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Moiré superlattices are an excellent playground for exploring how soft mechanical degrees of freedom can be coupled to the charge and spin of electrons, leading to emergent functionalities. Some of these responses can be used to characterize the broken (structurally or spontaneously) symmetries of these materials. Nonlinear effects are instrumental for this purpose. From the theory standpoint, these observables help us to constrain the models by identifying the most important physical processes taking place on the multiple scales of these superlattices.
When a graphene layer is rotated with respect to the other, two things happen. First, the lattice relaxes, trying to amplify the local twist angle in regions of high-energy stacking. This produces a sharper beating pattern, as the figure illustrates, forming domain walls. This is not exclusive of twisted devices, one can play the same game introducing a lattice mismatch via hetero-strain, as we demonstrated in this work.
The second thing is that when charge is added to the moiré, most of it tends to concentrate in the beating pattern maxima. Electrons do not want to be that close together due to their mutual Coulomb repulsion, so in fact the electronic spectrum is largely reshaped by doping.
Electric backaction on moiré mechanics
What is the interplay between these two effects? I have started to study the intertwined dynamics of charge/electrons and moiré mechanics/stackings. Some preliminary thoughts are in this recent article, where I showed that lateral electric fields produce layer-shear mechanical forces. In the simplest theory, the coefficients of these forces have a natural geometrical interpretation in terms of sliding Chern numbers, which track the charge density measured from neutrality. The simplest manifestation of this effect is an apparent enhancement of the friction between layers when one of them can slide but charge following adiabatically the moiré pattern (assumed the system is insulating) cannot leave the system. As represented in the figure below, this charge accumulation creates a mechanical force (purple arrow) opposing the motion of the blue layer. Quantum mechanically, the spectral flow associated with this charge accumulation is possible due to the existence of edge modes associated with the moiré pattern.
Chiral and nonlinear optical responses ...
Twisting one layer with respect to the other breaks all the inversion and reflection symmetries of the system and imprints a chirality on the electrons. This is manifested in the optical activity of the bilayer (despite being so thin); for example, the different optical absorption for left- and right-handed light or circular dichroism (CD). The calculations in the figure correspond to twisted boron-nitride layers. As we discussed in this letter, the magnitude of the CD depends on subtle properties of the electronic wave functions encoded in current counter-flows generated by the incident fields. Another good example is the second harmonic generation in twistable interfaces of hexagonal boron nitride .
... and photocurrents
More recently, in a collaboration with Fernando Peñaranda and Fernando de Juan at DIPC, we have been exploring how to extract useful information about twisting devices from DC currents generated by shining light. In this letter we studied the intrinsic photogalvanic effects at off-normal incidence engendered by the chirality of the structure. We found an interesting sign reversal across the magic angle associated with a concomitant inversion of the flat bands at the zone center. We are also studying how magnetic injection can help to distinguish different states with broken time-reversal symmetry; some preliminary results can be found here.
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