How can one see it from BCS wavefunction and BCS Hamiltonian? i.e.
HBCS=∑kσϵkc†kσckσ−Δ∗∑kc†k↑c†−k↓+h.c.
and:
ΨBCS=Πk(uk+vkc†k↑c†−k↓)|0⟩
If it has this symmetry, what significance does it has?
Answer
The Hamiltonian is time-reversal invariant: ck↑→c−k,↓,ck↓→−c−k,↑. You can check that explicitly. The ground state is also invariant, because Cooper pairs are all spin singlet.
One of the significant implications of time-reversal symmetry for s-wave superconductors is the Anderson's theorem: the pairing (e.g. the critical temperature) is not affected by time-reversal-invariant impurities (i.e. non-magnetic), as long as the impurities are not strong enough to cause localization.
No comments:
Post a Comment