Research Progress

Emptying Dirac valleys in bismuth using high magnetic fields

author: time:2017-05-19 clicks:

Transverse magnetoresistance of a bismuth crystal up to 65T at T=1.56K. This study reveals emptying one or two Dirac valleys along bisectrix or binary respectively in bismuth around 40T lead to the drastic drops, providing clues for other low-carrier-density samples beyond their quantum limit.

(Nature Communications 8, 15297(2017))


As a traditional semimetal, bismuth plays an important role in condensed matter physics. Scientists found a lot of important physical phenomena, such as Seebeck effect, Nernst effect, quantum oscillation and giant magnetoresistance. Since the discovery of topological materials with low carrier density, the behavior of 3D electron gas in high magnetic field in that materials has been a hot research topic. And recently, some topological materials also show intriguing properties beyond quantum limit. The exploration of bismuth in high-field would shed light to these researches also other strong-correlated materials beyond their quantum limit.

What we discover?

The Fermi surface of elemental bismuth consists of three small rotationally equivalent electron pockets, offering a valley degree of freedom to charge carriers of electrons. Because of its small Fermi energy, electrons can be easily confined to their lowest Landau level, reaching its quantum limit, in a modest magnetic field approximate 9T. When the magnetic field is along its high symmetry directions, binary or bisectrix, the magnetoresistance suddenly drops at about 40T. This drastic drop in magnetoresistance had been suggested to be due to the evacuation of the hole Landau level in previous studies. By a throughout study of the magnetoresistance with angle in binary-bisectrix plane, combined with the theoretical calculation, we directly reveal the empting Dirac valley leads to the drop of magnetoresistance. When a magnetic field is beyond a threshold field, Bempty, one or two Dirac valleys will be completely empty to other Dirac valleys. As the electrons transfer from high mobility Dirac valleys to low mobility Dirac valleys, the conductance increases manyfold, eventually resulting a sharp drop in magnetoresistance.

Why is this important?

This study shows a certain magnitude of field Bemptycan empty one or two valleys, leading to the drop of magnetoresistance. It identifies bismuth as the first solid in which cyclotron energy is strong enough to dry up a Fermi sea.

Why did they need WHMFC?

In this research, to empty one or two Dirac valleys need around 40T to reveal the drop in magnetoresistance happens about 40T. The angle-dependence of magnetoresistance up to 65T can help us to reveal the details of the Landau level and the behaviors of carriers.

Who did the research?

Zengwei Zhu1,2,*, Jinhua Wang1, Huakun Zuo1, Benoît Fauqué3,4,Ross D. McDonald2, Yuki Fuseya5, and Kamran Behnia1,3

1Wuhan National High Magnetic Field Center and School of Physics,

Huazhong University of Science and Technology, Wuhan 430074, China

2MS-E536, NHMFL, Los Alamos National Laboratory,Los Alamos, New Mexico 87545, USA

3Laboratoire Physique et Etude de Matériaux (CNRS-UPMC)ESPCI Paris, PSL Research University,75005 Paris, France

4JEIP, USR 3573 CNRS, Collège de France,PSL Research University, 11 place Marcelin Berthelot,75231 Paris Cedex 05, France

5Department of Engineering Science, University of Electro-Communications, Chofu, Tokyo 182-8585, Japan


This work was supported by the 1000 Youth Talents Plan, the National Science Foundation of China (Grant No. 11574097), the National Key Research and Development Program of China (Grant No.2016YFA0401704), 111 project and our university’s high-end foreign experts project.

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