  Chiral molecules are instrumental for molecular recognition in living
organisms. Distinguishing between two opposite enantiomers, the mirror twins of
the same chiral molecule, is both vital and challenging. Photoelectron circular
dichroism (PECD), an extremely sensitive probe of molecular chirality via
photoionization, outperforms standard optical methods by many orders of
magnitude. Here we show that the physical origin of PECD in chiral molecules is
linked to the concept of geometric magnetism, which enables a broad class of
phenomena in solids including the anomalous electron velocity, the Hall effect,
and related topological phenomena. We uncover the geometric field in molecular
photoionization, which leads to a new class of enantio-sensitive observables
emerging due to ultrafast excitation of chiral electronic or vibronic currents
prior to ionization. Next, we introduce the first member of this new class:
enantio-sensitive orientation of chiral molecules via photoionization. This
effect opens new routes to both enantio-separation and imaging of chiral
dynamics on ultrafast time scales. Our work suggests that geometric fields in
photoionization provide the bridge between the two geometrical properties,
chirality and topology.
