Simultaneous detection of quantum oscillations from bulk and topological surface states in metallic

Abstract

Shubnikov–de Haas (SdH) oscillations in metallic are studied in magnetic fields up to 35 Tesla. It is demonstrated that two characteristic frequencies determine the quantum oscillations of the conductivity. Angle dependent measurements and calculations of the Berry phase show that the two frequencies and describe oscillations from surface and bulk carriers, respectively. At low magnetic fields, only SdH oscillation from topological surface states can be detected whereas at high magnetic field the bulk oscillations dominate. The origin of the separation of bulk and surface SdH oscillations into different magnetic field ranges is revealed in the difference of the cyclotron masses . The bulk is nearly three times larger than the surface cyclotron mass resulting in a stronger attenuation of the bulk oscillation amplitude upon decreasing magnetic field. This makes it possible to detect and characterise the surface SdH oscillations in the low-field range and the bulk oscillations at high magnetic fields.

Keywords:

• Topological insulator
• Shubnikov–de Haas oscillations
• surface states
• bulk states

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported in part by the T.L.L. Temple Foundation, the John J. and Rebecca Moores Endowment, the State of Texas through TCSUH, the US Air Force Office of Scientific Research [grant number FA9550-15-1-0236], and at LBNL through the U.S. Department of Energy. V. M. acknowledges support from the Bulgarian National Science Fund [project FNI-T-02/26]. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by National Science Foundation [cooperative agreement number DMR-1157490] and the State of Florida. The work at Idaho National Laboratory is supported by Department of Energy, Office of Basic Energy Sciences, Materials Sciences and Engineering Division [grant number DOE FG02-01ER45872].