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.论文《石墨烯非平衡费米子揭示伴随马赫超音速与朗道速度效应的多普勒频移磁声子共振》的补充资料。对石墨烯开展的振荡磁阻测量已揭示了大量新颖物理现象，这类现象通常在低电流条件下开展研究。当处于高电流环境时，电子会被驱动至与原子晶格振动远偏离平衡的状态，其动能可超过声子的热能。本文报道了高电流条件下单层石墨烯中的三种非平衡物理现象：（i）电子发生朗道能级（LL）间跃迁时所发射的横向声学（TA）声子频率出现类多普勒（Doppler-like）频移与劈裂；（ii）当电子接近超音速时，伴随横向声学声子发射的朗道能级内马赫效应；（iii）在临界载流子漂移速度下出现弹性朗道能级间跃迁，该现象与超流体朗道速度类似。上述三种量子现象可通过单一共振方程进行统一描述，该研究为其他二维费米子体系的非平衡现象研究提供了新方向。