The Fractional Quantum Hall Effect Without a Magnet

To observe the fractional quantum Hall effect, physicists usually need to build an extreme environment. The standard recipe requires temperatures hovering just above absolute zero and a magnetic field stronger than the ones used in MRI machines. Under these conditions, the two-dimensional motion of electrons changes. Instead of scattering like billiard balls, they coordinate, behaving as collective quasiparticles that carry exactly one-third or one-fifth of an electron's fundamental charge.

In 2023, a research team led by Xiaodong Xu at the University of Washington bypassed the massive external magnets entirely.

By stacking two atomically thin sheets of a semiconductor called molybdenum ditelluride ($\text_2$), the researchers created a crystal lattice that generates its own internal topological state. The electrons inside the material interacted so strongly that they mimicked the fractional quantum Hall state on their own, even when the external magnetic field was dialed down to zero.

Measured.

The Moire Superlattice

To understand the measurement, one must look at the geometry of the crystal stack. The University of Washington team exfoliated single-atom-thick layers of molybdenum ditelluride from bulk crystals. They stacked two of these layers on top of each other, but with a deliberate twist.

Rotating one layer relative to the other by a tiny angle—roughly 1.6 degrees—creates a moiré pattern. This twist introduces a periodic variation in the local atomic alignment. The resulting superlattice has a much larger unit cell than the individual crystal sheets, which radically flattens the energy bands of the migrating electrons.

In a typical conductor, electrons possess high kinetic energy and fly past one another with minimal coordination. But in these flat bands, the kinetic energy of the electrons drops to nearly zero. With their motion slowed, the electrostatic repulsion between the electrons becomes the dominant physical force. The particles have no choice but to organize their movements to minimize repulsion.

Instead of an external magnetic field forcing the electrons into circular cyclotron orbits, the intrinsic spin-orbit coupling within the heavy molybdenum and tellurium atoms acts as an effective, built-in magnetic field. The system develops a spontaneous magnetic polarization. The electrons form a highly correlated quantum fluid, exhibiting what physicists call the fractional anomalous Hall effect.

Inside the Cryostat

The experimental setup required to confirm this state did not rely on indirect transport measurements alone. The researchers coupled electrical transport measurements with optical spectroscopy inside a helium-3 cryostat, cooling the sample to sub-kelvin temperatures.

The sample itself was fabricated into a dual-gated device. By adjusting the voltages on the top and bottom metallic gates, the team could continuously tune the density of the electrons in the moiré lattice.

To detect the fractional states, the team measured the Hall resistance—the voltage that develops perpendicular to the direction of the electrical current. In a classical conductor without a magnetic field, this transverse voltage is zero. In this twisted semiconductor device, as the gate voltage swept through specific electron densities, the Hall resistance did not change smoothly. Instead, it stalled, forming flat plateaus at precise quantum values.

These plateaus occurred at fractional values of the resistance quantum, specifically at $h/e^2$ multiplied by three halves or other fractional denominators. This plateauing is the exact signature of quasiparticles carrying fractional charges, such as $e/3$. The measurement confirmed that the electrons were organizing into fractionalized states purely through their mutual repulsion within the twisted lattice.

Removing the Magnet

The implications of this measurement stretch beyond cataloging a new quantum state.

In conventional fractional quantum Hall setups, the massive solenoids required to generate tesla-level magnetic fields take up entire rooms and prevent the integration of these materials into standard microelectronic chips. Removing the requirement for an external magnetic field simplifies the physical architecture needed to study topological quantum states.

Furthermore, the self-generated topological state in twisted molybdenum ditelluride is highly tunable. By simply adjusting the external gate voltages, researchers can transition the material from a normal insulator to a fractional quantum Hall state, and then into a metallic state, without physically altering the device or cycling the magnetic field.

The experiment demonstrates that the complex collective behavior of electrons, once thought to require hostile and extreme magnetic environments, can be engineered directly into the geometry of a semiconductor interface.

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