Superconductivity’s Weblog

“Quantum protector” (QP) is a macroscopic quantum (for example quantum Hall effect and flux quantization of superconductivity) that is usually unaffected by imperfection, impurities and thermal fluctuations. In this state the excitations are collective excitations of the whole system rather than usual elementary excitations in many-body systems such as in Fermi liquid. P.W. Anderson believes that all phases of HTSCs (Fig. 1), not only the superconducting phase, seem to be QP and its source is the spin-charge separation (SCS). In SCS systems the elementary excitations are not consist of quasiparticles having both charge and spins, but for example in phase I of Fig. 1 there is a large charge gap (~2 eV) while there is no spin gap and in other phases there is neither a charge nor spin gap. In one dimensional, SCS always occurs but two dimensional is the critical dimension for this separation.   

Reasons for QP in different phases:

• Phase I: there are no phonon contributions to the electron self-energy and no extraneous energy scale in the simple scaling relation of conductivity, σ=ωF(T/ω)     which means that there are no interaction and scattering. Not even conventional electron-electron scattering would show the striking linear rise of scattering rate 1/τ ~ ω above the Debye frequency. Resistivity saturation due to strong phonon scattering is also absent in this phase. The strong scattering of the Zn and Ni substituted at the Cu in the CuO₂ planes, could be related to the Kondo scattering of the spin degrees of freedom not charge, and behaves completely different from other impurities.  

• Phase II: the pseudogap which is a one-electron gap in antinodal direction, is the most striking evidence for SCS, whereas there is not evidence for a gap for charge excitations (except in systems with static stripes).

• Phase III: almost all cuprate superconductors are strongly self-doped (~10-20%), but there is no evidence that T_c is even affected by the degree of purity or by phonon scattering which is pair breaking for d-wave. It also seems that high value of T_c can be achieved in a QP in which scattering dose not affect the collective state.

• Phase IV: the spin waves which are Goldstone bosons are weakly scatted by phonons and conventional impurities and are not scattered at all in the limit of ω and Q→0. They are in QP because the spin and charge dynamics are independent, and perturbations that interact primarily with charge and create large charge gap do not much affect spins.

Anderson discusses there are two sources for QP which are not entirely independent but physically distinct. 1) Spinons are relatively weakly scatter because they are the “Goldstone fermions” that express fundamental symmetries of the spin system. 2) In the SCS state, as observed by ARPES, the one-electron density of states vanishes at ω=0 as a power law, i.e. N(ω)~ω^p with 0.5<p<1. Thus, any perturbation that couples to electrons, in particular any time reversal invariant other than substitution in the copper site renormalize to zero at low frequencies. This discussion holds for phases I and II and more direct than the No. 1.

Finally, he notes that although the precise mechanism of superconductivity in HTSCs is of course still in question, reduction of the frustrated kinetic energy of the system could determine T_c. 

Ref.: P.W. Anderson, Science 288 (2000) 480.