Tell me if you think it’s two-dimensional.” Dr. Xiu Faxian, professor of physics, held up a piece of A4-size paper. “This paper is down to only dozens of micrometers thick, but a two-dimensional object is only some layers of atoms thick, some nanometers or 1/10000 of this paper thick.”
Quantum Hall effect is one of the most important scientific discoveries in the area of condensed matter physics since the last century and so far there have been four Nobel Prizes awarded for relevant studies. However, for more than 100 years, developments related to quantum Hall effect never transcended beyond two-dimensions.
Recently, the research team led by Dr. Xiu Faxian made a major breakthrough: quantized conductivity is observed along a Weyl orbit in wedge-shaped samples of the topological semimetal Cd3As2, providing evidence of the quantum Hall effect in three dimensions.
On December 17, their findings titled Quantum Hall effect based on Weyl orbits in Cd3As2 was published online in Nature (DOI: 10.1038/s41586-018-0798-3.), Dr. Xiu Faxian being the corresponding author while Zhang Cheng, a PhD candidate in physics, Zhang Yi, a Fudan alumnus and postdoctoral fellow at Cornell University and Yuan Xiang, PhD candidate in physics being the co-first authors.
Make rules for electrons: Does 3D Hall effect exist?
Electrons, like visitorsbustling about a farmers’ market, move in random directions inside a conductor, producing heat and generating energy loss.
However, it is different in the case of a highway, where cars stay in their own lanes and head only forward so that the chance of a crash is minimized. If electrons could act the same and move in a certain order, energy loss would be significantly reduced during transmission.
As early as 130 years ago, American scientist Edwin Hall found that a voltage difference could be produced across an electrical conductor, transverse to an electric current in the conductor when an magnetic field was applied perpendicularly to the current. When restricted in a two-dimensional plane, in the presence of a strong magnetic field, electrons will move along the one-dimensional edge of a conductor, “following rules” and “acting obediently”.
However, evidence showed that quantum Hall effect only happens in two-dimensional or quasi-two -dimensional systems. “Think about this room. It has the upper and lower surfaces, and a space in the center.” Prof. Xiu pointed in the air. “So we already know that electrons move along the edge of “the ceiling” and “the floor”, one row forward and another backward like two trains passing each other along their own rail tracks. But what happens in the center space? ”
Does quantum Hall effect exist in three dimensions? If so, what would the trajectory of electrons look like?
Tilt the room and Voila!
“We were astonished to see the phenomenon in Cd3As2 nanostructures. How could it even happen in a three-dimensional system?” Dr. Xiu and his team were so thrilled as if they saw cars flying in the air when they first observed quantum Hall effect in a high-quality Cd3As2 nano sample in October 2016.
Soon they published their discovery in Nature. Later scientists in Japan and the U.S. successfully repeated the experiment after referring to the findings previously published by Dr. Xiu’s team for sample preparation. But based on the experiment result back then, the trajectory of electrons was not clear.
The team assumed that electrons might have traveled vertically from the upper surface to the lower surface, or they might have existed in both upper and lower surfaces: quantum Hall effect happen in two planes independently.
The team decided to get to the bottom of the matter. But how were they even going to do this experiment? With material as thin as 1/100 of a hair and electrons move as fast as lightning, they had no idea where to start at the beginning.
“We tilted the ‘room’!” Tiny as the their material was, the team was inspired by everyday life. Dr. Xiu’s team came up with an idea to use wedge-shape samples for variable thickness. “The roof is slanted to change the distance between the upper and lower surfaces.” Dr. Xiu gestured a trapezoid lying on its back with his fingers.
Quantum Hall steps can be calculated by measuring the magnetic field of the quantum Hall platform. As discovered in the experiment, the energy of electrons is modulated by the thickness of the sample. This indicates that the time it takes for electrons to travel changes along with the thickness of sample. Therefore, this transport though the bulk is confirmed: electrons make vertical movements according to the thickness of the sample.
“An electron travels a quarter of a loop on the upper surface and traverses to the lower surface. After going for another a quarter of a loop, it traverses back to the upper surface. Up to this point, half of a closed loop is formed and the transport suffers no energy loss. Electrons are still in the quantum state during the loop transport.” According to Dr. Xiu, the trajectory of electrons in Cd3As2 nanostructures was the Weyl Orbit in three dimensions that creates quantum Hall effect.
Voila, the secret of 3D quantum Hall effect is revealed.
Click below to watch the animated 3D quantum Hall effect:
Link to the article in Nature: https://www.nature.com/articles/s41586-018-0798-3