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Unable to Resist
Published in Sharon Ann Holgate, Understanding Solid State Physics, 2021
In reality, most Fermi surfaces are not spherical. In fact, they can have extraordinary shapes. The shape of the Fermi surface determines the electrical properties of a metal because the conductivity is due to changes in the occupancy of states near the Fermi surface. The surface shape is influenced strongly by the numbers of valence electrons of each particular metal.
Effect of Magnetic Field on the Transport Phenomena in Quantum Nanostructures
Published in Jyoti Prasad Banerjee, Suranjana Banerjee, Physics of Semiconductors and Nanostructures, 2019
Jyoti Prasad Banerjee, Suranjana Banerjee
The electrons lying on the Fermi surface take part in conduction. At T = 0 K, Fermi–Dirac (F–D) function, f(E) is a step function so that E = EF (T = 0 K) = kBTF, where TF is the Fermi temperature. In case of free electrons or electrons near the band edges, the dispersion relation is parabolic given by E=ℏ2k22m. The Fermi wave number corresponding to EF (T = 0) is kF and related to Fermi energy by EF=ℏ2kF22m or kF=2mEFℏ.
Electronic properties of metals
Published in David Jiles, Introduction to the Electronic Properties of Materials, 2017
We have discussed the concept of a Fermi energy EF and a Fermi level which is the highest occupied energy state in a metal in its ground state. Now we will generalize this idea further to the Fermi surface [1]. Excellent introductions to the Fermi surface have been given by Ziman [2] and by Mackintosh [3]. The Fermi surface is the plot of the Fermi level in three-dimensional k-space. The volume contained within the Fermi surface represents all the occupied energy levels when the material is in its ground state.
Effect of the nonmonotonic d-wave superconducting gap on the electronic Raman scattering of electron-doped cuprate superconductors
Published in Philosophical Magazine, 2020
Yuchen Zhang, Sheng Xu, Feng Yuan, Huaisong Zhao, Yong Zhou
To see this effect of the nonmonotonic d-wave SC gap clearly, the nonmonotonic d-wave SC gap function along the Fermi surface from the antinodal region to the nodal region in a quarter of Brillouin zone for B = 0 (dotted line), B = 1.0 (dashed line), B = 2.0 (dash-dotted line), B = 4.0 (solid line) with parameters , , eV, eV are plotted in Figure 1(a). Then we have calculated the electron spectral function by the electron diagonal Green's function , . The Fermi surface can be obtained by the electron spectral function at the Fermi energy . We map the electron spectral function for B = 0 (Figure 1(b)), B = 2.0 (Figure 1(c)), B = 4.0 (Figure 1(d)) in comparison with the corresponding experimental data of the hole-doped cuprate CaNaCuOCl, electron-doped cuprates NdCeCuO and PrLaCeCuO [13,20,44], respectively (inset).
Effects of a k⃗-dependent Hybridisation on the Fermi surface of an extended d–p Hubbard model
Published in Philosophical Magazine, 2020
D. M. Lalis, E. J. Calegari, L. C. Prauchner, S. G. Magalhaes
The density of states at the chemical potential can provide important information about the topology of the Fermi surface. The density of states for the region near μ is shown in Figure 3 for different sets of parameters. The evolution of for distinct dopings is shown in 3(a). For δ decreasing from 0.25 until 0.15, the density of states at the chemical potential increases. Nevertheless, for the decreases due to the presence of the pseudogap observed in the spectral function of Figure 1(d). Another important feature in 3(a), is the position of a van Hove singularity associated with the antinodal points and . When the doping decreases, the van Hove singularity crosses the chemical potential at that is the same doping for which the Lifshitz transition occurs. The effect of the interaction U on the van Hove singularity is shown in Figure 3(b). Note that the van Hove singularity crosses the chemical potential for U between and which is the same range in which the Lifshitz transition occurs due to change of the Fermi surface topology (see Figure 2(a)). In Figure 3(c), we can see that the van Hove singularity crosses the chemical potential for . Such value of is very close to the one for which the Lifshitz transition occurs as seen in Figure 2(b). In Figure 3(d), it can be noted that the hybridisation parameter is also related to the crossing of the van Hove singularity through the chemical potential, therefore, can also be used as a control parameter of the Lifshitz transition.
Theoretical study of structural, electronic and lattice dynamical properties of novel AlNiP half-Heusler alloy
Published in Philosophical Magazine, 2020
Yuhit Gupta, M. M. Sinha, S. S. Verma
The electrons in the vicinity of the Fermi energy level are mainly accountable for the presence of superconductivity in the material. Moreover, the Fermi surface (FS) plays a significant impact on the electronic band structure of metallic materials. The shape of the Femi surface reflects the arrangement of atoms and gives the path to determine the properties of the material. Therefore, the Fermi surfaces are calculated for the present HH alloy at ambient conditions and high pressure. From the analysis of electronic band structure, it is revealed that only bands crossing the Fermi level play role in the Fermi surfaces sheets. The analysis of Fermi surfaces can be made by the study of the energy distribution curve along different wave vectors in the Brillouin zone. The Fermi surfaces (FS) of AlNiP at 0 and 38 GPa are plotted for those bands which are traversing over the Fermi energy level and are shown in Figure 7. From the electronic band structure at high pressure, it is found that band structure is similar for spin-up and spin-down states, therefore, the Fermi-surfaces for both states will also be identical. Hence, the Fermi-surfaces at high pressure are only plotted for one state. The four Fermi surface (FS) sheets are obtained for each at ambient condition and high-pressure condition and are shown in Figure 7(a-d) and Figure 7 (e-h). These four FS sheets can be understood by the study of different bands in the energy band structure. The bands 8th, 9th and 10th cross over the Fermi level and thus, form three FS sheets. The first two FS sheets corresponding to bands 8 and 9 dominate towards the hole pockets at Γ point and the third FS emerged from band 10th is mainly due to electron pocket in the direction from Γ→X point. The fourth plotted FS sheet is the merged FS sheet of the other three sheets (for ambient condition as well as for high-pressure condition). The range of energy for the band 8th, 9th and 10th at ambient condition (at high pressure 38 GPa) are −3.01 eV (−4.21eV) to 0.62 eV (0.56 eV) and −2.76 eV (−3.93 eV) to 0.62 eV (0.56eV) and −0.17 eV(0.11 eV) to 1.97 eV(2.20 eV) respectively. From the electronic band structure both at ambient condition and at high-pressure conditions, the hole pocket is heavy due to the dominance of two bands (8th and 9th) as compared to the electron pocket. This heavy hole pocket criteria may cause superconductivity in the alloy. The difference in the topology of the Fermi surface occurs due to the change in interatomic distances and degree of occupancy of bands. Besides, the change in the colour of the Fermi surfaces occurs due to the variation in the velocity of electrons. The red colour present in FS indicates the high velocity of electrons and the violet colour describes the slow velocity. The intermediate colour in the Fermi surface shows the intermediate velocity of electrons.