Cottrell Scholar Awards - 2016
Experimental Investigation of One-Dimensional Topological Phases
Most people have been taught that matter can exist in four phases (or states) -- solid, liquid, gas and plasma. But there are additional, exotic, phases known mostly to physicists and chemists.
Sergey Frolov, assistant professor ofphysics at the University of Pittsburgh, is studying two forms of one exotic phase of matter.
He and his associates will investigate the “one-dimensional topological phase,” which in one variation manifests as a “spin helical liquid,” and in another as “topological superconductivity.” In general, the topological order of matter occurs only under extremely cold conditions – near absolute zero (-459.67 degrees Fahrenheit). In that realm, atoms and their electrons behave differently than they do in ordinary matter, a fact which greatly interests scientists such as Frolov.
The size of the matter under investigation also affects how electrons behave. Frolov is looking at topological effects in “one-dimensional” matter – that is, he is essentially concerned with electron behavior in matter that is one-atom thick. His investigations are carried out on bits of matter at the incredibly tiny nanoscale – one nanometer equals one-billionth of a meter.
Frolov’s ultimate goal, however, is to find an efficient method of producing copious amounts of an exotic material called a Majorana quasiparticle. In general terms a “quasiparticle” is a packet (quantum) of energy induced by the interaction of conventional particles that can be treated, for all practical purposes, as a particle.
As Frolov explains: “The story begins with Paul Dirac, a British physicist who managed to combine in one equation the two greatest developments of modern physics — Einstein’s Theory of Relativity and Quantum Mechanics. Dirac’s equation showed that along with matter there exists anti-matter. All properties of anti-matter are completely opposite to ordinary matter. It is as if you went through the looking glass with Lewis Carroll’s Alice. For example, an electron has a negative charge, but a positron, because it is the anti-particle of an electron, has a positive charge. A young Italian theoretician Ettore Majorana took this idea and thought about it. In the 1930s he was able to prove that there can be a particle living right on the boundary between matter and anti-matter, on the surface of a looking-glass. A notion of a Majorana fermion was born, a particle that is also its own antiparticle.”
Frolov’s work is based on the fact that an electron, besides carrying a negative electrical charge also displays a characteristic called “spin,” which relates to its angular momentum as well as its “magnetic moment,” which has to do with the strength of its magnetic field. Electron spin comes in two varieties, up or down.
A spin helical liquid, then, is a supercold state of matter in which spin-up electrons move only to the right, while spin-down electrons move only to the left. Near absolute zero, electrical resistance disappears in some materials, including the semiconductor nanomaterial Frolov will be using. (The atoms and molecules in a semiconductor are arranged in a crystalline structure, which endows them with interesting properties for transporting electrons.)
The point of using the spin helical liquid to achieve topological superconductivity of electrons lies in the fact, which Frolov has verified in a previous experiment, that Majorana quasiparticles tend to appear at the boundaries of the material.
Specifically, Frolov and his research associates will fabricate nanoscale electronic devices to explore what is called the “valence band” of their supercold nanomaterial. It is the highest range of energies in which electrons are normally present at absolute zero. The valence band is the researchers’ happy hunting ground for electron spin-orbit interaction, “the key component in both topological phases,” Frolov notes. (“Spin-orbit interaction” refers to an electron’s spin as well as its motion around the nucleus of the atom, a combination which causes shifts in its energy levels. These levels can be read by a spectrograph.)
“The ultimate evidence of new phases [of matter] is the observation of an energy gap in the electronic spectrum,” Frolov says. Essentially, he’s looking for gaps revealing the presence of Majorana quasiparticles, which have an energy level of zero because their positive and negative states cancel out.
“The realization of helical and Majorana states in a robust form will have implications for spintronics and quantum computing,” he predicts.
For the education component of the Cottrell Scholar Award, Frolov will create a laboratory course in which the facilities of Pittsburgh Quantum Institute and Petersen Institute of Nanoscience and Engineering will be used for inquiry-based training in state-of-the-art nanofabrication, nanocharacterization and quantum transport and optics studies of novel materials such as graphene, nanowires and nanotubes.
“Students will receive a first impression of how research projects proceed, get introduced to the latest research and learn valuable technical, modelling and communication skills,” Frolov said.