Influence of the atomic-scale inhomogeneity of the pair interaction on extracted from the STM spectra characteristics of high-TcT_c superconductors

The influence of the atomic-scale inhomogeneities of the pairing interaction strength on the superconducting order parameter and the conductance spectra measurable by STM is studied in the framework of weak-coupling BCS-like theory for two-dimensional lattice model. First of all, it is found that the inhomogeneity having the form of atomic-scale regions of enhanced pair interaction increases the ratio of the local low-temperature gap in differential conductance spectra to the local temperature of vanishing the gap $2\Delta_g/T_p$. Even in the framework of mean-field treatment this ratio is shown to be larger than the one corresponding to the homogeneous case. It is shown that the effect of thermal phase fluctuations of the superconducting order parameter can further increase this ratio. Taking them into account in the framework of a toy model we obtained the ratio $2\Delta_g/T_p$ to be $\sim 7-8$. It is found that the additional atomic-scale hopping element disorder and weak potential scatterers, which can also take place in cuprate materials, have no considerable effect on the statistical properties of the system, including the distribution of the gaps, $T_p$ and the ratio $2\Delta_g/T_p$. The second consequence of the atomic-scale order parameter inhomogeneity is the anticorrelation between the low-temperature gap and the high-temperature zero-bias conductance. The obtained results could bear a relation to recent STM measurements.Comment: 14 pages, 13 figure

All Abelian Quotient C.I.-Singularities Admit Projective Crepant Resolutions in All Dimensions

For Gorenstein quotient spaces $C^d/G$, a direct generalization of the classical McKay correspondence in dimensions $d\geq 4$ would primarily demand the existence of projective, crepant desingularizations. Since this turned out to be not always possible, Reid asked about special classes of such quotient spaces which would satisfy the above property. We prove that the underlying spaces of all Gorenstein abelian quotient singularities, which are embeddable as complete intersections of hypersurfaces in an affine space, have torus-equivariant projective crepant resolutions in all dimensions. We use techniques from toric and discrete geometry.Comment: revised version of MPI-preprint 97/4, 35 pages, 13 figures, latex2e-file (preprint.tex), macro packages and eps-file

Electron spin relaxation in graphene: the role of the substrate

Theory of the electron spin relaxation in graphene on the SiO$_2$ substrate is developed. Charged impurities and polar optical surface phonons in the substrate induce an effective random Bychkov-Rashba-like spin-orbit coupling field which leads to spin relaxation by the D'yakonov-Perel' mechanism. Analytical estimates and Monte Carlo simulations show that the corresponding spin relaxation times are between micro- to milliseconds, being only weakly temperature dependent. It is also argued that the presence of adatoms on graphene can lead to spin lifetimes shorter than nanoseconds.Comment: 5 pages, 4 figure

Spin-density induced by electromagnetic wave in two-dimensional electron gas

We consider the magnetic response of a two-dimensional electron gas (2DEG) with a spin-orbit interaction to a long-wave-length electromagnetic excitation. We observe that the transverse electric field creates spin polarization perpendicular to the 2DEG plane. The effect is more prominent in clean systems with resolved spin-orbit-split subbands, and reaches maximum when the frequency of the wave matches the subband splitting at the Fermi momentum. The relation of this effect to the spin-Hall effect is discussed.Comment: Final published for

Diverging Entanglement Length in Gapped Quantum Spin Systems

We prove the existence of gapped quantum Hamiltonians whose ground states exhibit an infinite entanglement length, as opposed to their finite correlation length. Using the concept of entanglement swapping, the localizable entanglement is calculated exactly for valence bond and finitely correlated states, and the existence of the so--called string-order parameter is discussed. We also report on evidence that the ground state of an antiferromagnetic chain can be used as a perfect quantum channel if local measurements on the individual spins can be implemented.Comment: 4 page