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

Geometric fields and new enantio-sensitive observables in photoionization of chiral molecules