Tunable discrete scale invariance in transition-metal pentatelluride flakes

Yanzhao Liu,Huichao Wang,David Mandrus,Ji-Yan Dai,Haipeng Zhu,Junfeng Wang,Yanan Li,Jun Ge,Robert Joynt,Jian Wang,Liang Li,Jiaqiang Yan

doi:10.1038/s41535-020-00290-6

Abstract

Log-periodic quantum oscillations discovered in transition-metal pentatelluride give a clear demonstration of discrete scale invariance (DSI) in solid-state materials. The peculiar phenomenon is convincingly interpreted as the presence of two-body quasi-bound states in a Coulomb potential. However, the modifications of the Coulomb interactions in many-body systems having a Dirac-like spectrum are not fully understood. Here, we report the observation of tunable log-periodic oscillations and DSI in ZrTe5 and HfTe5 flakes. By reducing the flakes thickness, the characteristic scale factor is tuned to a much smaller value due to the reduction of the vacuum polarization effect. The decreasing of the scale factor demonstrates the many-body effect on the DSI, which has rarely been discussed hitherto. Furthermore, the cut-offs of oscillations are quantitatively explained by considering the Thomas-Fermi screening effect. Our work clarifies the many-body effect on DSI and paves a way to tune the DSI in quantum materials.

Highlights

One of the most important concepts in the area of phase transitions is scale invariance
In the topological transition-metal pentatelluride ZrTe5, the quantum oscillations with log-periodicity have revealed the existence of Discrete scale invariance (DSI) in a solid-state system[10]
A schematic measurement structure of standard six-electrode-method is illustrated in the inset of Fig. 1c

Summary

INTRODUCTION

One of the most important concepts in the area of phase transitions is scale invariance. In the topological transition-metal pentatelluride ZrTe5, the quantum oscillations with log-periodicity have revealed the existence of DSI in a solid-state system[10]. It is interesting to study the log-periodic quantum oscillations in the transition-metal pentatelluride flakes with different carrier density by thickness control, which may provide insights into many-body effects on DSI. A relatively smaller scale factor λ ~ 1.6 can be extracted in the MR and Hall traces of flakes with a thickness of about 160 nm This index λ decreases with increasing the effective charge of impurities that compose quasi-bound states responsible for the DSI and the log-periodicity. This work reveals a thickness-tuned scale factor of logB quantum oscillations in ZrTe5 and HfTe5 flakes and provides a perspective on the DSI in solidstate systems

RESULTS

15 K c 30 10

DISCUSSION

METHODS

CODE AVAILABILITY