Bogoliubov Transformation — BCS Superconductivity
BCS PARAMETERS
Gap Δ / E_F
0.20
Chemical potential μ / E_F
1.00
Temperature T / T_c
0.00
u²(k_F)
—
v²(k_F)
—
E_gap
—
ξ_0 (coherence)
—
BOGOLIUBOV EQUATIONS
E_k = √(ξ_k² + Δ²)
ξ_k = ħ²k²/2m − μ
u_k² = ½(1 + ξ_k/E_k)
v_k² = ½(1 − ξ_k/E_k)
γ_k = u_k c_k − v_k c†_{-k}
Bogoliubons: mixture of e⁻ & hole