A topological electronic crystal (TEC) in which the quantum Hall effect emerges without the need for an external magnetic field has been unveiled by an international team of physicists. Led by Josh Folk at the University of British Columbia, the group observed the effect in a stack of bilayer and trilayer graphene that is twisted at a specific angle.
In a classical electrical conductor, the Hall voltage and its associated resistance appear perpendicular both to the direction of an applied electrical current and an applied magnetic field. A similar effect is also seen in 2D electron systems that have been cooled to ultra-low temperatures. But in this case, the Hall resistance becomes quantized in discrete steps.
This quantum Hall effect can emerge in electronic crystals, also known as Wigner crystals. These are arrays of electrons that are held in place by their mutual repulsion. Some researchers have considered the possibility of a similar effect occurring in structures called TECs, but without an applied magnetic field. This is called the “quantum anomalous Hall effect”.
Anomalous Hall crystal
“Several theory groups have speculated that analogues of these structures could emerge in quantized anomalous Hall systems, giving rise to a type of TEC termed an ‘anomalous Hall crystal’,” Folk explains. “This structure would be insulating, due to a frozen-in electronic ordering in its interior, with dissipation-free currents along the boundary.”
For Folk’s team, the possibility of anomalous hall crystals emerging in real systems was not the original focus of their research. Initially, a team at the University of Washington had aimed to investigate the diverse phenomena that emerge when two or more flakes of graphene are stacked on top of each other, and twisted relative to each other at different angles
While many interesting behaviours emerged from these structures, one particular stack caught the attention of Washington’s Dacen Waters, which inspired his team to get in touch with Folk and his colleagues in British Columbia.
In a vast majority of cases, the twisted structures studied by the team had moiré patterns that were very disordered. Moiré patterns occur when two lattices are overlaid and rotated relative to each other. Yet out of tens of thousands of permutations of twisted graphene stacks, one structure appeared to be different.
Exceptionally low levels of disorder
“One of the stacks seemed to have exceptionally low levels of disorder,” Folk describes. “Waters shared that one with our group to explore in our dilution refrigerator, where we have lots of experience measuring subtle magnetic effects that appear at a small fraction of a degree above absolute zero.”
As they studied this highly ordered structure, the team found that its moiré pattern helped to modulate the system’s electronic properties, allowing a TEC to emerge.
“We observed the first clear example of a TEC, in a device made up of bilayer graphene stacked atop trilayer graphene with a small, 1.5° twist,” Folk explains. “The underlying topology of the electronic system, combined with strong electron-electron interactions, provide the essential ingredients for the crystal formation.”
After decades of theoretical speculation, Folk, Waters and colleagues have identified an anomalous Hall crystal, where the quantum Hall effect emerges from an in-built electronic structure, rather than an applied magnetic field.
Beyond confirming the theoretical possibility of TECs, the researchers are hopeful that their results could lay the groundwork for a variety of novel lines of research.
“One of the most exciting long-term directions this work may lead is that the TEC by itself – or perhaps a TEC coupled to a nearby superconductor – may host new kinds of particles,” Folk says. “These would be built out of the ‘normal’ electrons in the TEC, but totally unlike them in many ways: such as their fractional charge, and properties that would make them promising as topological qubits.”
The research is described in Nature.
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