NEW CRITICAL IMPURITY DENSITY IN METAL-INSULATOR TRANSITION, OBTAINED IN N(P)- TYPE DEGENERATE HELIUM-FERMI LIQUID, BEING JUST THAT OF THE CARIERS, LOCALIZED IN EXPONENTIAL BAND TAILS. (IX)

Abstract

By basing on the same physical model and treatment method, as used in our recent work[1], we will investigate the critical impurity densities in the metal-insulator transition (MIT), obtained in n(p)-type degenerate Helium-Fermi Liquid (He-FL), being due to the effects of the size of donor (acceptor) d(a)-radius, , and the high d(a)-density, N, assuming that all the impurities are ionized even at T=0 K. In such the n(p)-type He-FL, some important remarks are obtained and discussed in the following. (i)-In Tables 1a-1d in Appendix 1, the numerical results of the isothermal bulk modulus, , the pressure variation, , and the strain-energy variation, , are obtained and computed, using Equations (2, 3). It should be noted that, for a given, those increase with increasing reduced effective mass, in good agreement with Landau’s remarks on the Fermi Liquid.[2] (ii)-In Tables 2a-5d in Appendix1, the numerical results of the critical impurity density in the metal-insulator transition (MIT), as that given in Eq. (8), by using an empirical Mott parameter , are obtained and discussed. (iii)-Further, also in Tables 2a-5d in Appendix 1, for a given , the numerical results of the density of electrons (holes) localized in the exponential conduction (valence)-band tails (EBT), , are obtained, using Eq. (26), and taking the empirical Heisenberg parameter, , as that given in Eq. (15), giving raise to: with a precision of the order of , as that given in Table 3a in Appendix 1. In other words, such the critical d(a)-density is just the density of electrons (holes) localized in the EBT, , respectively.