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In this work we predict the existence of a novel species of Wannier excitonswhen exposed to crossed electric and magnetic fields. In particular, we presenta theory of giant-dipole excitons in $\textrm{Cu}_2\rm O$ in crossed fields.Within our theoretical approach we perform a pseudoseparation of thecenter-of-mass motion for the field-dressed excitonic species, therebyobtaining an effective single-particle Hamiltonian for the relative motion. Forarbitrary gauge fields we exactly separate the gauge-dependent kinetic energyterms from the effective single-particle interaction potential. Depending onthe applied field strengths and the specific field orientation, the potentialfor the relative motion of electron and hole exhibits an outer well at spatialseparations up to several micrometers and depths up to $380\, \mu \rm eV$,leading to possible permanent excitonic electric dipole moments of around threemillion Debye.

Excitonic giant-dipole potentials in cuprous oxide