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Long-lived binary tunneling spectrum in the quantum Hall Tomonaga-Luttinger liquid

The existence of long-lived non-equilibrium states without showing thermalization, which has previously been demonstrated in time evolution of ultracold atoms, suggests the possibility of their spatial analogue in transport behavior of interacting electrons in solid-state systems. Here we report long-lived non-equilibrium states in one-dimensional edge channels in the integer quantum Hall regime. An indirect heating scheme in a counterpropagating configuration is employed to generate a non-trivial binary spectrum consisting of high- and low-temperature components. This unusual spectrum is sustained even after travelling 5 - 10 {\mu}m, much longer than the length for electronic relaxation (about 0.1 {\mu}m), without showing significant thermalization. This observation is consistent with the integrable model of Tomonaga-Luttinger liquid. The long-lived spectrum implies that the system is well described by non-interacting plasmons, which are attractive for carrying information for a long distance.