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URL : https://hal.archives-ouvertes.fr/jpa-00213853

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, Fermi surface of Sodium in the first Brillouin zone of the body centered cubic lattice from Lee [5]. b) Fermi surface of lead in the first Brillouin zone of a cubic face centered Bravais lattice

, Schematic representation of the typical band structure of metals, semi-conductors, semi-metals, zero-gap systems and insulators. Examples of materials corresponding to each class are indicated. Figure from, vol.7

]. .. , Evolution of the electronic density of states and band structure with increasing doping in a semi-conductor. Doping increases from a to e. Coloured area represents filled states

. .. , 13 2.2 Illustration of an Umklapp inter-electronic collisions on a top view of the Fermi surface of WP 2 . The arrows illustrate wave-vectors during an interband Umklapp and small-angle scattering event.k i,n andk f ,n are carrier momenta,k f ,2 k i,2 =q andk f ,1 k i,1 =G +q, Sketch of the evolution of the maximum phonon wave-vector with temperature. b)

, Predicted phononic thermal conductivity as a function of temperature. Regions A,B,C and D correspond respectively to the ballistic, hydrodynamic, Ziman and diffusive regimes phonons

, Quantized energy levels of a 3D electron gas in a magnetic field. The electrons are confined in Landau cylinders for B 6 = 0. Only states within the Fermi sphere, |k| < k F are occupied. b) First observation of QO in magnetization measurement (dHvA effect) of Bismuth at T = 14.2K, p.23

, zz of a kish graphite sample up to B = 90.5T at T = 1.4K from Zhu et al. [26]. Sketches show the measurement geometries. b) Field dependence of r zz /r xx . The QL as well as the three phases are indicated by dotted lines. The zero-field anisotropy reaches 500. c) (B 1 , T ) phase diagram of graphite with inputs from Zhu, dependence of the in-plane resistivity r xx and the out-of-plane resistivity r, p.41

, NG-1) of high quality. b) In-plane magnetoresistivity R xx plotted as a function of B up to B = 86T at various temperature for sample NG-1, -plane resistivity R a plotted as a function of temperature for a sample of natural graphite

. .. T-f-=-130k, Sample is a slab of dimension (0.75x0.5x6) mm 3 . The dotted vertical line indicates the value of u-InAs Fermi temperature, p.44

, Longitudinal ( j Q k B) magnetoresistance r zz as a function of magnetic field up to B = 14T for the same array of temperatures. Both datasets were acquired during the same experimental run. c) Magnetoresistance r as a function of the magnetic field for various angle q = (j Q ,B) from transverse (q = 0 ) to longitudinal (q = 90 ) geometries. Temperature was set to at T = 2.15K. d) Magnetoresistance r q plotted as r q /r q =0 as a function of the angle q = (j Q ,B) for static magnetic fields at T = 2.15K. All sets of data were acquired during the same experimental run, magnetoresistance ( j Q ? B) r xx as a function of magnetic field up to B = 14T for different temperatures. b)

, Right axis : r xx plotted as a function of magnetic field at T = 2.0K b) Logarithm of the amplitude of the QO (d r xx determined by removing a polynomial background to the magnetoresistance) plotted as log d r xx /T as a function of temperature. The straight line fit corresponds to an effective mass m ? = 0.023 ? m 0 determined at B = 3.85T. The inset shows the evolution of m ? with field. c) Evolution of the QO plotted as a function of B 1 for different angles q . The inset shows the extracted frequency of QO as a function of the angle, Left-axis : computed Fermi energy E F plotted as a function of magnetic field for u-InAs

, Inelastic electrical resistivity d r caused by phonon scattering in WP 2 (Black) and Ag (Red) as a function of T 5 . b) Inelastic thermal resistivity, dW T , in WP 2 (Black) and Ag (Red) as a function of T 3 . The ratio of the two slopes is similar for heat and charge transport

, Brillouin zone for the rhombohedral structure. c) Representation of the Fermi surface of Sb from [122]. d) Fermi surface of the electron pockets (at the L-point) and hole pockets (at the T-point) according to the Liu and Allen [121] tightbinding model. Close to the T-point the 6 ellipsoids merge to form a unique object. Experimentally no evidence allows to conclude whether or not the ellipsoids merge

