Supplementary information files for Graphene’s non-equilibrium fermions reveal Doppler-shifted magnetophonon resonances accompanied by Mach supersonic and Landau velocity effects

Supplementary files for article Graphene’s non-equilibrium fermions reveal Doppler-shifted magnetophonon resonances accompanied by Mach supersonic and Landau velocity effects.Oscillatory magnetoresistance measurements on graphene have revealed a wealth of novel physics. These phenomena are typically studied at low currents. At high currents, electrons are driven far from equilibrium with the atomic lattice vibrations so that their kinetic energy can exceed the thermal energy of the phonons. Here, we report three non-equilibrium phenomena in monolayer graphene at high currents: (i) a “Doppler-like” shift and splitting of the frequencies of the transverse acoustic (TA) phonons emitted when the electrons undergo inter-Landau level (LL) transitions; (ii) an intra-LL Mach effect with the emission of TA phonons when the electrons approach supersonic speed, and (iii) the onset of elastic inter-LL transitions at a critical carrier drift velocity, analogous to the superfluid Landau velocity. All three quantum phenomena can be unified in a single resonance equation. They offer avenues for research on out-of-equilibrium phenomena in other two-dimensional fermion systems.

附加文件为文章《石墨烯非平衡费米子揭示多普勒移位磁声子共振伴随马赫超音速和朗道速度效应》提供补充。对石墨烯的振荡磁阻测量揭示了丰富的物理现象。这些现象通常在低电流下进行研究。在高电流下，由于电子与原子晶格振动远离平衡，其动能可以超过声子的热能。在此，我们报道了单层石墨烯在高电流下的三种非平衡现象：（i）当电子经历跨朗道能级（LL）跃迁时，横波声子（TA）频率的“多普勒类似”移位和分裂；（ii）当电子接近超音速时，朗道能级内马赫效应伴随TA声子的发射；（iii）在临界载流子漂移速度下弹性跨朗道能级跃迁的开始，类似于超流体的朗道速度。这三种量子现象可以统一在一个共振方程中。它们为研究其他二维费米子系统中的非平衡现象提供了研究途径。