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PauliLimit< Gauge Invariance and gauge symmetry breaking (Higg's mechanism) | Index | Superconductivity.HighTc > Pauli limit (see Tinkham p. 390-394 on pair breaking). For a superconductor where spin orbit pairing is negligible a first order transition to the normal state occurs at a field {$H_P$} {$ \mu_B H_P=\frac{\Delta(0)}{\sqrt{2}}$} i.e. {$H_P=1.84 T_c$} Tesla at {$T=0$}, where {$\Delta$} is the gap. If this field is smaller than {$H_{c2}$} then the superconductor will break before the pairing breaks. Also known as Clogston-Chandrasekhar limit. The derivation by Clogston (Phys. Rev. Lett 9 (1962) 266) is very simple. The superconducting state is favoured by the presence of a gap, i.e. its free energy gain in zero field is: {$ F_S=F_N - \frac 1 2 N(0)\Delta^2(0) $} at zero temperature, where {$N$} is the electron density of states at the Fermi energy. In the presence of a magnetic induction {$\mu_0H$} the Meissner-Ochsenfeld effect amounts to an additional magnetic free energy term for the superconducting state, equal to {$ H^2$}. However the normal metal experiences a free energy reduction by {$\mu_0\chi_P H^2$}, where {$\chi_P=2 \mu_B^2 N(0)$} is the Pauli susceptibility of the free electron gas. Now a new limit might be considered, where superconductivity is on the verge of being destroyed, i.e the Meissner effect is negligible. In this case we anticipate a first order transition to the normal state when {$F_N(H_P)=F_S(H_P)$}, which leads to: {$ \mu_B^2 N(0) H_P^2= \frac 1 2 N(0)\Delta^2(0)$} which yields the first equation. < Gauge Invariance and gauge symmetry breaking (Higg's mechanism) | Index | Superconductivity.HighTc > |