Abstract
In layered cuprates, the application of an in-plane magnetic field $(\mathbf{H})$ changes the c-axis optical sum rule and superfluid density ${\ensuremath{\rho}}_{s}.$ For pure incoherent c-axis coupling, $\mathbf{H}$ has no effect on either quantities but it does if an additional coherent component is present. For the coherent contribution, different characteristic variations on $\mathbf{H}$ and on temperature result from the constant part ${(t}_{\ensuremath{\perp}})$ of the hopping matrix element and from the part ${(t}_{\ensuremath{\varphi}})$ which has zero on the diagonal of the Brillouin zone. Only the constant part ${(t}_{\ensuremath{\perp}})$ leads to a dependence on the direction of $\mathbf{H}$ as well as on its magnitude.
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