Berry-induced nonlinear Hall effect in a graphene - bilayer WSe₂ system

Charge transport in two-dimensional nanodevices has become increasingly important due to its technological applications. Very significant in this field was the discovery of the integer quantum Hall effect (IQHE), which revealed the quantization of the resistance transversal to an applied bias current. Remarkably, this relies on the breaking of time reversal (TR) symmetry owed to the presence of a strong external magnetic field or, as in the anomalous Hall effect, magnetic order. The search for a Hall-like effect that shows up even in TR symmetric systems has led to the discovery of the nonlinear Hall effect (NLHE), that occurs in systems with TR but lacking an inversion center. Notably, this effect can only be observed at second order in the applied bias. In this work, we investigate this phenomenon in a superstructure made up of graphene and 60^o twisted bilayer tungsten diselenide. Of all the mechanisms leading to NLHE, we focus on the Berry dipole contribution, which depends solely on the geometry of the Bloch wavefunction. Although there exist effective, symmetry-based two-band models giving the NLHE, here we use first principle (DFT) and tight binding calculations to find a Hamiltonian for graphene alone and calculate the nonlinear current in a semiclassical formalism, with a focus on energies around the charge neutrality point. With this, we get a sense of the order of magnitude of the nonlinear current and compare it with the current literature.