the two-body quasi-bound states can be responsible for the DSI feature. Our work provides a new perspective on the ground state of topological materials beyond the QL.

Quasiparticle interference from different impurities on the surface of pyrochlore iridates: Signatures of the Weyl phase

Weyl semimetals are gapless three-dimensional topological materials where two bands touch at an even number of points in the bulk Brillouin zone. These semimetals exhibit topologically protected surface Fermi arcs, which pairwise connect the projected bulk band touchings in the surface Brillouin zone. Here, we analyze the quasiparticle interference patterns of the Weyl phase when time-reversal symmetry is explicitly broken. We use a multi-band $d$-electron Hubbard Hamiltonian on a pyrochlore lattice, relevant for the pyrochlore iridate R$_2$Ir$_2$O$_7$ (where R is a rare earth). Using exact diagonalization, we compute the surface spectrum and quasiparticle interference (QPI) patterns for various surface terminations and impurities. We show that the spin and orbital texture of the surface states can be inferred from the absence of certain backscattering processes and from the symmetries of the QPI features for non-magnetic and magnetic impurities. Furthermore, we show that the QPI patterns of the Weyl phase in pyrochlore iridates may exhibit additional interesting features that go beyond those found previously in TaAs.

Universal signatures of Fermi arcs in quasiparticle interference on the surface of Weyl semimetals

Weyl semimetals constitute a newly discovered class of three-dimensional topological materials with linear touchings of valence and conduction bands in the bulk. The most striking property of topological origin in these materials, so far unequivocally observed only in photoemission experiments, is the presence of open constant-energy contours at the boundary--- the so-called Fermi arcs. In this Rapid Communication, we establish the universal characteristics of Fermi-arc contributions to surface quasiparticle interference. Using a general phenomenological model, we determine the defining interference patterns stemming from the existence of Fermi arcs in a surface band structure. We then trace these patterns in both simple tight-binding models and realistic ab initio calculations. Our results show that definitive signatures of Fermi arcs can be observed in existing and proposed Weyl semimetals using scanning tunneling spectroscopy.

Helical Fermi arcs and surface states in time-reversal invariant Weyl semimetals

Weyl semimetals are gapless three-dimensional topological materials where two bands touch at an even number of points in the Brillouin zone. In this work we study a zinc-blende lattice model realizing a time-reversal invariant Weyl semimetal. The bulk dynamics is described by 12 helical Weyl nodes. Surface states form a peculiar quasi-two-dimensional helical metal fundamentally different from the Dirac form typical for topological insulators. The allowed direction of velocity and spin of low-energy surface excitations are locked to the cubic symmetry axes. The studied system illustrates the general properties of surface states in systems with common crystal symmetries.