Transport through edge-channels is responsible for conduction in quantum Hall (QH) phases. The equilibration among the edges dictates the electrical and thermal transport coefficients, and its robust quantization relies on the nature of equilibration: coherent vs. incoherent process. The classic example of symmetry broken graphene p-n junction in the QH regime. Its primary importance appears at ultralow temperatures: typically, below ~ 4K and at high magnetic fields of the order of few Tesla, where chirally opposite quantum hall edge states co-propagate along the junction. These co-propagating edge states have been utilized to study phenomena like equilibration, propagation, and scattering of spin-wave or magnons and they also hold the promise to form an on-chip electron interferometer. We find that the equilibration is selective based on the polarization of the edge states. The quantum noise studies as a function of both p and n side filling factors reveal that the equilibration is fully tunable from incoherent to the coherent regime with the increasing number of QH edges at the p-n junction, shedding crucial insights into graphene-based electron interferometer. The observation has been ascribed as an effect of velocity-dependent phase coherence of the quantum Hall edge states at the junction.

**References:**

Physical Review B 98 (15), 155421 (2018)

Communications Physics 3 (171), 1-7 (2020)

Left: optical image of a graphene p-n junction. The device is a hBN encapsulated and two graphite gated device. Right: schematic for conductance and shot noise measurement setup.

(Up-left): Spin configuration of the edge states for two different ways of Landau level (LL) degeneracy lifting with increasing magnetic field (B): spin and valley polarized ground states. Red and black color indicates valley degrees of freedom. (Up-right) Measured transmittance t (open circles) with error bar (standard deviation of t from average value) of the PNJ as a function of filling factor νn for νp = −1. The calculated t for full equilibration (t-full) and spin-selective equilibration (t-spin) for spin-polarized ground state is shown by blue and red dashed lines, respectively. (bottom-left): measured shot noise as a function of injected current. The red line is the fir to extract the Fano factor. (Bottom-right): Fane dependence on different combination of filling factors across the PNJ.