, Magnetoresistance of selected semimetals ((r(B) r 0 )/r 0 ) : Sb (red), Bi (blue) and WTe 2 (green) as a function of magnetic field at T = 2K from, vol.106

, Quantum oscillations appear for B > 3T. c) Oscillating part of the resistivity d r as a function of B 1 at T = 2K. The inset shows a sketch of the Fermi surface of Sb and the direction along which the field is applied. d) Fourier transform of the oscillations, vol.106, p.83

. Millimetric-sb-sample, The full line corresponds to k, the line with markers (circles) refers to k ph and the broken line is k e . The graph is from [130]. b) The high-field thermomagnetoresistivity g 11 = L 0 T /k as a function of magnetic field

, The inset explicitly defines s and the orientation of the crystals. Note that the s=1.26mm sample displays irregular dimensions and poor orientation. b) The same r 22 plotted here as a function T 2 . The red markers refer to data from Fauqué et al. [106] with a sample geometry defined by s=0

S. Thermopower, . Xx, and . Xx-/t, as a function of temperature at fixed magnetic fields. b) Nernst coefficient n plotted as n as a function of magnetic field at fixed temperatures. d) Thermopower S XX plotted as S XX /T as a function of magnetic field at fixed temperatures. Inset shows the Fourier transform of S xx /T at T = 3.3K

, for different magnetic fields applied to S3. Data points are shown as markers while the dotted line correspond to L 0 /r(B). The Wiedemann-Franz law is satisfied if the intercept of k/T matches the dotted line in the T = 0K limit. The broken line serves as a guide for the eyes

, contribution k ph as a function of temperature for the large Sb sample. b) k e plotted as a function of temperature for the three Sb samples. c) Electronic Lorenz ratio plotted as a function of temperature for the three sample. L e /L 0 = 1 indicates the recovery of the WFL. d) Thermal resistivity (W T ) = L 0 T /k e plotted as a function of temperature for the small and large samples

, Electrical resistivity r 22 plotted as a function of T 2 in the three Sb samples. b) Thermal resistivity (W T ) plotted as a function of T 2 in the large and small Sb samples. The dotted lines correspond to fits to T 2 -resistivities. Different x-axis ranges are used in the two plots

, T ) resistivities plotted as a function of magnetic field for T = 3K. b) Quantum oscillations extracted, from top to bottom, from r 22 , k and N (Nernst coefficient) in arbitrary units. All sweeps were realised at T = 3K. The vertical dotted lines serve as guides for the eye, vol.22

, Error-bars are evaluated from both experimental noise and numerical analysis. The inset compares the Fourier transform (FT) of k (red) and r 22 at the same temperatures. Also featured as an inset is a sketch of an acoustic phonon absorbed by an electron in the N th LL scattered to the (N + 1) th LL, with temperature of the amplitude the Fourier transform of the f 1 = 100T peak in k ph (A FT (d k)) of Sb sample S3. Inset shows A FT

, The different curves correspond to different 3 He densities while the solid and open circles indicate two different experimental setups for the measurement

, Experimental points by the 45 phase method for pure 3 He. Curve A represents a saturated solution of 3 He in 4 He, curve B represents pure 3 He by Betts

, Curve C represents a solution of around 5% 4 He in 3 He, p.117

. C-=-gt, These compounds are indicated by boxes. b) Plot of the B 2 thermal T 2 -prefactor as a function of fermionic specific heat g. Data from 3 He, vol.166

, Electrical resistivity r and thermal resistivity (W T ) plotted as a function of T 2 for WP 2 . The arrows indicate the value of the residual resistivity r 0

. =-w-0-t, electrical resistivity (associated with MR scattering) r at T 2 = 75K 2 and the T 2 thermal resistivity (associated with MC collisions) at at T 2 = 75K 2 . We observe that in the vicinity of T 2 = 75K 2 , MC and boundary collisions dominates strongly over resistive scattering, p.121