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

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.

References in corpus (9)

• Quantum transport evidence for a three-dimensional Dirac semimetal phase in Cd3As2
• Atomic Collapse and Quasi-Rydberg States in Graphene
• Observation of Efimov Resonances in a Mixture with Extreme Mass Imbalance
• Evidence for a Strong Topological Insulator Phase in $\mathrm{ZrT}{\mathrm{e}}_5$
• Lifshitz transition mediated electronic transport anomaly in bulk ZrTe5
• Vacuum polarization of graphene with a supercritical Coulomb impurity: Low-energy universality and discrete scale invariance
• Induced anomalous Hall effect of massive Dirac fermions in ZrTe5 and HfTe5 thin flakes
• Tunable discrete scale invariance in transition-metal pentatelluride flakes
• Evolution with Magnetic Field of Discrete Scale Invariant Supercritical States in Graphene

Cited by in corpus (1)

• Atomic collapse of high-order singular potentials in graphene