Discrete scale invariance of the quasi-bound states at atomic vacancies in a topological material

TL;DR

This paper reports the experimental observation of discrete scale invariance in quasi-bound states around atomic vacancies in HfTe5, revealing geometric states with DSI features and their magnetic field dependence, advancing understanding of atomic collapse phenomena.

Contribution

It demonstrates the existence of geometric quasi-bound states with DSI in atomic vacancies of HfTe5 and visualizes their behavior under magnetic fields, linking to atomic-collapse physics.

Findings

Quasi-bound states exhibit DSI features around vacancies.

Magnetic fields alter the energy and visibility of these states.

States shift towards the Fermi energy with increasing magnetic field.

Abstract

Recently, log-periodic quantum oscillations have been detected in topological materials zirconium pentatelluride (ZrTe5) and hafnium pentatelluride (HfTe5), displaying intriguing discrete scale invariance (DSI) characteristic. In condensed materials, the DSI is considered to be related to the quasi-bound states formed by massless Dirac fermions with strong Coulomb attraction, offering a feasible platform to study the long-pursued atomic-collapse phenomenon. Here, we demonstrate that a variety of atomic vacancies in the topological material HfTe5 can host the geometric quasi-bound states with DSI feature, resembling the artificial supercritical atom collapse. The density of states of these quasi-bound states are enhanced and the quasi-bound states are spatially distributed in the "orbitals" surrounding the vacancy sites, which are detected and visualized by low-temperature scanning tunneling microscope/spectroscopy (STM/S). By applying the perpendicular magnetic fields, the quasi-bound states at lower energies become wider and eventually invisible, meanwhile the energies of quasi-bound states move gradually towards the Fermi energy (EF). These features are consistent with the theoretical prediction of a magnetic-field-induced transition from supercritical to subcritical states. The direct observation of geometric quasi-bound states sheds light on the deep understanding of the DSI in quantum materials.