Emptying Dirac valleys in bismuth using high magnetic fields

Abstract

The Fermi surface of elemental bismuth consists of three small rotationally equivalent electron pockets, offering a valley degree of freedom to charge carriers. A relatively small magnetic field can confine electrons to their lowest Landau level. This is the quantum limit attained in other dilute metals upon application of sufficiently strong magnetic field. Here we report on the observation of another threshold magnetic field never encountered before in any other solid. Above this field, Bempty, one or two valleys become totally empty. Drying up a Fermi sea by magnetic field in the Brillouin zone leads to a manyfold enhancement in electric conductance. We trace the origin of the large drop in magnetoresistance across Bempty to transfer of carriers between valleys with highly anisotropic mobilities. The non-interacting picture of electrons with field-dependent mobility explains most results but the Coulomb interaction may play a role in shaping the fine details.

Critical point for Bose–Einstein condensation of excitons in graphite

“…In a compensated semimetal, charge neutrality does not impede a concomitant evolution of the density of electrons and holes with increasing magnetic field across the quantum limit. This is indeed what happens in semimetallic bismuth at high magnetic fields: at 30 T, the carrier density increases to more than five times its zero field value (42). However, this is unlikely to happen in graphite because of its band structure (30, 31) ( Fig.…”

Magnetic field-induced electronic phase transition in the Dirac semimetal state of black phosphorus under pressure

“…In Dirac electron systems, Zeeman energy results in an energy shift in the n = 0 Landau level instead of a splitting [36,37]. Anomalous transport behaviors can emerge as the chemical potential touches the bottom of n = 0 Landau level (when Zeeman energy equals E F ) [10]. However, this happens at an extremely high magnetic field $200 T in black phosphorus (using g $ 2 and E F = 11.8 meV).…”

“…Different instabilities would be induced in such highly degenerate state, like spin density wave (SDW), charge density wave (CDW) or excitonic insulator state [6][7][8]. Since the QL fields are usually quite high and beyond the experimental access in metals, such instabilities are mostly observed in a few low-carrier-density materials such as graphite [6][7][8], bismuth [9][10][11] and doped SrTiO 3 [12]. The recently discovered topological semimetal, a family of 3D topological materials including Dirac semimetal, Weyl semimetal and node-line semimetal [13][14][15][16][17][18][19][20][21][22], serves as a good system to test the behaviors of 3D pseudorelativistic electron gas under high magnetic field, as its members usually have low QL fields and weak impurity scatterings [23][24][25].…”

Investigation of growth characteristics and semimetal–semiconductor transition of polycrystalline bismuth thin films

“…Nagao et al found that the property of metal surface states was identical with varied thicknesses and then confirmed that the metal states were formed by spin-orbitalsplit surface states (Nagao et al, 2004;Hirahara et al, 2006). In addition, Bi is also a key element of many functional materials such as topological insulators, thermoelectric materials, valleytronic materials and superconductors Poudel et al, 2008;Zhu et al, 2011Zhu et al, , 2017. Therefore, Bi has recently attracted renewed interest and has become one of the hot research topics.…”