Landau-Level-Resolved Mode Mixing and Shot Noise in Gate-Defined Graphene Quantum Point Contacts

Graphene quantum point contacts (QPCs) in the quantum Hall regime host competing transport mechanisms including chiral edge propagation, valley degeneracy, and gate-induced mode mixing. Their interplay is not visible in conductance alone. Shot noise directly probes the statistics of transmission eigenvalues, revealing microscopic mode partitioning that conductance cannot access. We develop a hybrid framework combining tight-binding simulations of gate-defined graphene QPCs with random matrix theory (RMT) to predict shot noise and Fano factor signatures across different quantum Hall regimes, validated against experimental conductance maps of hBN-encapsulated graphene Hall bars. Three distinct regimes are identified: adiabatic propagation, sharp mode filtering, and multi-mode mixing driven by localized states beneath the split gate. For higher Landau levels ($N_L > 0$), complete mode mixing produces the universal chaotic-cavity limit $F \simeq 1/4$. Strikingly, the zeroth Landau level ($N_L = 0$) converges to $F = 1/3$. This distinct value originates in the sublattice polarization of the $N_L = 0$ edge state: coupling to mixed-sublattice localized states beneath the gate is suppressed, confining transport to an effective single channel ($N = 1$). Complete mixing within this single channel yields a flat transmission eigenvalue distribution and hence exactly $F = 1/3$ from single-channel RMT, numerically coincident with but mechanistically distinct from pseudo-diffusive zero-field graphene transport. The $F = 1/3$ versus $F = 1/4$ crossover is a Landau-level-resolved noise signature absent in conductance, providing a direct discriminator between single-channel and multi-channel chaotic transport in graphene QPCs.