Ab initio theory of complex electronic ground state of superconductors: II.

Abstract

a b s t r a c tBased on Q, P-dependent modification of the Born-Oppenheimer approximation (BOA), the ab initio theory of complex electronic ground state of superconductors is presented. As an illustrative example, application of the theory to superconductors of a different character and to the corresponding nonsuperconducting analogues is presented. It is shown that due to electron-phonon (EP) interactions, which drive system from adiabatic into antiadiabatic state, adiabatic translation symmetry is broken and system is stabilized in antiadiabatic state at distorted geometry with respect to adiabatic equilibrium high-symmetry structure. Stabilization effect in the antiadiabatic state is due to strong dependence of the electronic motion on the instantaneous nuclear kinetic energy, i.e. on the effect that is neglected on the adiabatic level within the BOA. At distorted geometry, antiadiabatic ground state is geometrically degenerated with fluxional nuclear configurations in the phonon modes that drive system into this state. It has been shown that until the system remains in antiadiabatic state, nonadiabatic polaron-renormalized phonon interactions are zero in the well-defined k-region of reciprocal lattice. This, along with geometric degeneracy of the antiadiabatic state, enables formation of mobile bipolarons that can move over lattice as supercarriers without dissipation. Moreover, it has been shown that due to EP interactions at transition into antiadiabatic state, k-dependent gap in one-electron spectrum has been opened. Gap opening is associated with shift of the original adiabatic Hartree-Fock orbital energies and with the k-dependent change in density of states of particular band(s) at Fermi level. Corrected one-particle spectrum enables to derive thermodynamic properties in full agreement with corresponding thermodynamic properties of superconductors.Based on the complex ab initio theory, it has been shown that Frö hlich's effective attractive electron-electron interaction term represents correction to electron correlation energy at transition from adiabatic into antiadiabatic state due to EP interactions. It has been shown that increased electron correlation is a consequence of stabilization of the system in superconducting electronic ground state, but not the reason for its formation.

Fröhlich polaron and bipolaron: recent developments

“…Moreover electronic nanoscale disorder and long-range strain fields can interweave with the microscopic mechanisms of polaronic transport (Phillips et al , 2003). Hence ab-initio calculations of the phonon spectrum, EPI and polaron properties beyond the adiabatic Born-Oppenheimer approximation are required in many cases for which the theory and experiment can be compared in detail (Banacky , 2008;Shluger and Stoneham , 1993).…”

Microscopic insight into the pump–probe relaxation dynamics of superconductors: Model study of MgB2 relaxation within nonlinear response theory

“…on nuclear dynamics. It is a problem beyond the Born-Oppenheimer approximation (BOA), and it was studied [21][22][23][24] in details. We present here the final form of corrections to zero and one-particle electronic energy terms, which are the consequence of non-adiabatic electron-vibration coupling, and are relevant for our model.…”

“…In these circumstances, not only is Migdal-Eliashberg (ME) theory invalid (ME holds true only if E F is much larger than any other energy scale of the system) [38,39], but BOA is suddenly broken. Anti-adiabatic theory [21][22][23] reflects this possibility and the calculated [25] correction to the ground state energy, see Equation (1), is in this case     and the system obeys the adiabatic condition with nuclear geometry, as it corresponds to the equilibrium structure on an adiabatic level (Figure 1a). It should be stressed that the remaining optical phonon modes in MgB 2 (i.e.…”

Large diameter multiwall nanotubes of MgB2: Structural aspects and stability of superconducting nanotubular magnesium boride

“…The electronic BS of bulk MgB 2 is unstable in electron-phonon (EP) coupling to B-B stretching vibrations in the E 2g phonon mode, e.g., see Refs. [35,36]. Figure 4 Electronic band structure of a two-wall MgB 2 nanotube: (a) at equilibrium geometry and (b) with an induced instability, fluctuation of the s-band across the Fermi level with electron-phonon coupling to the E 2g phonon mode for B-atom displacements of AE0.032 Å/atom in the stretching vibration mode.…”