Author: Manuel Suárez-Rodríguez just completed his PhD in the Nanodevices Group at CIC nanoGUNE. Currently, he is a postdoctoral researcher at the Materials Physics Center (CSIC – UPV/EHU).

When Georg Ohm wired up pieces of copper in 1827, he struck a rule so robust that it still underpins every phone and supercomputer on Earth: double the current, double the voltage. Simple, linear, universal—or so we thought. Over the past decade physicists have discovered that this bedrock principle crumbles the moment a crystal loses a particular kind of mirror-like balance known as inversion symmetry. Tip such a material slightly out of symmetry and electrons begin to behave asymmetrically, producing voltages that rise with the square of the current instead of its first power. In other words, the current–voltage graph bends into a parabola, signalling the breakdown of Ohm’s law.

Researchers at CIC nanoGUNE, working with collaborators at Donostia International Physics Center and Centro de Física de Materiales institutes, have just published ¹ the first broad survey of this frontier in Nature Materials. The review maps the terrain from the fundamental physics to the earliest device concepts, and explains why symmetry matters so much for tomorrow’s electronics.

symmetry-broken

Artistic representation of the breakdown of Ohm’s law and the resulting nonlinear effects in a non-centrosymmetric crystal. Illustration: Manuel Suárez-Rodríguez

Why symmetry rules electronics

Most everyday conductors possess inversion symmetry: flip their atomic lattice through a point, and it looks identical. That innocuous property guarantees that electrons travelling left or right feel the same environment, making the voltage rise linearly with current. Break the inversion symmetry, however, and the two directions are no longer equivalent; the crystal itself acts like a built-in diode. Add time-reversal symmetry (the rule that physics runs the same backwards) and things get even richer: magnetic fields or internal magnetisation can further skew the flow.

Put simply, once inversion symmetry is broken the crystal adds two brand-new “gears” to its electrical gearbox. One kicks in by itself, producing a voltage that bends upward with the square of the current—this is the non-linear conductivity (NLC) mode. The other gear engages only when you throw a magnetic field into the mix, giving another quadratic response called non-linear magnetoconductivity (NLMC).

A tour of symmetry-broken matter

Polar materials—whose lattices have a built-in “up-down” axis—were the first to reveal NLC. In 2018 tungsten ditelluride (WTe₂) shocked researchers by generating a transverse voltage in the absence of magnetic fields, the first Hall effect ever recorded under strict time-reversal symmetry ² ³.

Chiral crystals take asymmetry a step further. Like left and right hands, their mirror images cannot be superimposed. In elemental tellurium, where atoms spiral into left- or right-handed helices, the review authors themselves showed that both NLC ⁴ and NLMC ⁵ ⁶ flip sign when you switch from a left- to a right-handed crystal—an on-board “chirality meter.” Similar handedness can be engineered in van der Waals materials simply by stretching or twisting atomic layers ⁷.

Even bulk crystals that look perfectly symmetric reveal an imbalance at their surfaces. In topological insulators and oxide two-dimensional electron gases, electric current flows through a skin only nanometres thick—an intrinsically inversion-broken region. Gate voltages can turn this surface transport on and off, making it a versatile platform for sensing technologies.

Magnetic crystals add one more twist: they combine inversion breaking with internal magnetic order, opening an “anomalous” NLMC channel, where the magnetic order plays the role of an external magnetic field. In antiferromagnetic CrSBr, the review team demonstrated that the non-linear voltage can be reversed either by switching the magnetisation or by flipping the Néel vector, underscoring the effect’s promise for magnetic memory and logic devices ⁸.

From hidden geometry to practical signals

Where do these exotic voltages come from? Part of the answer lies in quantum geometry. In non-magnetic, centrosymmetric lattices, the Berry curvature—imagined as a magnetic field in reciprocal space—forms hills and valleys that average to zero. Break the symmetry and the landscape tilts, creating a net “dipole” that drives electrons sideways when a current distorts their distribution. Add a magnetic field and the curvature itself shifts, producing still richer responses tied to the so-called Berry-connection polarizability. Extrinsic mechanisms, in which impurities deflect electrons preferentially in one direction, often amplify the intrinsic signal.

