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Register a new userImpurity-Induced Virtual Bound States in d-Wave Superconductors
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It is shown that a single, strongly scattering impurity produces a bound or a virtual bound quasiparticle state inside the gap in a $d$-wave superconductor. The explicit form of the bound state wave function is found to decay exponentially with angle-dependent range. These states provide a natural explanation of the second Cu NMR rate arising from the sites close to Zn impurities in the cuprates. Finally, for finite concentration of impurities in a $d$-wave superconductor, we reexamine the growth of these states into an impurity band, and discuss the Mott criterion for this band.
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We study the effect of strong spin-orbit coupling (SOC) on bound states induced by impurities in superconductors. The presence of spin-orbit coupling breaks the $mathbb{SU}(2)$-spin symmetry and causes the superconducting order parameter to have generically both singlet (s-wave) and triplet (p-wave) components. We find that in the presence of SOC the spectrum of Yu-Shiba-Rusinov (YSR) states is qualitatively different in s-wave and p-wave superconductor, a fact that can be used to identify the superconducting pairing symmetry of the host system. We also predict that in the presence of SOC the spectrum of the impurity-induced bound states depends on the orientation of the magnetic moment $bf{S}$ of the impurity and, in particular, that by changing the orientation of $bf{S}$ the fermion-parity of the lowest energy bound state can be tuned. We then study the case of a dimer of magnetic impurities and show that in this case the YSR spectrum for a p-wave superconductor is qualitatively very different from the one for an s-wave superconductor even in the limit of vanishing SOC. Our predictions can be used to distinguish the symmetry of the order parameter and have implications for the Majorana proposals based on chains of magnetic atoms placed on the surface of superconductors with strong spin-orbit coupling.
We investigate the mutual influence of impurities in two-dimensional d-wave superconductors involving self-consistent solutions of the Bogoliubov-de Gennes equations. The local order parameter suppression, the local density of states (LDOS) as well as the interference of impurity-induced structures are analyzed. We employ an impurity position averaging scheme for the DOS that does not neglect these interference effects, as the commonly used $T$-matrix approaches do.
Andreev bound states at boundaries of d-wave superconductors are strongly influenced by the boundary geometry itself. In this work, the zero-energy spectral weight of the local quasiparticle density of states is presented for the case of wedge-shaped boundaries with rounded corners. Generally, both orientation of the d-wave and the specific local reflection properties of the rounded wedges determine, whether Andreev bound states exist or not. For the bisecting line of the wedge being parallel to the nodal direction of the d-wave gap function, strong zero-energy Andreev bound states are expected at the round part of the boundary.
We study the influence of surface Andreev bound states in d-wave superconductors on the Bean-Livingston surface barrier for entry of a vortex line into a strongly type-II superconductor. Starting from Eilenberger theory we derive a generalization of London theory to incorporate the anomalous surface currents arising from the Andreev bound states. This allows us to find an analytical expression for the modification of the Bean-Livingston barrier in terms of a single parameter describing the influence of the Andreev bound states. We find that the field of first vortex entry is significantly enhanced. Also, the depinning field for vortices near the surface is renormalized. Both effects are temperature dependent and depend on the orientation of the surface relative to the d-wave gap function.
We analyze the complex interplay of the strong correlations and impurities in a high temperature superconductor and show that both the nature and degree of the inhomogeneities at zero temperature in the local order parameters change drastically from what are obtained in a simple Hartree-Fock-Bogoliubov theory. While both the strong electronic repulsions and disorder contribute to the nanoscale inhomogeneity in the population of charge-carriers, we find them to compete with each other leading to a relatively smooth variation of the local density. Our self-consistent calculations modify the spatial fluctuations in the pairing amplitude by suppressing all the double-occupancy within a Gutzwiller formalism and prohibit the formation of distinct superconducting-`islands. In contrast, presence of such `islands controls the outcome if strong correlations are neglected. The reorganization of the spatial structures in the Gutzwiller method makes these superconductors surprisingly insensitive to the impurities. This is illustrated by a very weak decay of superfluid stiffness, off-diagonal long range order and local density of states up to a large disorder strength. Exploring the origin of such a robustness we conclude that the underlying one-particle normal states reshape in a rich manner, such that the superconductor formed by pairing these states experiences a weaker but spatially correlated effective disorder. Such a route to superconductivity is evocative of Andersons theorem. Our results capture the key experimental trends in the cuprates.
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