New Device Directly Detects Crystal ‘handedness’, Opening Doors to Advanced Materials Design

Chirality, a property influencing diverse phenomena from chemical reactions to quasiparticle behaviour, lacks a definitive macroscopic detection method, particularly in materials exhibiting time reversal symmetry and weak circular dichroism. Nikolai Peshcherenko, Ning Mao, and Claudia Felser, all from the Max Planck Institute for Chemical Physics of Solids, alongside Yang Zhang from the University of Tennessee, now present a novel approach in their work detailing the “Chiralometer”. This mechanical detection method probes chirality by inducing an imbalance in angular momentum, generating a measurable torque. Their first-principles calculations and semiclassical transport theory reveal that temperature gradients or electric fields create uncompensated angular momentum in phonons and electrons, resulting in a macroscopic mechanical torque detectable by existing torque magnetometry and cantilever sensors. This research establishes mechanical torque as a key order parameter for chirality, potentially revolutionising fields such as orbitronics and chiral quantum technologies.

Direct mechanical detection of crystal chirality via induced angular momentum imbalance

Scientists have developed a novel method, termed the “Chiralometer”, for directly detecting crystal chirality through mechanical torque measurements. This research addresses a long-standing challenge in materials science, the lack of a macroscopic probe for chirality, particularly in systems exhibiting time reversal symmetry and weak circular dichroism.

The work demonstrates that applying a temperature gradient to insulators or an electric field to metals induces an imbalance in angular momentum within phonons and electrons, respectively. This imbalance generates a measurable macroscopic mechanical torque, estimated to be approximately 10−11 N⋅m, well within the capabilities of existing torque magnetometry and cantilever-based sensors.

Using first-principles calculations and semiclassical transport theory, researchers established a connection between chirality and mechanical torque, identifying robust signatures in chiral crystals including tellurium, silicon dioxide, and the topological semimetal cobalt silicide. The study reveals that driving a system out of equilibrium creates a non-equilibrium distribution of angular momentum carriers, such as phonons or electrons, leading to a physical rotation of the crystal lattice.

This rotation manifests as a detectable mechanical torque, effectively establishing mechanical torque as a fundamental order parameter for chirality. Specifically, the research details how a temperature gradient excites chiral phonons in insulators, while an electric field drives electrons in metals, both resulting in uncompensated angular momentum.

Calculations predict that for sample dimensions of 500μm×200μm×100μm, the resulting mechanical torque is readily measurable with current technology. The findings have significant implications for the field of orbitronics, offering a transformative tool for investigating chiral quantum materials and a wide range of physical phenomena dependent on chirality.

This innovative approach generalizes the Einstein, de Haas effect, traditionally associated with spin angular momentum, to encompass orbital angular momentum in time-reversal-symmetric systems without requiring a magnetic field. The “Chiralometer” provides a direct and unambiguous method for characterising chirality, circumventing the limitations of indirect measurements such as the chirality-induced spin selectivity effect or negative longitudinal magnetoresistance, which can be influenced by extraneous factors. The work establishes a new pathway for exploring and harnessing chirality in advanced materials.

Chiral torque generation via non-equilibrium angular momentum carriers

A mechanical detection method, termed the “Chiralometer”, forms the basis of this research into probing crystal chirality by driving angular momentum carriers out of equilibrium. First-principles calculations and semiclassical transport theory were employed to demonstrate that applying a temperature gradient to insulators or an electric field to metals induces uncompensated angular momentum in phonons and electrons, respectively.

This induced imbalance subsequently generates a macroscopic mechanical torque, estimated to be approximately τ ∼10−11N·m, which is well within the detection limits of contemporary torque magnetometry and cantilever-based sensors. The study investigates chirality in several materials, specifically identifying robust signatures in chiral crystals such as tellurium, silicon dioxide, and the topological semimetal cobalt silicide.

Researchers modelled phonon-mediated chirality probes for insulators, utilising a temperature gradient to excite chiral phonons, with laser beam illumination proposed as a convenient excitation method. The approach generalises the Einstein, de Haas effect to time-reversal-symmetric systems, probing orbital angular momentum properties without an applied magnetic field.

