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Thermodynamic evidence for valley-dependent density of states in bulk bismuth


Electron-like carriers in bismuth are described by the Dirac Hamiltonian, with a band mass becoming a thousandth of the bare electron mass along one crystalline axis1. The existence of three anisotropic valleys offers electrons an additional degree of freedom, a subject of recent attention2. Here, we map the Landau spectrum by angle-resolved magnetostriction, and quantify the carrier number in each valley: while the electron valleys keep identical spectra, they substantially differ in their density of states at the Fermi level. Thus, the electron fluid does not keep the rotational symmetry of the lattice at low temperature and high magnetic field, even in the absence of internal strain. This effect, reminiscent of the Coulomb pseudogap in localized electronic states, affects only electrons in the immediate vicinity of the Fermi level. It presents the most striking departure from the non-interacting picture of electrons in bulk bismuth.

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Figure 1: Angle-dependent magnetostriction measurements.
Figure 2: High-field Landau spectrum in the Bθ plane.
Figure 3: Valley-dependent DOS.


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We would like to thank C. Geibel, P. Gegenwart, J. Alicea, L. Balents, M. Doerr, B. Fauqué and Y. Fuseya for valuable discussions, as well as T. Lühmann and N. Oeschler for technical and organizational support. R.K. is supported by the DFG Research Unit 960 (Quantum Phase Transitions). K.B. is supported by ANR through the QUANTHERM project and acknowledges the hospitality of the Aspen Center for Physics.

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R.K. designed and fabricated the dilatometer and built the experimental set-up. R.K. and L.S. performed the measurements. M.B. and R.D. contributed to the data analysis. L.S., R.K. and K.B. wrote the manuscript with input from all other authors. K.B. instigated the project.

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Correspondence to R. Küchler or L. Steinke.

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Küchler, R., Steinke, L., Daou, R. et al. Thermodynamic evidence for valley-dependent density of states in bulk bismuth. Nature Mater 13, 461–465 (2014).

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