  Let f be a Bianchi modular form, that is, an automorphic form for GL(2) over
an imaginary quadratic field F, and let P be a prime of F at which f is new.
Let K be a quadratic extension of F, and L(f/K,s) the L-function of the
base-change of f to K. Under certain hypotheses on f and K, the functional
equation of L(f/K,s) ensures that it vanishes at the central point. The
Bloch--Kato conjecture predicts that this should force the existence of
non-trivial classes in an appropriate global Selmer group attached to f and K.
In this paper, we use the theory of double integrals developed by Barrera
Salazar and the second author to construct certain P-adic Abel--Jacobi maps,
which we use to propose a construction of such classes via "Stark--Heegner
cycles". This builds on ideas of Darmon and in particular generalises an
approach of Rotger and Seveso in the setting of classical modular forms.
