An exotic phase to manipulate spin

“Berry’s phase is a ubiquitous and fundamental notion in quantum physics,” says Murakawa. Berry’s phase gives rise to emergent phenomena such as the quantum version of the classical Hall effect—a transverse electrical current induced by an external magnetic field—as well as novel materials called topological insulators, which act as insulators in their bulk but conduct electricity on their surfaces.

“In quantum mechanics, an electron’s motion, behavior and state are described by its wavefunction, which is characterized by an amplitude and a phase,” explains Murakawa. “Typically, the phase reflects the time evolution of the electronic state and depends on energy and momentum terms. Berry's phase, on the other hand, is independent of time and reflects the system geometry. Geometrical information can therefore be encoded in the wavefunction and govern the motion of electrons.”

It is these geometrical properties, such as the relative orientation of an electron’s spin or momentum, that can give rise to Berry’s phase. Most commonly, Berry’s phase occurs in systems that are subjected to gradually changing cyclic processes that do not involve the transfer of heat or matter between the system and its surroundings. This condition is generally only met when the system has time to adapt its configuration to the changing conditions, such as when particles undergo rotation or translation.

“When the spin Berry's phase exists,” says Murakawa, “novel phenomena such as spin-polarized charge flow without enegy dissipation can be realized. Despite its ubiquity and importance, however, experimental observation of Berry’s phase stemming from electron spin is challenging.”

An electron’s spin can be either ‘up’ or ‘down’. In most materials, electrons in spin-up states have almost identical energy to those in spin-down states. This leads to a phenomenon called energy degeneracy, in which the two states are difficult to distinguish. In their search for real manifestations of Berry’s phase, Murakawa and his colleagues had to overcome the complication of energy degeneracy. They did so by focusing their attention on the semiconductor bismuth tellurium iodide (BiTeI)—a material with an unusual atomic structure consisting of stacked layers of its three individual component elements (Fig. 1).

The interfaces between the layers in BiTeI destroy the symmetry of the atomic lattice and give rise to a strong coupling between electron spin and motion, known as spin–orbit interaction. The overall result, known as Rashba splitting, is the removal of energy degeneracy, allowing different states to be easily observed (Fig. 2).

“Rashba semiconductors have not been applied practically until now, mainly due to the lack of an ideal system,” says Murakawa. “The three-dimensional crystal structure of BiTeI allows a Rashba spin split to occur on a bulk scale, resulting in a huge number of spin-polarized electrons.”