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arXiv:cond-mat/0112044

Interaction Effects on Quasiparticle Localization in Dirty Superconductors

M. S. Jeng, Ludwig, A. W. W., T. Senthil, Claudio Chamon

Published Dec 4, 2001• 2 citations
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Abstract

We study how quasiparticle interactions affect their localization properties in dirty superconductors with broken time reversal symmetry -- for example in a magnetic field. For SU(2) spin-rotation invariant (class C) systems, the only important coupling is the spin-spin triplet interaction, which we study within a renormalization group approach. Either an additional Zeeman coupling or a complete breaking of spin rotation symmetry renders all interactions irrelevant. These two situations realize, respectively, the non-interacting unitary Anderson and the ``thermal'' (class D) universality class. Our results imply a stable metallic phase in 2D for class D. Experimental implications are discussed.

DOI
10.48550/arxiv.cond-mat/0112044

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We study how quasiparticle interactions affect their localization properties in dirty superconductors with broken time reversal symmetry -- for example in a magnetic field. For SU(2) spin-rotation invariant (class C) systems, the only important coupling is the spin-spin triplet interaction, which we study within a renormalization group approach. Either an additional Zeeman coupling or a complete breaking of spin rotation symmetry renders all interactions irrelevant. These two situations realize, respectively, the non-interacting unitary Anderson and the ``thermal'' (class D) universality class. Our results imply a stable metallic phase in 2D for class D. Experimental implications are discussed.
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In this paper, a delocalization-localization transition within a superconducting state is explored. The symmetries of the Bogoliubov deGennes Hamiltonian endow the two associated superconducting phases---the thermal metal and the thermal insulator---and the critical point between them, with properties that are in stark contrast with analogous phases in normal systems. Here, for systems preserving spin-rotational invariance and time-reversal symmetry in three dimensions, the transition is shown to be of a different universality class from its normal partner by extracting and comparing the localization length exponent. The density of states, which may be regarded as the ``order parameter'' for the field theory describing the superconducting system, is studied for its unusual properties about criticality.
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We study the density of quasiparticle states of dirty d-wave superconductors. We show the existence of singular corrections to the density of states due to quantum interference effects. We then argue that the density of states actually vanishes in the localized phase as ∣E∣|E|∣E∣ or E2{E}^{2}E2 depending on whether time-reversal is a good symmetry or not. We verify this result for systems without time-reversal symmetry in one dimension using supersymmetry techniques. This simple, instructive calculation also provides the exact universal scaling function for the density of states for the crossover from ballistic to localized behavior in one dimension. Above two dimensions, we argue that in contrast to the conventional Anderson localization transition, the density of states has critical singularities which we calculate in a $2+\ensuremath{\epsilon}$ expansion. We discuss consequences of our results for various experiments on dirty high-Tc{T}_{c}Tc​ materials.
Spin ordering and its effect on low-energy quasiparticles in a p-wave superconducting liquid are investigated.We study the properties of a two-dimensional ͑2D͒ p-wave superconducting liquid where the ground state is spin rotation invariant.In quantum spin disordered liquids, the low-energy quasiparticles are bound states of the bare Bogolubov-De Gennes ͑BdeG͒ quasiparticles and zero energy skyrmions, which are charge neutral bosons at the low-energy limit.Further more, spin collective excitations are fractionalized ones carrying a half-spin and obeying fermionic statistics.In thermally spin disordered limits, the quasiparticles are bound states of bare BdeG quasiparticles.The latter situation can be realized in some layered p-wave superconductors where the spin-orbit coupling is weak.
We study in detail a critical line on the phase diagram of the Cho-Fisher network model separating three different phases: metallic and two distinct localized phases with different quantized thermal Hall conductances. This system describes noninteracting quasiparticles in disordered superconductors that have neither time-reversal nor spin-rotational invariance. We find that in addition to a tricritical fixed point WT{W}_{T}WT​ on the critical line, separating two localized phases, there exists an additional repulsive fixed point WN{W}_{N}WN​ (where the vortex disorder concentration WN<WT{W}_{N}<{W}_{T}WN​<WT​), which splits RG flow into opposite directions: toward a clean Ising model at W=0W=0W=0 and toward WT{W}_{T}WT​.