Some of the most interesting quantum states appear where simple theories suggest they should not. Even-denominator fractional quantum Hall states are one example, but what makes them unusual?
When electrons are confined to a thin material, cooled to extremely low temperatures and exposed to a strong magnetic field, they can begin to behave collectively. Under these conditions, electrical resistance changes in precise steps, producing the quantum Hall effect.

In the fractional quantum Hall effect, interactions between electrons create additional states at fractional fillings. The filling factor describes how electrons occupy the available energy levels. A filling factor of 1 means the lowest level is full, while 1/2 means it is half full.

Most established fractional quantum Hall states in the lowest energy level have odd denominators, such as 1/3 or 2/5. Even-denominator states, including 1/2 and 3/4, are much rarer because simpler theories generally predict conducting behaviour at these fillings.

Even-denominator states have been seen in previous experiments but it’s probably not surprising that creating and studying them in the laboratory is very challenging. This is where the new work from Princeton University comes in.

They looked at electrons confined within a 72.5-nanometre-wide gallium arsenide quantum well and cooled to about 33 millikelvin. By changing the electron density, they could control whether the electrons behaved as a single group or as two interacting layers. They were able to identify clear states at 3/4 and 5/4, as well as a previously reported state at 3/2.

The strongest evidence came from deliberately shifting a small amount of charge from one layer to the other. The new states rapidly weakened or disappeared, showing that they depend on a nearly equal charge distribution between both layers.

The authors proposed that interactions within each layer and between the layers stabilise the states and make them possible. Their results increase the range of known fractional quantum Hall behaviour and provide a useful system for investigating how collective quantum states form. They also found hints that the 5/4 state may appear in a second, more fragile form, although that interpretation needs further testing.

The work reveals how interactions between electron layers can create unexpected quantum states, opening new opportunities to understand collective behaviour in quantum matter.