In this talk I will review some existing experimental
methods, as well as a few recent theoretical proposals, to tune the
interactions in a number of low-dimensional systems exhibiting the fractional
quantum Hall effect (FQHE). The materials in question include GaAs wide quantum
wells and multilayer graphene, where the tunability of the electron-electron
interactions can be achieved via modifying the band structure, dielectric
environment of the sample, by tilting the magnetic field or varying the mass
tensor, and by mixing of electronic subbands and Landau levels.
Because the interesting topological (and in particular,
non-Abelian) states arise solely due to strong interactions, the ability to
tune them is essential for ``designing" more robust FQHE states.
Furthermore, I will argue that some of these mechanisms can also be used to
probe the subtle aspects of FQHE physics, such as the breaking of particle-hole
symmetry between the Moore-Read Pfaffian and anti-Pfaffian states, and the
transition between FQHE fluids and broken-symmetry states due to the
fluctuation of the intrinsic geometric degree of freedom.