  The superconducting diode effect refers to an asymmetry in the critical
supercurrent $J_c(\hat{n})$ along opposite directions, $J_c(\hat{n})\neq
J_c(-\hat{n})$. While the basic symmetry requirements for this effect are
known, it is, for junction-free systems, difficult to capture within current
theoretical models the large current asymmetries $J_c(\hat{n})/J_c(-\hat{n})$
recently observed in experiment. We here propose and develop a theory for an
enhancement mechanism of the diode effect arising from spontaneous symmetry
breaking. We show - both within a phenomenological and a microscopic theory -
that there is a coupling of the supercurrent and the underlying
symmetry-breaking order parameter. This coupling can enhance the current
asymmetry significantly. Our work might not only provide a possible explanation
for recent experiments on trilayer graphene but also pave the way for future
realizations of the superconducting diode effect with large current
asymmetries.
