Ultrafast jamming of electrons into an amorphous entangled state

New emergent states of matter in quantum systems may be created under non-equilibrium conditions if - through many body interactions - its constituents order on a timescale which is shorter than the time required for the system to reach thermal equilibrium. Conventionally non-equilibrium ordering is discussed in terms of symmetry breaking, nonthermal order-disorder, and more recently quenched topological transitions. Here we report a fundamentally new and unusual metastable form of amorphous correlation-localized fermionic matter, which is formed in a new type of quantum transition at low temperature either by short pulse photoexcitation or by electrical charge injection in the transition metal dichalcogenide 1T-TaS2. Scanning tunnelling microscopy (STM) reveals a pseudo-amorphous packing of localized electrons within the crystal lattice that is significantly denser than its hexagonally ordered low-temperature ground state, or any other ordered states of the system. Remarkably, the arrangement is not random, but displays a hyperuniform spatial density distribution commonly encountered in classical jammed systems, showing no signs of aggregation or phase separation. Unexpectedly for a localized electron system, tunnelling spectroscopy and multi- STM-tip surface resistance measurements reveal that the overall state is gapless and conducting, which implies that localized and itinerant carriers are resonantly entangled. The amorphous localized electron subsystem can be understood theoretically to arise from strong correlations between polarons sparsely dispersed on a 2D hexagonal atomic lattice, while itinerant carriers act as a resonantly coupled reservoir distinct in momentum space.