Because each mechanism scales differently with the electron-scattering time, experimentalists can disentangle them by varying temperature and applying a gate voltage (which alters the scattering time), or carefully analysing how the non-linear voltage depends on crystal orientation and magnetic field. That detective work is now well underway in labs worldwide.

Two technological frontiers

Spintronics. In non-centrosymmetric materials with strong spin–orbit coupling, traveling electrons align their spins in a preferred direction—a phenomenon predicted by Edelstein in 1990. NLMC measurements offer a clean electrical probe of these spin textures. By tracking how the second-harmonic voltage varies with the angle of an applied magnetic field, researchers can read out the texture directly, paving the way for purely electrical information-readout technologies.

Microscale energy harvesters. Conventional radiofrequency (RF) rectennas rely on Schottky diodes, whose efficiency plummets below a threshold voltage. Non-centrosymmetric materials bypass that limit: the crystal itself rectifies the incoming wave—no diode required. The review authors have demonstrated RF rectification in tellurium without an antenna, shrinking the device dimensions to micrometre scales—a boon for self-powered, miniaturized sensors ⁹. Although current efficiencies remain modest, theory predicts sharp gains as researchers optimize resistivity and absorption. Moreover, these materials can be tuned to operate across an exceptionally broad spectrum, from RF through the far-infrared, including the visible and terahertz regimes.

The road ahead

For now, the message is clear: symmetry—often viewed as a mathematical nicety—turns out to be a powerful engineering tool. Break it thoughtfully and Ohm’s old straight line bends into curves that light up spins, harvest energy, and perhaps one day drive quantum circuits. After two centuries of linear thinking, electricity has learned a few new tricks.

The BRTA is a consortium that remains a step ahead of future socio-economic challenges worldwide and in the Basque Autonomous Community; it addresses them through research and technological development, thus projecting itself internationally. The BRTA centres collaborate to generate knowledge and transfer it to Basque society and industry so as to make them more innovative and competitive. The BRTA is an alliance of 17 R&D centres and cooperative research centres with the support of the Basque Government, the SPRI and the Chartered Provincial Councils of Araba, Bizkaia and Gipuzkoa.

References

Manuel Suárez-Rodríguez, Fernando de Juan, Ivo Souza, Marco Gobbi, Fèlix Casanova & Luis E. Hueso (2025) Nonlinear transport in non-centrosymmetric systems Nat. Mater. (2025). doi: 10.1038/s41563-025-02261-3 ↩
Ma, Q. et al. (2018) Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565, 337–342 ↩
Kang, K., Li, T., Sohn, E., Shan, J. & Mak, K. F. (2019) Nonlinear anomalous Hall effect in few-layer WTe₂. Nat. Mater. 18, 324–328 ↩
Manuel Suárez-Rodríguez, Beatriz Martín-García, Witold Skowroński, F. Calavalle, Stepan S. Tsirkin, Ivo Souza, Fernando De Juan, Andrey Chuvilin, Albert Fert, Marco Gobbi, Fèlix Casanova, and Luis E. Hueso (2024) Odd Nonlinear Conductivity under Spatial Inversion in Chiral Tellurium Phys. Rev. Lett. doi: 10.1103/PhysRevLett.132.046303 ↩
Calavalle, F. et al. (2022) Gate-tuneable and chirality-dependent charge-to-spin conversion in tellurium nanowires. Nat. Mater. 21, 526–532 doi: 10.1038/s41563-022-01211-7 ↩
Suárez-Rodríguez, M. et al. (2025) Symmetry origin and microscopic mechanism of electrical magnetochiral anisotropy in tellurium. Phys. Rev. B 111, 024405 doi: 10.1103/PhysRevB.111.024405 ↩
Du, L. et al. (2021) Engineering symmetry breaking in 2D layered materials. Nat. Rev. Phys. 3, 193–206 ↩
Jo, J. et al. (2025) Anomalous nonlinear magnetoconductivity in van der Waals magnet CrSBr. Adv. Mater. 37, 2419283 ↩
Suárez-Rodríguez, M. et al. (2024) Microscale chiral rectennas for energy harvesting. Adv. Mater. 36, 2400729 doi: 10.1002/adma.202400729 ↩

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