Rintaro Masaoka, a researcher in theoretical physics, has published a study that explores the unique properties of quadratic band touching in fermionic systems. Masaoka is affiliated with the University of Tokyo, where he conducts research in condensed matter theory. His work focuses on understanding the fundamental behaviors of quantum materials, with potential implications for the development of advanced technologies.
In the energy industry, understanding the behavior of electrons in materials is crucial for developing more efficient and advanced technologies, such as superconductors and semiconductors. Masaoka’s research delves into the behavior of electrons in materials with quadratic band touching, a phenomenon distinct from the more commonly studied linear Dirac points. This study reveals that a free-fermion model with quadratic band touching in (d+1) dimensions exhibits spatial conformal invariance. This means that the system’s properties remain unchanged under certain transformations, such as scaling and rotations.
Masaoka demonstrates that the equal-time ground-state correlation functions of this model are exactly captured by the d-dimensional symplectic fermion theory. This correspondence is established by mapping physical fermionic operators to the fields of the symplectic fermion theory. The implications of this correspondence are particularly significant in two spatial dimensions, where the symplectic fermion theory is a logarithmic conformal field theory with a central charge of c=-2.
In the corresponding (2+1)-dimensional systems, Masaoka identifies anyonic excitations originating from the underlying symplectic fermion theory. These anyonic excitations are quasiparticles that exhibit unusual statistical properties, different from the familiar bosons and fermions. Transporting these excitations along non-contractible loops generates transitions among topologically degenerate ground states, similar to those observed in topologically ordered phases. This finding suggests that systems with quadratic band touching could potentially be used to create and manipulate anyonic excitations for quantum computing and other advanced applications.
Moreover, the action of a 2π rotation on these excitations is represented by a Jordan block, reflecting the logarithmic character of the associated conformal field theory. This research provides a deeper understanding of the quantum critical behavior of systems with quadratic band touching and opens up new avenues for exploring topological phases of matter. The study was published in the journal Physical Review B, a leading publication in the field of condensed matter physics.
This article is based on research available at arXiv.