Impurity states and marginal stability of unconventional ...

Bogoliubov-Nambu Hamiltonian
background
Bogoliubov angle measures the relative weight between particle
And hole component in Bogoliubov deGennes quasiparticle
† † †
( )
ks ks
(
k ks −k −s
)
H = ε k c c + ∆ c c + h c
γ
= uc + vc
*
∗
k↑ k k↑ k −k↓
2
| ( )| 1/2 (
uk = 1 −ε
( k)/ Ek ( ))
2
| ( )| 1/2 (
vk = 1 + ε ( k)/ Ek ( ))
True excitations in SC state γ
k
That are quantum mechanical †
γ
Mixture of particle and hole
k
Ψ =
0
Ψ
0;
= Ψ
0 1
Important! Dual
nature of qp inSC
† †
γ ↑
Ψ
0
= Ψ1 ∝c ( k)|
k ↑
Ψ1
↓
and at the same time ∝c ( −k) | Ψ
1