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arXiv:cond-mat/0308427

Nodal quasiparticles in doped d-wave superconductors: self-consistent T-matrix approach

В. М. Локтев, Yu. G. Pogorelov

Published Aug 21, 2003• 1 citation
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Abstract

A comparative analysis has been done of the formerly established two self-consistent solutions for the density of quasiparticle states in doped d-wave superconductors, having strikingly different and disputed behavior near the Fermi energy. One of them (1) remains finite in this limit, while the other (2) tends to zero. To resolve this discrepancy, the known Ioffe-Regel criterion for band states, widely used for doped semiconductors, was applied to these solutions. It is shown that both them are valid in limited and different energy regions, where the corresponding quasiparticles are weakly damped. In particular, density of states of nodal quasiparticles near the Fermi level is provided by the (2) solution, while the (1) only applies far enough from this level.

DOI
10.48550/arxiv.cond-mat/0308427

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The long disputed issue of the limiting value of quasiparticle density of states $\r(0) = \r (\e \to 0)$ in a \emph{d-}wave superconductor with impurities (\emph{vs} its linear vanishing, $\r_0(\e) \propto |\e|/\D$, near the nodal point $\e = 0$ in a pure system with the gap parameter $\D$) is discussed. Using the technique of group expansions of Green functions in complexes of interacting impurities, it is shown that finite (˚0)\r(0)(˚​0) value is possible if the (finite) impurity perturbation VVV is spin-dependent (magnetic). The found value has a power law dependence on the impurity concentration ccc: $\r(0) \propto \r_N c^{n}$, where $\r_N$ is the normal metal density of states and n≥2n \geq 2n≥2 is the least number of impurities in a complex that can localize nodal quasiparticle. This result essentially differs from the known predictions of self-consistent approximation: $\r(0) \propto \r_N \sqrt {c/\r_N\D}$ (for the unitary limit V→∞V \to \inftyV→∞) or $\r(0) \propto (\D/cV^2)\exp(-\D/cV^2\r_N)$ (for the Born limit $|V|\r_N \ll 1$). We predict also existence of a narrow interval (mobility gap) around the Fermi energy, where all the states are localized on proper impurity clusters, leading to exponential suppression of low-temperature kinetics.
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