| Summary: | We study the effect of an in-plane magnetic field on the non-interacting dispersion of twisted bilayer graphene.
Our analysis is rooted in the chirally symmetric continuum model, whose zero-field band structure hosts exactly
flat bands and large energy gaps at the magic angles. At the first magic angle, the central bands respond to a
parallel field by forming a quadratic band crossing point (QBCP) at the moire Brillouin zone center. Over a large ´
range of fields, the dispersion is invariant with an overall scale set by the magnetic field strength. For deviations
from the magic angle and for realistic interlayer couplings, the motion and merging of the Dirac points lying
near charge neutrality are discussed in the context of the symmetries, and we show that small magnetic fields
are able to induce a qualitative change in the energy spectrum. We conclude with a discussion on the possible
ramifications of our study to the interacting ground states of twisted bilayer graphene systems.
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