The last decade has seen a rapid growth of digital information volume that emphasizes the need for novel energy-efficient and high-speed processing solutions based on innovative concepts and technologies. The use of degrees of freedom alternative to electric charge, as the electron spin, and the focus on topological materials with protected quasiparticles in momentum space (e.g. Dirac or Weyl), or those with topologically non-trivial real-space spin textures (e.g. skyrmions), are rapidly setting the path for a completely novel topological view of spintronic effects.

The key objective of BEAT is to control electrical transport in 3D topological insulators (Tis) via new device concepts involving long-range magnetic order, magneto-electricity and geometrical confinement. One of the central physical quantities in topological materials is the Berry curvature, which is known to capture the essence of quantum Hall and quantum spin Hall effects and describes pseudo magnetic fields arising from the quantum geometric properties of electron wave-functions. The BEAT objectives point toward ground-breaking directions in the research field of Berry phase engineering and spintronics. One route is to develop devices whose topological properties do not make direct use of magnetic fields and are instead robust to them. A second route instead points to explore new materials strategies for engineering Berry curvature and Hall effects without using sources of time-reversal symmetry breaking but rather exploiting surface nanostructuring.