Berry-Phase Induced Kondo Effect in Single-Molecule Magnets

Kondo effect in SMMs: detailed theoryeffective HamiltonianH = H SMM + H KondoH SMM = ∑ m ∗ E m ∗ |m ∗ 〉〈m ∗ |, E m ∗ = E −m ∗ [∆ m∗ ,−m ∗ (H ∗ x) = 0]H Kondo = ∑ k,α(ξ k + gµ BHxs ∗ )x2local exchange termψ † kα ψ kα + H exH ex = 1 2∑m∑ [j (m)+ Σ (m)k,k ′project it onto the {|m} subspace+ ψ † k↓ ψ k ′ ↑ + j (m)−Σ (m)−ψ † k↑ ψ k ′ ↓ + j z(m) Σ (m)z()]ψ † k↑ ψ k ′ ↑ − ψ † k↓ ψ k ′ ↓pseudo-spin flipping termspseudo-spin operatorsΣ (m)z(|m〉〈m| − | − m〉〈−m|)= 1 2Σ (m)± = | ± m〉〈∓m|anisotropic coupling constantsj (m)z= 2J z 〈m|S z |m〉j (m)± = J ± 〈±m|S ± | ∓ m〉