After 25 years:
German and American researchers were able to measure the geometric phase in solids. This phase was discovered 25 years ago by Professor Joshua Zak from the Technion and is named after him – the “Zak phase”
German and American scientists successfully measured the “Zak phase,” discovered by Professor Joshua Zak from the Technion 25 years ago. This finding was revealed in articles published in the prestigious scientific journals Nature Physics and Science.
In 1989, Professor Zak published an article in the scientific journal Physical Review Letters where he matched geometric phases to solids. In solid material there are energy bands and the electrons within them become accelerated when an electric field is applied upon them. In their motion they acquire a geometric phase (for example, the vertical angle positioning of a rope on a swing determines the phase of the swing). This phase which is acquired by the electrons was discovered by Professor Zak.
Geometric phases occur in many places in nature. One of the simplest examples is the Foucault pendulum: a tall pendulum free to swing in any vertical plane. Due to the earth’s rotation, the actual plane of swing rotates relative to the earth. It may be observed that every day the plane of rotation changes by a small “geometric” angle, associated to the spherical shape of the earth. A geometric phase in optics was discovered in 1956, by a famous Indian scientist, Shivaramakrishnan Pancharatnam. In quantum mechanics, there is a similar phenomenon which was discovered in 1984 by British physicist Sir Michael Berry who identified a geometric phase, which is now most commonly known as the “Berry phase.” Such quantum-mechanical phases can have a profound effect on material properties and are responsible for a variety of phenomena. Some examples are the dielectric polarization or the quantum Hall effect (used nowadays to define resistance standards).
Now, for the first time, scientists in the experimental group led by Professor Immanuel Bloch (from the Ludwig-Maximilians University, Munich and the Max Planck Institute of Quantum Optics Garching, Germany) in close collaboration with theoretical physicists from Harvard University, led by Professor Eugene Demler, have succeeded in measuring topological phases in one-dimensional solid-state like systems (optical lattice). This is called a Zak-phase after Professor Joshua Zak from the Faculty of Physics at the Technion.
Two objects have a different topological structure if there is no continuous way to change one into the other without having to cut it or puncture it with holes; for example, a cup of tea with one hole in its handle is topologically equivalent to a bagel, whereas a bagel and a soccer ball are not. Moreover, one can characterize different topological structures according to their geometric constructions relating to the shape of the object. But what is the connection between these geometrical phases to the properties of a real material? “Atoms in material are arranged in a manner that creates a periodic structure, in which electrons are affected by electric ion forces. As a result, the electrons ‘move’ inside the material in energy bands, which play the role of objects in the examples presented above and thus acquire a geometric phase,” explains Marcos Atala, a senior PhD student in the experimental group led by Professor Immanuel Bloch.
In 1989, Professor Zak identified the geometrical phases in the band theory of one-dimensional solids. When a particle travels “slowly” along the energy band and completes a closed loop it acquires a geometrical phase that has significant physical consequences for the properties of materials, which can be determined by the “quantum geometry” of the crystal. Therefore the identification of the topological properties of an energy band is fundamental to the understanding its physical properties. According to Professor Bloch, this new measurement scheme establishes a new general approach for studying the topological structure in solids, and may lead to the discovery of quantum phase topologies material that has unique features which can be useful in practical applications.
“I was glad to hear that more than half a dozen researchers in the US and Germany collaborated together and were successful at measuring the phase I predicted,” commented Professor Zak. “It is very important for theorists predicting a phenomenon to have his/her theory measured in an experiment. And this measurement has transformed my theory into practice.”
When developing the Zak phase, Professor Zak used additional discoveries he made in 1967 (kq-representation). The kq-representation is a fundamental discovery in quantum mechanics also named after him – Zak Transform – which is in practice till today in signal processing. Tens of thousands of engineers employ it in their work.
