Dr Braun is one of the pioneers in using mathematical methods in the field of topology in order to explain the behaviour of magnetic materials both classically and quantum mechanically. His predictions led among others to the choice of optimal materials for data storage and to the discovery of emergent spin currents and chirality in quantum spin systems via spin polarized neutron scattering.
In particular,he developed the theory for nonuniform thermally activated magnetization reversal in nanowires which now forms the basis for the industrial standard of perpendicular magnetic storage media that form the backbone of  Data Centres all over the world . Well before it was recognized experimentally, he theoretically predicted quasi one-dimensional behavior in magnetic nanowires and he introduced the now widely used notion of domain wall chirality. His work led to the prediction of the spontaneous emergence of spin currents in quantum spin chains, an effect that he and his collaborators subsequently observed via spin polarized neutron scattering in spin 1/2 antiferromagnet.  Furthermore he proposed and interpreted a series of experiments on nanolithographic arrays that led to the discovery of emergent monopoles in artificial spin ice together with his reasearch group and colleagues from the Paul Scherrer Institute (Switzerland). In addition to numerous publications in top research journals he also authored popular articles for the French and German versions of Scientific American and he holds two patents.

In 2014 he was elected IEEE Magnetics Society Distinguished Lecturer entailing 50 talks worldwide.