Fermi superlattice

Figure 1 2 1. The different types of 2.5 Lifshitz electronic topological transition (ETT) The upper panel shows the type (I) ETT where the chemical potential EF is tuned to a Van Hove singularity (vHs) at the bottom (or at the top) of a second band with the appearance (or disappearance) of a new detached Fermi surface region. The lower panel shows the type (II) ETT with the disruption (or formation) of a neck in a second Fermi surface where the chemical potential EF is tuned at a vHs associated with the gradual transformation of the second Fermi surface from a two-dimensional (2D) cylinder to a closed surface with three dimensional (3D) topology characteristics of a superlattice of metallic layers...

In the separable kernel approximation, the gap parameter has the same energy cut off h0)o as the interaction. Therefore it takes the values An (ky) around the Fermi surface in a range h(00 depending from the subband index and the superlattice wavevector ky... 

The interband pairing term enhances Tc [93-97,102] by tuning the chemical potential in an energy window around the Van Hove singularities, z =0, associated with a change of the topology of the Fermi surface from ID to 2D (or 2D to 3D) of one of the subbands of the superlattice in the clean limit. 

Figure 1 2 6. The Fermi surface of the second (red) and third subband (black) of a 2D superlattice of quantum wires near the type (III) ETT where the third suhhand changes from the one-dimensional (left panel) to two-dimensional (right panel) topology. Going from the left panel to the right panel the chemical potential EF crosses a vHs singularity at Ec associated with the change of the Fermi topology going from EF>EC to EF

If there is a superlattice, there is an additional group of forbidden energies similar to those connected with the main lattice reflections. Slater (17) has pointed out that the depression of the energy levels from the forbidden energies could be the source of energy for the formation of a superlattice if the Fermi level fell at a superlattice forbidden electron energy. He anticipated that order from this cause could be widespread. 

Fermi resonance interface modes in organic superlattices 9.2.1 Fermi resonance in molecules... 

Redistribution of the space-charge of the excited carriers is presented in Fig. 1. Therewith at low temperatures, as seen in Fig. 2, the tunable photoluminescence band maximum coincides with the difference of the quasi-Fermi levels AF, which in turn is close to the effective energy gap Eg of the doped superlattice. At... 

Figure 1. Space-charge distribution of the excited current carriers p along z-coordinate within one period of superlattice structures (a) No. 4 and (b) No. Ai as a function of the quasi-Fermi level difference AF at 20 K.

Figure 2. Dependence of the effective energy gap Eg on the quasi-Fermi level difference AF in the superlattice No. 4 at 20 K (a) and 300 K (b). Thin curves represent the quasi-Fermi level for electrons Fe relative to the top of the valence band, dashed curves correspond to the quantum energy of the spontaneous recombination spectrum maximum hvmax.

Essential changes in the concentrations of charge carriers and accordingly in the potential profile and emission spectra are observed when the quasi-Fermi level difference AF exceeds, e.g., for the superlattice No. 4 the value of 0.9 eV. Then, the chemical potential for electrons in the n-type layers becomes positive and the degeneration begins. For superlattice No. 4i it occurs at a smaller value of AF. 

There Is an additional element which appears In the case of the T1 superconductors which may be worthy of note and further speculation. We first recall that some years ago, Allender, Bray, and Bardeen (32) (ABB) proposed a specific excltonlc mechanism of superconductivity employing a model of semiconductor-metal Interfaces. In the ABB model, the metallic electrons at the Fermi energy tunnel Into the semiconductor and Cooper pair by exchanging virtual "excltons", l.e., virtual electron-hole pairs. As discussed above, the pDOS structure of Tl/2212 and Tl/2223 shows that both systems can be viewed as a metal-semiconductor (or metal-semlmetal) superlattice structure, where the CUO2 metal layers provide conduction electrons and the Tl-03-02 layers serve as low-gap semiconductors. Since the T1 s (d 2 nd 02, 03 P2 states are covalently hybridized, a virtual elicitation from the non-bonding Px,y states of 02 and 03 to the anti-bonding T1 s (d Pz state may... 

Fig. 13. Energy-band diagram for a-Si H/a-SiN , H superlattice showing the effect of pinning the Fermi level Ef by the substrate interface states is the band-bending potential, Xo the depletion width, and the discontinuity of the conduction bands at the a-Si H/a-SiN, H interface.

The change of the physical properties at the superlattice transition suggests the formation of a gap in the electronic spectrum around the Fermi level over a large fraction of the Fermi surface. In TaSe2 it is estimated that roughly 90% of the Fermi surface is destroyed by a gap. 

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