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

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, outperforms standard optical methods by many orders of magnitude. The net photoelectron current generated via photoionization of randomly oriented chiral molecules by circularly polarized light, the key enantio-sensitive observable in PECD, is directed oppositely in the opposite enantiomers. 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 condensed matter systems including the anomalous electron velocity, the Hall effect, and related topological phenomena. Following this link, we uncover the presence of a chiral geometric magnetic field in molecular photoionization and formulate fundamental principles that allow one to predict new enantio-sensitive observables associated with this field. Crucially, the emergence of these new observables is associated with ultrafast excitation of chiral electronic or vibronic currents prior to ionization and can be viewed as their unique signature. We illustrate our concept by introducing and quantifying a new effect: enantio-sensitive orientation of chiral molecules via photoionization. We name it "molecular orientation circular (or chiral) dichroism," MOCD. It opens new routes to both enantio-separation and imaging of chiral dynamics on ultrafast time scales. Our work ponders connections between the two geometrical properties, chirality and topology, and shows that geometrical fields generated by electrons provide the bridge between the two.