Abstract
We investigated the fundamental physical properties in the ultra-quantum limit state of bismuth through measurements of magnetoresistance, magnetization, magnetostriction, and ultrasound attenuation in magnetic fields up to 60T. For magnetic fields applied along the bisectrix direction of a single crystal, a drastic sign reversal in magnetostriction was observed at approximately 39T, which could be ascribed to the complete valley polarization in the electron Fermi pockets. The application of magnetic fields along the binary direction presented an anomalous feature at approximately 50T only in the magnetoresistance. The emergence of a field-induced splitting of a valley was proposed as a possible origin of this anomaly.
Highlights
Some materials have multiple constant energy surfaces [or Fermi surfaces (FSs)] at different positions in the reciprocal space, which are referred to as valleys
These three equivalent electron pockets are considered as three-fold degenerate electron valleys (e1, e2, e3) in zero magnetic field (Fig. 1a,b)
Their results suggested that complete valley polarization could be selectively achieved depending on the direction of the applied field: only one of the three electron valleys (e1) is occupied in magnetic fields B > 57T || binary, while two of the valleys (e2 and e3) are occupied in B > 39T || bisectrix (Fig. 1c)
Summary
Some materials have multiple constant energy surfaces [or Fermi surfaces (FSs)] at different positions in the reciprocal space, which are referred to as valleys. Zhu et al carried out angle-resolved magnetotransport measurements in bismuth up to 65T and deduced the underlying energy spectra of the Landau levels (LLs)[10] Their results suggested that complete valley polarization could be selectively achieved depending on the direction of the applied field: only one of the three electron valleys (e1) is occupied in magnetic fields B > 57T || binary, while two of the valleys (e2 and e3) are occupied in B > 39T || bisectrix (Fig. 1c). This interpretation is based on the model that takes into account quadratic B dependence in the Zeeman energy for the lowest LL, which we refer as the quadratic model in the following[11,18,20]. Magnetostriction is especially sensitive to the filling of the electronic states, and can provide us with the direct thermodynamic evidence of valley polarization in the ultra-quantum limit state as shown later
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