Researchers from Purdue University have demonstrated a phase transition that crosses two different phase categories, a result never observed before and one that could in time profoundly influence our understanding of matter and phases of matter. The transition from a topologically ordered to a broken symmetry phase was unexpected, and came while the scientists were studying gallium arsenide under both extreme pressure and at temperatures reaching 12mK.

“To our knowledge, a transition across the two groups of phases had not been unambiguously demonstrated before, and existing theories cannot describe it,” says Gábor Csáthy, an associate professor in Purdue’s Department of Physics and Astronomy who led the research. “It is something like changing water from liquid to ice, except the two phases we saw were very different from one another.”

A phase is a certain organization of matter. The ice, liquid and gas phases are well known. Lesser-known phases include magnetic ones that store data in electronic devices and liquid crystalline phases used to create images on certain electronic displays.

“Until not so long ago we basically thought that we understood the electronic phases in a very beautiful and relatively simple theory called Landau’s theory,” says Csáthy. Landau established his theoretical framework in 1937 and scientists used it exclusively to classify and explain phases until the late 1980s, when researchers discovered a set of phases that did not fit the theory. Those phases occurred at very low temperatures and are now called topological phases. Traditional phases, as classified by Landau, are called broken symmetry phases. Phase transitions are commonly recorded within one of these classifications but not across them, as seen in the Purdue research.

Topological phases have become an area of focus in the field of condensed matter physics because of special properties and potential technological applications. Csáthy specializes in the study of topological phases in semiconductors and his research aims to discover and characterize rare topological phases. The two-dimensional electron gas confined to ultrapure gallium arsenide semiconductor crystals he studies exhibits more than 100 different electronic phases or arrangements of electrons. Csáthy and his research partner Michael Manfra, a professor of Physics and Astronomy, Materials Engineering, and Electrical and Computer Engineering, have been collaborating on projects since 2009. The two-dimensional electron gas experiment in question began in April 2014.

“Our gallium arsenide is unique among semiconductors and other novel materials due to its extremely low level of disorder,” Manfra says. “The extremes required for this science—extreme purity, extreme temperatures—are not easily achieved, but it is worth the effort to discover new phenomena involving the entire sea of electrons acting in concert. This is the biggest kick for scientists like us and why we try to push our experimental techniques to the absolute limit.”

The team uses two cryogenic systems in the experiment, one to initially characterize the two-dimensional electron gas and another in combination with extreme pressure to trigger topological transitions within the crystals. Manfra grows the gallium arsenide crystals using a molecular beam epitaxy technique and thereafter tests for purity in a helium-3 system. At this point, his team can grow an individual wafer in about four hours, or two per day, though it required upwards of six months to condition the system for this level of purity. Initial wafer characterization follows the growth period. Within a day the team can characterize electron mobility, a process that basically measures how much disorder is inside the lattice.

“If the material system is heavily disordered then the electron motion is dominated by bumping into impurities and defects in the lattice,” says Manfra. “They can be of all different types, but let’s just say you had a road and the cars are going down the road and you stuck a telephone pole right in the middle of the road. Obviously, the cars would have to go around it. That’s sort of the analogy we have when we think of disorder in the crystal. If we just stuck a telephone pole— which means not a gallium or an arsenic atom—in there, we’d have a real problem with electron transport. So, our goal is to come up with novel techniques and designs in order to minimize the amount of disorder in the crystal.”

Manfra’s team uses a top-loading He3 system from Janis Research Co, Inc. (CSA CSM) for testing. The fridge has a small vessel (a few cubic centimeters) in its magnet space, where researchers condense liquid helium-3 at 1.5K until a little pool forms. Researchers then reduce the vapor pressure and bring the helium-3 down to 300mK. The system is non-circulating and produces a finite amount of helium-3, therein restricting the time available to researchers for experiments. “We can stay at 300mK for about 24 hours. So we do some fast measurements to see what’s going on with the samples and then we warm them back up and measure the next set of samples, Manfra says. “The good side of that is that it doesn’t take so much time to recycle samples from 300K [to] room temperature [and back] down to .3K. We can do that in a matter of four hours. So, we trade base temperature for speed of measurement and speed of recycling the samples.”

Materials grown by Manfra’s group have been shown to have an electron mobility measurement of 35 million centimeters squared per volt-second, a measurement that puts it among the highest levels of purity achieved by any group in the world.

Once Manfra’s team determines the viability of a wafer with this and other testing, the sample is brought to Csáthy’s lab where the experiment continues in a helium-3, helium-4 dilution refrigerator from Oxford Instruments. The fridge has a magnetic field of up to 12 Tesla, can drop to 12mK and includes a pressure cell that can apply up to 30 kilobar. Before placement in the fridge, the crystal wafer is cut into small pieces and wired for electricity. All the electrical wires and leads are carefully heat sunk and filtered so that no microwaves can travel along the wires and end up heating up the sample. The wafer piece is then placed in a copper pail (with attached pressure cell) that hangs inside the magnetic field. Pressure and cryogenic temperature are applied. The extremely low temperature encourages the electrons to enter into exotic states where they no longer obey the laws of single particle physics but instead are governed by mutual interactions. A collective motion of the electrons is then possible that is described by the laws of quantum mechanics instead of the laws of classical mechanics.

“In most materials, electrons are very restricted in what they can do because they bump into atomic-level defects that perturb them, scatter them and destroy fragile phases and correlated states,” Csáthy says. “The material grown by [Manfra’s team] is so pure and free from defects that it gives electrons the freedom to enter into more than 100 different phases, which is astonishing. Some of these phases simply couldn’t exist in other materials.”

Moving forward, the researchers say they will continue to explore both these newly discovered cross-phase transitions and their original research, exploring the electronic g factor, or the constant that defines how energies move in magnetic fields. Down the road, both Csáthy and Manfra say the research could lead to advances in understanding topological matter and may influence certain schemes of quantum computation, but for now they are focused on simply playing in what Manfra describes as an exciting scientific playground. “This is our bread and butter,” he says. “This is what we do.”