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Among all elements of the periodical table, elemental bismuth has the largest magnetoresistance, the highest thermoelectric figure of merit and the largest [average] diamagnetism. This intriguing solid has played an exceptional role in the history of condensed-matter physics. Numerous effects, ranging from thermoelectricity (Seebeck and Nernst effects) to quantum oscillations (Shubnikov-de Haas and de Haas-van Alphen), were first discovered in bismuth. The ultimate reason behind this is the presence of very light and extremely mobile electrons residing in three distinct anisotropic Dirac valleys.

I will review a number of recent experimental studies, which have that both Landau spectrum[1] and orbital magnetoresistance become exceptionally complex in bismuth. While most features can be explained in the band picture of non-interacting electrons, a number of unanswered questions remain. In particular, angle-dependent magnetoresistance loses the symmetry of the underlying lattice at low temperature[2]. Recent thermodynamic measurements document a valley-dependent density of states in presence of a quantizing magnetic field[3] and very recent experiments point to a phase transition to an ordered state in which the valley-degeneracy is spontaneously lost[4]. The microscopic origin of this “valley-nematic” phase transition is yet to be understood.

[1] Z. Zhu et al., PNAS 109, 14813 (2012)
[2] Z. Zhu et al., Nature Physics 8, 89 (2012)
[3] R. K&#252chler et al., Nature Materials 13, 461 (2014)
[4] A. Collaudin, B. Fauqu&#233, Yuki Fuseya, W. Kang and K. Behnia, ArXiv:1501.01584

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