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METALS, SUPERCONDUCTORS... 2009Angular dependence of the Nernst effect in elemental bismuthThe Fermi surface of bismuth consists of one pocket ofhole-like carriers with an ellipsoid shape whose long axisis along the trigonal direction, and three electron pockets,arrayed symmetrically around the hole ellipsoid (see figure89(a)) for a sketch). The electron pockets are muchmore anisotropic than the hole pocket. It is known thatin two directions the electronic bands are described by theDirac Hamiltonian [Wolf, J. Phys. Chem. Solids 25,1057(1964)]. The full volume of the Fermi surface occupies10 −5 of the volume of the Brillouin zone. One consequenceof this remarkable property is that the quantum limit can bereached for a magnetic field as low as 9 T, oriented alongthe trigonal axis. It has recently appeared that the Nernst effect(the transverse voltage induced by a longitudinal temperaturegradient, in the presence of a magnetic field) is avery sensitive probe of quantum oscillations in the vicinityof the quantum limit. Above 9 T, i.e. beyond the holequantum limit (QL), three unexpected anomalies were seenin the Nernst response of bismuth [Behnia et al., Science11, 1729 (2007)]. These anomalies were interpreted as signaturesof many-body effects. However, it has recently appearedthat the one-particle spectrum of bismuth is complex,and a small misalignment off the trigonal axis woulddrastically change the field position of the electron Landaulevels. In absence of an angular-resolved study, the additionalNernst anomalies could be explained in one-particlepicture with a small misalignment [Sharlai Mikitik, Phys.Rev. B 79, 081102(R) (2009)].In order to clarify the origins of these unexpected Nernstanomalies, we studied the angular dependence of the Nernsteffect in bismuth. For this purpose, we built our ownthermoelectric single and double rotator set-up based on apiezoelectric positionner (typical angular accuracy: 0.01 ◦ ).The orientation of the sample in the magnetic field was determinedby Hall probes. Figure 89(b)) presents the Nernstvoltage at T = 1.3 K for a magnetic field tilted in the trigonalbinary plane. The typical angular step is 0.5 ◦ . At lowfield, quantum oscillations with a main period of 0.15 T −1 ,corresponding to the hole ellipsoid can be seen. Over theangular range investigated here the QL of the hole pocketdoes not change significantly. Above the QL, we can resolvetwo quasi vertical lines in the (B, θ) plane, which aresymmetrical about θ = 0. These lines are more obvious onthe (B, θ) color map of the high magnetic Nernst voltage reportedin figure 89(c)) (deduced from figure 89(b))). Thesetwo lines define a cone which is reminiscent to the cone observedby torque [Li et al, Science, 321, 547 (2008)] andtransport measurement [Fauqué et al, Phys. Rev. B 79,245124 (2009)]. According to the recent calculation on theLandau levels spectrum of bismuth performed by [Aliceaand Balents, Phys. Rev. B 79, 081102(R) (2009)], this conecorresponds to the 0 + electron Landau level.Figure 89: (a) Sketch of the Fermi surface of bismuth: the holeand the electron pockets are respectively in red and green. (b)Nernst voltage as a function of B at T = 1.3 K for a magnetic fieldtilted in the trigonal binary plane. θ, the angle between the trigonalaxis and the magnetic field direction, varies from −8.4 ◦ to 8.5 ◦ .The curves are shifted for clarity. (c) Color map of the Nernstvoltage between 10.5 T and 28 T for a magnetic field tilted in thetrigonal binary plane. (d) Nernst voltage for θ=0 as a function ofthe magnetic field for various temperatures T = 1.3,2.3,3.4,5.5and 8.5 K.In addition to these lines, we can identify at least three additionallines inside and outside the cone. Each of these linesseems to be characterized by their own angular dispersionin the (B, θ) plane. Figure 89(d)) presents the evolution ofthe Nernst response with temperature, for a magnetic fieldoriented along the trigonal direction(θ=0). As seen in thefigure the anomalies fade away when the temperature exceeds3.4 K.In conclusion, our angular-dependent study reveals that: (i)the Nernst effect can reveal hole and electron Landau levelsspectrum (ii) the unexpected Nernst anomalies cannotbe explained by the electron Landau levels and are characterizedby their own angular dependence. The additionalNernst anomalies are unexpected in single-particle theoryand point to collective effects, which are yet to be understood.A.B. Antunes, L. MaloneH. Yang, B. Fauqué, K. Behnia (LPEM/ESPCI, Paris, France)66