The Coulomb interaction among massless chiral particles harbors unusual emergent phenomena in solids beyond the conventional realm of correlated electron physics. An example of such an effect is excitonic condensation of interacting massless Dirac fermions, which drives spontaneous mass acquisition and whose exact nature remains actively debated. Its precursor fluctuations growing prior to the condensate have been suggested by a recent nuclear magnetic resonance study in an organic material, hosting a pair of two-dimensional (2D) tilted Dirac cones at charge neutrality. Here, we theoretically study the excitonic transition in 2D tilted cones to understand the electron-hole pairing instability as functions of temperature (T), chemical potential (μ), and in-plane magnetic field (H). By solving a gap equation within a weak-coupling treatment and incorporating self-energy effects due to the Coulomb interaction through a renormalization-group technique, we calculate excitonic instability in a T-μ-H parameter space, and find that the pairing is promoted as H is increased but suppressed as μ moves away from the charge-neutrality point. We show that these findings are explained by enhanced or degraded Fermi-surface nesting between the Zeeman-induced pockets connecting the two tilted cones. Furthermore, to evaluate the precursor excitonic fluctuations in relation to this diagram, we consider the Coulomb interaction via a ladder-type approximation and calculate the nuclear spin-lattice relaxation rate, which provides rational ways to understand otherwise puzzling experimental results in the organic material by the μ and H dependence of the instability.

The effect of the Coulomb interaction in interlayer magnetoresistance is elucidated in collaboration with theory and experiments for the Dirac electron system in organic conductor α -(BEDT-TTF) 2 I 3 under a strong magnetic field. It is found that the effective g-factor enhanced by Coulomb interaction depends on the angle of the magnetic field, resulting in the field-angle dependence of a characteristic magnetic field in which interlayer resistance has a minimum due to spin splitting N = 0 Landau levels. The qualitative agreement between the theory and experimental results for the field-angle dependence of interlayer magnetoresistance is obtained.

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