Emergent chirality-dependent electromotive force in Weyl semimetals enabled by generalized unitary transformation

In the hidden world of solid materials, electrons do not always behave like tiny, independent marbles rolling through a wire. Sometimes, they act more like a fluid, moving in ways that are dictated by the very shape of the material they inhabit. For decades, physicists have been hunting for a special class of materials called topological semimetals. These are substances where the internal structure creates a unique landscape for electrons, forcing them to move as if they were massless particles traveling at incredible speeds. Within this landscape, a specific type of material known as a Weyl semimetal stands out. Here, electrons are locked into a relationship where their direction of travel is inextricably tied to their internal spin, a property that can be thought of as a tiny, intrinsic compass needle. This locking mechanism means that if an electron moves forward, its compass needle points in a specific direction, and if it moves backward, the needle flips. This connection between motion and spin is not just a curiosity; it is the key to a new kind of electronics that could one day process information with far less energy than current technology allows.

The challenge for scientists has been to harness this connection to generate electricity from magnetic movement. In standard magnets, if you move a magnetic wall—a boundary between two regions of different magnetic alignment—past an electric current, it can push the electrons and create a voltage. This phenomenon, known as a spin-motive force, is like a generator that runs on the movement of magnetic textures rather than a spinning turbine. However, calculating exactly how this force works in the exotic environment of a Weyl semimetal has been a stumbling block. The mathematical tools used for ordinary magnets fail here because the electrons in Weyl materials are so tightly bound to their momentum that a simple rotation of the magnetic field does not simplify the problem. The complexity of the math has kept researchers from fully understanding how to extract energy from these systems or how to measure the unique properties of the electrons inside them.

A team of researchers at Azarbaijan Shahid Madani University has now cleared this mathematical hurdle by developing a new way to look at the problem. They devised a method to simplify the complex equations governing these electrons without losing the essential physics. Imagine trying to untangle a knot by first loosening one specific loop and then cutting away the excess string to see the core shape; this is what the team did with the mathematics. They applied a series of transformations to the equations that describe the electrons, effectively stripping away the complicated sideways movements that were obscuring the view. This allowed them to isolate the core interaction between the moving magnetic wall in the material's substrate and the electrons flowing on top of it.

Their calculations reveal a striking new rule: the voltage generated by this moving magnetic wall depends entirely on the "handedness" of the electrons. In these materials, electrons come in two varieties, distinguished by the direction their internal compass points relative to their motion. The researchers found that if the material contains an equal mix of both types of electrons, the voltages they generate cancel each other out, resulting in no net electricity. However, if there is an imbalance—a situation where one type of electron is more common than the other—a measurable voltage emerges. This means that the spin-motive force in a Weyl semimetal acts as a direct probe for this imbalance, or what scientists call chirality polarization.

The study shows that the strength of this generated voltage is not constant; it changes based on how fast the magnetic wall is moving and how wide the wall is. The researchers determined that for the effect to be strong and detectable, the magnetic wall needs to be smooth and wide enough to allow the electrons to adjust gradually as they pass through. If the wall is too sharp or the movement too sudden, the delicate quantum connection breaks down, and the effect vanishes. Furthermore, the voltage is directly proportional to the speed of the wall's motion, suggesting that faster-moving magnetic textures could generate stronger electrical signals.

This work does more than just explain a theoretical possibility; it offers a practical path forward for measuring the hidden properties of these materials. Because the voltage only appears when there is an imbalance in the electron types, scientists can now use this effect to detect and quantify chirality polarization in Weyl semimetals. This is a significant step because chirality polarization is difficult to measure with other methods. The findings suggest that by controlling the magnetic environment and the flow of current, researchers could potentially create new types of sensors or energy harvesters that rely on the unique topology of these materials. The research confirms that the interplay between magnetic motion and the locked spin of electrons in Weyl semimetals creates a distinct, chirality-dependent electrical force, opening a window into a realm where the geometry of the material dictates the flow of energy.