In equilibrium, time-reversal symmetry ensures cancellation of opposite-momentum contributions, however, driving the system out of equilibrium creates a non-equilibrium distribution of angular momentum carriers. Applying external perturbations, such as the aforementioned temperature gradient or electric field, generates this uncompensated angular momentum.

To conserve total angular momentum, this internal imbalance induces a physical rotation of the crystal lattice, resulting in a measurable macroscopic mechanical torque. Quantitative predictions were then provided for a series of chiral insulators, alongside the topological semimetal CoSi, establishing mechanical torque as a feasible order parameter for chirality.

Mechanical torque generation via non-equilibrium angular momentum carriers

Calculated mechanical torques reach magnitudes of approximately 10−11 N⋅m for sample dimensions of 500μm × 200μm × 100μm, well within the sensitivity limits of 10−18 N⋅m achievable with modern torque magnetometry and cantilever-based sensors. This work introduces the “Chiralometer”, a mechanical detection method designed to probe chirality by driving angular momentum carriers out of equilibrium.

First-principles calculations and semiclassical transport theory demonstrate that a temperature gradient in insulators or an electric field in metals induces uncompensated angular momentum in phonons and electrons, respectively. The total angular momentum of phonons is expressed as Lph = X σ Z d3q (2π)3 lσ(q) n(ωσ,q) + 1 2, where lσ(q) represents the angular momentum of band σ at momentum q and n(ωσ,q) is the phonon distribution function.

The resulting mechanical torque, τ = δLph/τrel, is derived, with τrel denoting the phonon relaxation time. Calculations reveal that the mechanical torque is dependent on the temperature gradient and the angular momentum distribution of acoustic phonon bands. For silicon dioxide, the acoustic bands exhibit contributions of both positive and negative angular momentum, leading to a non-monotonic temperature dependence of the mechanical torque when the thermal energy exceeds the maximum energy of only one band.

In the high-temperature limit, where kBT ≫ ħωD, the mechanical torque becomes temperature independent due to the equilibrium distribution function satisfying neq(ω) ≈ kBT/ħω. Conversely, at low temperatures, the torque vanishes due to the absence of thermally excited phonons in equilibrium. The study extends the concept of probing chirality to conducting systems, focusing on electric-field driving to isolate the electronic contribution.

A tight-binding model of a quasi-1D chiral crystal, consisting of three atoms per unit cell arranged helically, predicts a mechanical torque oriented along the z axis, given by τz = X n Z dk 2π e(vn(k)E) [−∂εfeq(En{k})] ln z (k). Results indicate either exponential or power law scaling with temperature, and the electronic contribution remains non-zero even at the lowest temperatures.

Mechanical Torque Reveals Chirality via Angular Momentum Imbalance

Researchers have developed a novel method, termed the “Chiralometer”, for detecting crystal chirality through mechanical torque measurements. This technique exploits the principle that applying a temperature gradient to insulators or an electric field to metals generates an imbalance in angular momentum within phonons and electrons.

The resulting uncompensated angular momentum manifests as a measurable macroscopic mechanical torque, offering a direct probe of chirality even in systems lacking strong circular dichroism. Calculations demonstrate the feasibility of detecting this torque in chiral crystals including tellurium, silicon dioxide, and the semimetal cobalt silicide.

The magnitude of the mechanical torque is linked to fundamental material properties such as the Chern number and crystal symmetry, requiring only the breaking of inversion symmetry for its emergence. Demonstrations using both a two-band lattice model and first-principles calculations for cobalt silicide predict a saturation of the mechanical torque at low temperatures, with values achievable using current torque magnetometry and cantilever-based sensor technologies.

Specifically, calculations for a one millimetre cubed sample of cobalt silicide, subjected to a moderate electric field, yield a torque of approximately 10−11 Newton metres. The authors acknowledge that their two-band lattice model explicitly breaks both time reversal and inversion symmetry, although a time-reversal invariant model can be constructed through a doubling procedure.

Future research could focus on a more complete analysis of the symmetry properties governing the torque response in both conducting and insulating systems. This mechanical torque measurement establishes a new order parameter for chirality and provides a potentially transformative tool for advancements in orbitronics and chiral quantum technologies.