Nonmagnetic impurity in the spin-gap state

Abstract

The effects of nonmagnetic strong scatterers (unitary limit) In this paper we shall explain these two aspects, i.e. , transport and magnetic properties of the underdoped samples, in a unified way from the standpoint of the resonating-valence-band theories. In the framework of the slave-boson mean-field theory, the local-spin moments are due to the Anderson localization of the spinons in the d-wave pairing state whereas in the slave-fermion mean-field theory, they appear because of the strong (staggered) gauge interaction which binds spinons to the nonmagnetic impurities. In both theories the resistivity is determined by the residual resistivity of the holons by the Boltzmann transport theory.First let us consider the local moment induced by the nonmagnetic impurities. We have two examples in 1D where the local moment is induced by the nonmagnetic impurity.An example is the double-chain Heisenberg antiferromagnet, where the gap for the triplet excitations is opened. In this system a nonmagnetic impurity gives rise to a spin--, '. However the local-spin moment does not appear near the edge of the sample as will be described below. Another well-known example with the gap is the Haldane system with 5 =1. ' If one introduces a nonmagnetic impurity and cuts the chain, the local spin--, ' appears near the edge of the chain within the extent of the order of J/EH times the lattice constant (J exchange coupling, EH Haldane gap). Although these are onedimensional (1D) examples, we shall embody below the analogy between one and two dimensions.

Density of states of ad-wave superconductor in the presence of strong impurity scatterers: A nonperturbative result

“…Our solution is valid under the assumption of unitary limit, meaning that V 0 is the largest scale in the problem. As shown in 22,23,20 , to non interacting single impurities is associated the creation of a bound states decaying as 1/(R ln R). Following Balatsky et al ( 20 ) this would lead to delocalization due to the formation of an impurity band.…”

“…The effective potential at the impurity site can be evaluated exactly 22,23 and is given byV = V 0 1−V 0 |ω| ln|D/ω| . In the unitary limit ( V 0 → ∞) we getV = −1 |ω| ln|D/ω| .…”

“…The origin of this singular density of states is the existence of impurity bound states at the Fermi energy (E F = 0). It has been shown 22,23 that one single impurity in the unitary limit creates a bound state at E = 0, with a spatial envelope that decays as 1/(R ln R). For many impurities these states overlap, but our result indicates that a singular density of states remains at zero energy of the form ρ(ω) = n i / 2|ω| ln 2 |ω/∆ 0 | .…”

Kondo Effect in High-TcCuprates

“…In the underdoped cuprates with spin gap, it is found experimentally that a local moment of S = 1/2 appears on neighboring Cu sites [2][3][4][5][6][7][8][9][10][11]. We believe this localized spin is not screened by the conduction electron spins because of the reduced density of states for spins at the Fermi energy E F in the presence of the spin gap [12,13]. Once the spin gap collapse with the increased hole concentration, the density of states for spins at E F recovers and also the Kondo screening, i.e., the singlet formation between localized spin and conduction spins, occurs.…”

“…Next we argue that the potential will form a spinon bound state, which is responsible for the local moment. This has been shown to be the case in the spin gap phase if the spinon spectrum has point nodes, and a linear density of states [12,13]. Now we treat all the Cu sites using the SU(2) formulation.…”