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Register a new userAxionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves
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In recent theoretical and experimental investigations, researchers have linked the low-energy field theory of a Weyl semimetal gapped with a charge-density wave (CDW) to high-energy theories with axion electrodynamics. However, it remains an open question whether a lattice regularization of the dynamical Weyl-CDW is in fact a single-particle axion insulator (AXI). In this Letter, we use analytic and numerical methods to study both lattice-commensurate and incommensurate minimal (magnetic) Weyl-CDW phases in the mean-field state. We observe that, as previously predicted from field theory, the two inversion- ($mathcal{I}$-) symmetric Weyl-CDWs with $phi = 0,pi$ differ by a topological axion angle $deltatheta_{phi}=pi$. However, we crucially discover that $neither$ of the minimal Weyl-CDW phases at $phi=0,pi$ is individually an AXI; they are instead quantum anomalous Hall (QAH) and obstructed QAH insulators that differ by a fractional translation in the modulated cell, analogous to the two phases of the Su-Schrieffer-Heeger model of polyacetylene. Using symmetry indicators of band topology and non-abelian Berry phase, we demonstrate that our results generalize to multi-band systems with only two Weyl fermions, establishing that minimal Weyl-CDWs unavoidably carry nontrivial Chern numbers that prevent the observation of a static magnetoelectric response. We discuss the experimental implications of our findings, and provide models and analysis generalizing our results to nonmagnetic Weyl- and Dirac-CDWs.
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Charge-density waves (CDWs) in Weyl semimetals (WSMs) have been shown to induce an exotic axionic insulating phase in which the sliding mode (phason) of the CDW acts as a dynamical axion field, giving rise to a large positive magneto-conductance. In this work, we predict that dynamical strain can induce a bulk orbital magnetization in time-reversal- (TR-) invariant WSMs that are gapped by a CDW. We term this effect the dynamical piezomagnetic effect (DPME). Unlike in [J. Gooth et al, Nature 575, 315 (2019)], the DPME introduced in this work occurs in a bulk-constant (i.e., static and spatially homogeneous in the bulk) CDW, and does not rely on fluctuations, such as a phason. By studying the low-energy effective theory and a minimal tight-binding (TB) model, we find that the DPME originates from an effective valley axion field that couples the electromagnetic gauge field with a strain-induced pseudo-gauge field. We further find that the DPME has a discontinuous change at a critical value of the phase of the CDW order parameter. We demonstrate that, when there is a jump in the DPME, the surface of the system undergoes a topological quantum phase transition (TQPT), while the bulk remains gapped. Hence, the DPME provides a bulk signature of the boundary TQPT in a TR-invariant Weyl-CDW.
We propose a two-dimensional non-Hermitian Chern insulator with inversion symmetry, which is anisotropic and has staggered gain and loss in both x and y directions. In this system, conventional bulk-boundary correspondence holds. The Chern number is a topological invariant that accurately predicts the topological phase transition and the existence of helical edge states in the topologically nontrivial gapped phase. In the gapless phase, the band touching points are isolated and protected by the symmetry. The degenerate points alter the system topology, and the exceptional points can destroy the existence of helical edge states. Topologically protected helical edge states exist in the gapless phase for the system under open boundary condition in one direction, which are predicted by the winding number associated with the vector field of average values of Pauli matrices. The winding number also identifies the detaching points between the edge states and the bulk states in the energy bands. The non-Hermiticity also supports a topological phase with zero Chern number, where a pair of in-gap helical edge states exists. Our findings provide insights into the symmetry protected non-Hermitian topological insulators.
Second harmonic generation (SHG) is a fundamental nonlinear optical phenomenon widely used both for experimental probes of materials and for application to optical devices. Even-order nonlinear optical responses including SHG generally require breaking of inversion symmetry, and thus have been utilized to study noncentrosymmetric materials. Here, we study theoretically the SHG in inversion-symmetric Dirac and Weyl semimetals under a DC current which breaks the inversion symmetry by creating a nonequilibrium steady state. Based on analytic and numerical calculations, we find that Dirac and Weyl semimetals exhibit strong SHG upon application of finite current. Our experimental estimation for a Dirac semimetal Cd$_3$As$_2$ and a magnetic Weyl semimetal Co$_3$Sn$_2$S$_2$ suggests that the induced susceptibility $chi^{(2)}$ for practical applied current densities can reach $10^5~mathrm{pm}cdotmathrm{V}^{-1}$ with mid-IR or far-IR light. This value is 10$^2$-10$^4$ times larger than those of typical nonlinear optical materials. We also discuss experimental approaches to observe the current-induced SHG and comment on current-induced SHG in other topological semimetals in connection with recent experiments.
We report intertwined Weyl phases, which come from superposing topological phases by crystalline symmetry. In the intertwined Weyl phases, an unconventional Weyl phase where Weyl points possess a higher charge (monopole charge>1) due to rotation symmetry, and a higher-order topological phase enforced by rotation symmetry, are superposed. The two phases are no longer separable, but intertwine with each other, resulting in the novel phase. Remarkably, the intertwining leads to a prominent characteristic feature of the intertwined Weyl phases: $textit{the change of Fermi-arc topology}$ in a periodic pattern, i.e., the way how Fermi arcs connect to Weyl points changes drastically with respect to surface orientation, which exhibits a periodic pattern. Such a phenomenon is absent in any individual phase alone. Moreover, we elaborate on how to emulate the intertwined double-Weyl phase in cold atoms. Our theory is quite promising for generating new topological phases based on existing ones.
Although charge density waves (CDWs) are omnipresent in cuprate high-temperature superconductors, they occur at significantly different wavevectors, confounding efforts to understand their formation mechanism. Here, we use resonant inelastic x-ray scattering to investigate the doping- and temperature-dependent CDW evolution in La2-xBaxCuO4 (x=0.115-0.155). We discovered that the CDW develops in two stages with decreasing temperature. A precursor CDW with quasi-commensurate wavevector emerges first at high-temperature. This doping-independent precursor CDW correlation originates from the CDW phase mode coupled with a phonon and seeds the low-temperature CDW with strongly doping dependent wavevector. Our observation reveals the precursor CDW and its phase mode as the building blocks of the highly intertwined electronic ground state in the cuprates.
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