Chiralometer: Direct Torque Detection of Crystal Chirality

Abstract

Chirality governs phenomena ranging from chemical reactions to the topology of quasiparticle charge carriers. However, a direct macroscopic probe for crystal chirality remains a significant challenge, especially in time reversal symmetric systems with weak circular dichroism signal. Here, we propose the ``Chiralometer'', a mechanical detection method that probes chirality by driving angular momentum carriers out of equilibrium. Using first-principles calculations and semiclassical transport theory, we demonstrate that a temperature gradient in insulators or an electric field in metals induces uncompensated angular momentum in phonons and electrons, respectively. This imbalance generates a macroscopic mechanical torque ($τ\sim 10^{-11} N \cdot m$) well within the sensitivity of modern torque magnetometry and cantilever-based sensors. We identify robust signatures in chiral crystals such as Te, SiO$_2$, and the topological semimetal CoSi. Our work establishes mechanical torque as a fundamental order parameter for chirality, offering a transformative tool for orbitronics and chiral quantum materials.

Figures (4)

• Figure 1: (a) Schematic of the principal 'chiralometer' setup. Uncompensated angular momentum is excited by external perturbations. (b) A chiral phononic (or electronic) system with broken inversion symmetry hosts a compensated total angular momentum at equilibrium due to time-reversal symmetry. When driven out of equilibrium, the system acquires an uncompensated angular momentum, resulting in a measurable mechanical torque. (c) Non-equilibrium population imbalance between opposite chiralities.
• Figure 2: Calculated phonon dispersion and mechanical torque components for chiral crystals of (a) Te, (b) CoSi, (c) SiO$_2$, (d) PdGa. We assume a temperature gradient of $\nabla T=100\,\mathrm{K}/\mathrm{m}$ applied along the $x$, $y$ or $z$ axis (indicated by different colors) for a sample with dimensions $500\,\mu\mathrm{m}\times200\,\mu\mathrm{m}\times100\,\mu\mathrm{m}$. Here, $\tau_{ii}$ denotes the $i$-th torque component when $\nabla T$ is applied along the $x_i$ axis. Off-diagonal torque components are symmetry-forbidden phonon_ang_momentum. The colorbar represents the angular momentum of each phonon branch.
• Figure 3: (a) Schematics of a helical molecule with three atoms per unit cell. As a minimal non-trivial model, each site hosts three orbitals with angular momentum $l=1$. (b) Band structure for varying chemical potential positions, with the angular momentum of each band indicated by color. (c) - (e) Calculated mechanical torque for chemical potential values of $\mu =0.15\,\mathrm{eV}$, $0\,\mathrm{eV}$ and $0.075\,\mathrm{eV}$, respectively. The zero temperature saturation values are indicated by red dashed lines.
• Figure 4: Results of mechanical torque calculations for a two-band model and the real material CoSi. Panels (a)-(c) display the two-band model results with the chemical potential $\mu$ set to (a) $\mu=0$,(b) $\mu=0.8$, (c) $\mu=1.0$; the zero temperature saturation values are indicated by red dashed lines. Panel (d) presents the real material results for CoSi, corresponding to the angular momentum induced by electronic orbital motion. The calculations assume a driving electric field $E=10^4\,\mathrm{V/m}$ and crystal dimensions $1\,\mathrm{mm}\times 0.2\,\mathrm{mm}\times0.1\,\mathrm{mm}$. Owing to the cubic symmetry of CoSi, the response is isotropic, i.e., $\tau_{xx}=\tau_{yy}=\tau_{zz}$.