Nonlinear Transport Signatures of Hidden Symmetry Breaking in a Weyl Altermagnet

TL;DR

The paper demonstrates that Ca$_3$Ru$_2$O$_7$ hosts Weyl-chain semimetal states in two competing ground-state structures, $Bb2_{1}m$ (AFM) and $Pn2_{1}a$ (altermagnet), with tiny lattice distortions evading conventional probes. By combining DFT+$U$ with SOC and Wannier-based modeling, it shows that the subtle symmetry breaking in $Pn2_{1}a$ distorts Weyl chains and drastically enhances quantum-geometric nonlinear transport, particularly a longitudinal nonlinearity along the polar axis that is absent in $Bb2_{1}m$. The nonlinear response is dominated by the quantum metric dipole (QMD), enabling a robust diagnostic of hidden order and altermagnetism, corroborated by recent experiments. This work highlights a route to identify hidden symmetry breaking through the interplay of crystal symmetry, topology, and nonlinear quantum transport, with broader implications for polar, strongly correlated materials.

Abstract

Phase transitions in solids are often accompanied by structural changes, but subtle lattice distortions can remain hidden from conventional crystallographic probes, hindering the identification of the correct order parameters. A case in point is Ca$_3$Ru$_2$O$_7$, a correlated polar ruthenate with well-characterized phase transitions, whose ground state structure has recently become a subject of debate. This uncertainty stems from extremely small atomic displacements ($\sim$0.001 Å) between competing phases, beyond the resolution of X-ray diffraction, neutron scattering, or optical second-harmonic generation. In this work, we propose a method to detect hidden symmetry breaking by leveraging nonlinear transport induced by quantum geometry. We show that Ca$_3$Ru$_2$O$_7$ is a Weyl chain semimetal in both phases. The low-symmetry phase, classified as an altermagnet by symmetry, features distorted topological surface states that are asymmetric along the polar ($b$) axis. However, the nonrelativistic spin splitting is too weak ($\sim$0.1 meV) to be resolved directly, regarding the altermagnetism. In contrast, Weyl chains generate a large quantum metric at the Fermi surface, leading to nonlinear conductivities that are orders of magnitude stronger in the low-symmetry phase. A longitudinal nonlinear conductivity along the polar axis emerges exclusively in this phase, providing a sensitive probe to qualitatively distinguish it from the high-symmetry structure and demonstrate the emergence of altermangetism, which is confirmed by a recent experiment. Our work establishes a route for identifying hidden symmetry breaking in complex quantum materials through the interplay of crystal symmetry, topology and nonlinear quantum transport.

Figures (4)

• Figure 1: Crystal structure and electronic structure of Ca$_3$Ru$_2$O$_7$ with an antiferromagnetic order. (a) Unit cell in the $Bb2_{1}m$ phase with $\tau \mathcal{T}$ symmetry. (b) Unit cell in the $Pn2_{1}a$ phase without $\tau \mathcal{T}$, showing altermagnetism. Yellow and green colors denote breathing-in and -out, respectively, octahedra inside the bilayer. (c) Effect of Hubbard $U$ on the magnetic moment per Ru atom. (d) Bulk and surface Brillouin zones. (e) Band structure of $Bb2_{1}m$ phase within LDA and $U = 2$ eV. The inset shows the symmetric Weyl chain due to crossing valence and conduction bands near the Fermi energy around the $M_1$ point. (f) Band structure of $Pn2_{1}a$ phase calculated with PBEsol and $U = 1.6$ eV.The inset shows the disorted Weyl chain near the $M_{1}$ point.
• Figure 2: Evolution of the Weyl chain with respect to the Hubbard $U$. (a) Schematic of the Weyl chain structure and band structure near $M_1$. The glide planes $\mathcal{G}_{x}$ (purple) and $\mathcal{G}_{z}$ (orange) are preserved. Band crossings between HOB and LUB are marked by purple dots (protected by $\mathcal{G}_{x}$) while the crossings between HOB and the second HOB (protected by $\mathcal{G}_{z}$) are marked by orange dots. (b-e) show the evolution of Weyl rings on $\mathcal{G}_{x}$ and $\mathcal{G}_{z}$ planes. (b-c) and (d-e) correspond to $Bb2_{1}m$ and $Pn2_{1}a$, respectively.
• Figure 3: Topological surface states (TSSs). (a) Energy spectrum along $k_{y}$ direction on the (100) surface and (b) corresponding Fermi surface contour at $E = -0.03$ eV for the $Bb2_{1}m$ phase. (c) Zoomed-in view of TSSs. Weyl nodes from $\mathcal{G}_{x}$ ring and $\mathcal{G}_{z}$ ring, are marked as purple and orange circles, respectively. (d) Energy spectrum on the (001) surface. (e-h) Same as (a-d) but in $Pn2_{1}a$ phase. The Fermi surface contour in (f) is plotted at $E$ = $E_{F}$.
• Figure 4: Nonlinear transport. (a,b) Schematics of the second harmonic generation for transverse and longitudinal transport, where the electric field $E^\omega$ generates a nonlinear current $j^{2\omega}$. The dashed line denotes the polar axis $b$. (c-f) Band structure with the projected conductivity contributed by Berry curvature dipole (BCD) and quantum metric dipole (QMD) in the $Bb2_{1}m$ phase (c,d) and $Pn2_{1}a$ phase (e,f). (g,h) The nonlinear conductivity as a function of chemical potential.