Mesoscopic physics is the realm of micron-size objects composed of trillions of constituents, yet behaving as single quantum entities. An example thereof are 3D topological insulator nanowires, whose insulating bulk is enclosed by highly conducting Dirac-like surface states. Electrons can cross the wires only propagating on their surfaces, and at low temperatures they do so as quantum waves of (pseudo)relativistic nature. The magnetotransport properties of the wires are thus ruled by intereference. The latter is determined/modulated by external magnetic fields and by the Berry curvature of the system, as demonstrated in a recent collaboration with experimentalists from the Universitaet Regensburg (Germany).



Soon afterwards we also showed that the geometrical shape of a nanowire can have dramatic consequences on its magnetotransport properties. Crucially, in shaped topological insulator nanowires electrons propagate on a curved surface, and may thus feel effective gravitational effects. Such emerging gravity takes place on scales which are comparable to the characteristic quantum scales of the system, much as in black holes – nanowires can however be built in labs with current technology, black holes not quite.



Among the numerous open questions in this rapidly growing field, two are most relevant for this project: (i) How are Dirac surface states modified in curved space? (ii) Can a quantum transport signature of effective gravitational nature be singled out in a realistic setup? To answer these both analytical and numerical methods (tight-binding simulations) will be employed.