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We consider different effects that arise when time-reversal symmetry breakingsuperconductors are subjected to an external magnetic field, thus rendering thesuperconductor to be in the mixed state. We focus in particular on twotime-reversal symmetry breaking order parameters which are believed to berealized in actual materials: $p+\i p'$-wave and $d+\i s$- or $d+\i d'$-wave.The first order parameter is relevant for Sr$_2$RuO$_4$, while the latter orderparameters have been suggested to exist near surfaces in some of the high-$T_c$cuprates. We investigate the interplay between surface states and vortex statesin the presence of an external magnetic field and their influence on both thetunneling conductance and the local density of states. Our findings may behelpful to experimentally identify the symmetry of unconventional time-reversalsymmetry breaking superconducting states.

physical review. b, condensed matter and materials physics

Tunneling conductance and local density of states in time-reversal  symmetry breaking superconductors under the influence of an external magnetic  field