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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
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
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
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
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
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 ,