Emergent Chiral Metal Phase in Compressible Quantum Hall Fluids
We report transmitted conductance measurements between a source and reflection-less contacts connected to a compressible quantum Hall fluid with filling fraction $\nu$. We observe that total sum of transmitted conductances universally approaches Hall conductance $\nu(e^2/h)$. The universality of this sum rule is established experimentally across integer and fractional quantum Hall regimes, remaining invariant under variation in temperatures, sample geometries, material qualities and quasi-particle interactions. Chiral transport in compressible quantum Hall fluids, characterized by suppressed dissipative transport with a distinct handedness, is confirmed by floating contact measurements. Consequently, this sum rule emerges as a conduction law of the chiral metal phase. Theoretically, we argue that time-reversal-symmetry breaking under a strong magnetic field within this chiral metal gives rise unidirectional trajectories of carriers in a nearly flat potential landscape with point-like disorder potentials, a regime realized when the screening length is smaller than the magnetic length. Within this chiral framework, longitudinal resistance does not originate from bulk dissipation but primarily from the equilibration of electrochemical potentials at the contacts. Our study introduces a new paradigm of chiral transport across a broad class of gapless two-dimensional systems characterized by short-range screening and broken time-reversal symmetry.