Nuclear and electron spins in a quantum wire may spontaneously form an ordered state at very low temperatures, according to work recently carried out by an international team of physicists. The team was studying the conductance of gallium-arsenide quantum wires and discovered that, at temperatures of 0.1 K and lower, the conductance of the wires dropped below the universal quantized value. This reduced quantization is explained using a theoretical model that proposes that the nuclear and electron spins order themselves in a helical formation at these temperatures.
A queue of electrons
A quantum wire confines electrons to a single direction of movement. As a consequence, and unlike a regular wire, its conductance is quantized – the flow of current is not proportional to the voltage applied. The conductance takes discrete values in multiples of 2e2/h where e is the elementary charge and h is Planck’s constant. The factor of two comes from the fact that the spin of electrons in an unordered state can take one of two values.
Dominik Zumbühl from the University of Basel in Switzerland, along with colleagues at Harvard and Princeton universities in the US, measured the conductance of gallium-arsenide quantum wires at temperatures ranging from 20 K to 0.01 K. They noted that, at the higher temperatures, the wires did indeed exhibit the universal quantized conductance in units of 2e2/h. At lower temperatures, however, they saw something new.
Bringing order to randomness
“Conductances in gallium-arsenide quantum wires had previously been measured only down to 0.3 K,” explains Zumbühl. “It is very difficult to cool such samples to temperatures as low as 0.01 K. A significant amount of work went into filtering and thermalizing both the electrical wires and the sample.” When the scientists reduced the temperature of the system to 0.1 K, the conductance of the wires dropped by a factor of two to e2/h. The conductance was unaffected by moderate magnetic fields and remained at this value as the temperature was lowered further to 0.01 K. This is interpreted as being caused by the spontaneous ordering of the electron and magnetic spins within the quantum wire.
According to a 2009 model developed by Daniel Loss of the University of Basel and colleagues, if the spins inside a quantum wire spontaneously align in the shape of a helix, the conductance should be lowered by a factor of two from its universal quantized value. After considering several alternatives, Zumbühl and colleagues concluded that such a helical spin arrangement was the most likely cause of the observed phenomenon.
Commenting on the paper for the Journal Club for Condensed Matter Physics, Leon Balents of the University of California, Santa Barbara writes, “This proposal [the helical interpretation] explains the insensitivity to [magnetic] fields, and roughly the right temperature scale for the experiment. While conceptually simple, the idea is audacious and I for one am amazed it might be true!”
Direct measurements of spin ordering needed
The spontaneous ordering of nuclear spins has been observed experimentally before, but only at even lower temperatures, typically in the microkelvin range, and never in quantum wires. Should Zumbühl and colleagues’ interpretation, that the drop in conductance is caused by spin ordering, be correct, writes Balents, “spontaneous nuclear magnetism is occurring at a temperature 50 times higher here”. He exercises some caution, though, explaining that the connection to nuclear ordering is circumstantial and that “nothing attributable to the proposed spin helix was observed”.
Zumbühl agrees. “Our data stem from electrical measurements alone with no direct nuclear spin data. More experiments are needed to investigate the nuclear spins,” he says. However, he further explains that the researchers have “data that agree with the helical model without contradictions, while other known models prove to be inconsistent with our observations. We show evidence for a novel state of quantum matter consisting of a system with helical electron spin tightly linked with a nuclear spin helix.”
This electron–nucleus coupling, according to Zumbühl, is at the heart of the arrangement that allows the reduced conductance to manifest at higher temperatures than before. Applying a gate voltage on the wire can expel the electrons, dissolving the electron–nucleus coupling and consequently the helical order. “The reason for the exceptionally high nuclear ordering temperature”, Zumbühl explains, “is the 1D nature of the wire and the resulting strong electron–electron interactions.”
Of course, Zumbühl admits, there remain unanswered questions. “In addition to probing the phenomenon magnetically, we also want to understand the timescales for electron and nuclear magnetization build up and decay, upon admitting or removing the electrons with a gate,” he says.
“Regardless,” notes Balents, “the observation is a dramatic one, and it is an impressive experiment.”
The research is published in Physical Review Letters.