A sideways voltage that some crystals produce when a current flows through them, with no magnetic field – one that grows with the square of the current rather than in proportion to it. The ordinary needs a magnetic field or a magnet to push electrons sideways. Crystals lacking a centre of symmetry can do it through the quantum shape of their electrons’ states. Because the voltage follows the square of the current, it appears at twice the current’s frequency and has a steady part: it turns an alternating signal into a direct one, a rectifier with no junction.
As the site uses it
TaIrTe4 has no inversion centre in bulk, but a single layer does, so the second-order nonlinear Hall effect of its Berry-curvature dipole belongs to stacks of two layers or more.
The ordinary Hall effect needs a magnetic field. Without one, a crystal lacking inversion symmetry can still push electrons sideways if its Berry curvature is lopsided: a current shifts the occupied states and the curvature no longer cancels. The voltage follows the square of the current – twice its frequency, plus a steady part.
A Hall effect without a magnet
The ordinary Hall voltage needs a magnetic field, or the internal magnetism of a : without broken , a Hall voltage proportional to the current is forbidden. That rule applies only to the linear response. Sodemann and Fu showed in 2015 that a sideways current second order in the field – growing with the square of the applied voltage – is allowed in nonmagnetic crystals without a centre of inversion, both as a steady current and at twice the driving frequency.
Its origin is quantum geometry. Electrons in many crystals carry , which deflects them sideways as they move; with time-reversal symmetry, electrons moving in opposite directions carry opposite curvature, and the deflections cancel. A current shifts the electrons’ distribution, and if the Berry curvature is lopsided across the occupied states – a Berry curvature dipole – the cancellation is no longer complete and a net sideways current flows.
First seen in WTe2
WTe2 was the first test. A current along one crystal axis produced, with no magnetic field, a voltage across it at twice the current’s frequency and quadratic in the current; it dominated the nonlinear response along the current, a Hall angle close to 90°. Gates that set the electron density and the field across the bilayer changed its size and reversed its sign several times, and the authors traced the signal to Berry curvature carried by Dirac electrons on one layer or the other (Ma and colleagues, 2019).
In few-layer TaIrTe4 the response is present at room temperature and grows strongly on cooling: about 20 µm V−1 Ω−1 at 2 K in six layers, 350 times its room-temperature value, boosted by a that forms below 60 K (Jiang and colleagues, 2025).
A rectifier, and look-alikes
Because the voltage follows the square of the current, an alternating input gives a steady output: the effect rectifies, with no junction and no threshold. Bilayer WTe2 reached a of 104 volts per watt of input power, and rectifiers working this way at room temperature, in films that can be grown rather than exfoliated, are an open goal.
Not every sideways voltage at twice the frequency comes from a Berry curvature dipole. In the noncentrosymmetric PbTaSe2, a signal of the same kind, with no magnetic field, grows by orders of magnitude around the superconducting transition, where and antivortices carry it (Itahashi and colleagues, 2022). The symmetry of the signal shows that is broken; the mechanism needs more evidence than that.
For specialists
A transverse response second order in the driving field, allowed with time-reversal symmetry intact in crystals without inversion symmetry, in a form fixed by the point group. Its intrinsic part comes from the dipole of the Berry curvature over the occupied states, which gives current-carrying electrons a net anomalous velocity; it appears at zero and at twice the drive frequency. Bilayer WTe2 showed it first, with a quadratic current–voltage characteristic, a Hall angle near 90° and a sign that gates can reverse; few-layer TaIrTe4 shows it at room temperature, enhanced on cooling by a charge-density wave.
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