Abstract

Graphene quantum point contacts (QPCs) in the quantum Hall regime host several 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 and thereby reveals microscopic mode partitioning, which conductance measurements cannot access. We develop a hybrid theoretical framework combining realistic tight-binding simulations of gate-defined graphene QPCs with random matrix theory (RMT) to predict shot noise and Fano factor signatures across different transport regimes. We validate the tight-binding model against experimental conductance maps of hBN-encapsulated graphene Hall bars. The model reproduces mode-selective transmission and identifies three distinct regimes: adiabatic propagation, sharp mode filtering, and multi-mode mixing driven by localized states beneath the split gate. Translating these microscopic transmission eigenvalue distributions into noise statistics via RMT, we find that the Fano factor exhibits a universal crossover as a function of the Landau level index. For higher Landau levels (NL > 0), complete mode mixing in an effectively chaotic cavity produces an asymptotic saturation limit of F ≃1/4, consistent with RMT predictions for a chaotic scatterer. In contrast, the zeroth Landau level (NL = 0) converges to a limit of F = 1/3. We show that this distinct value has a microscopic origin in the sublattice polarization of the NL = 0 edge state. The generically mixed-sublattice localized states beneath the gate are strongly suppressed, confining transport to an effective single channel (N = 1). Complete mixing within this single channel yields a flat eigenvalue distribution and hence exactly F = 1/3, the same numerical value as pseudo-diffusive zero-field graphene transport, but arising here from single-channel RMT rather than Dirac-point evanescent mode physics. The F = 1/3 versus F = 1/4 crossover constitutes a Landau-level-resolved noise signature that is absent in conductance. It provides a direct discriminator between multi-channel chaotic mixing and single-channel transport in graphene QPCs, and offers quantitative benchmarks for experimental noise measurements.

Abstract

Graphene quantum point contacts (QPCs) in the quantum Hall regime host several 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 and thereby reveals microscopic mode partitioning, which conductance measurements cannot access. We develop a hybrid theoretical framework combining realistic tight-binding simulations of gate-defined graphene QPCs with random matrix theory (RMT) to predict shot noise and Fano factor signatures across different transport regimes. We validate the tight-binding model against experimental conductance maps of hBN-encapsulated graphene Hall bars. The model reproduces mode-selective transmission and identifies three distinct regimes: adiabatic propagation, sharp mode filtering, and multi-mode mixing driven by localized states beneath the split gate. Translating these microscopic transmission eigenvalue distributions into noise statistics via RMT, we find that the Fano factor exhibits a universal crossover as a function of the Landau level index. For higher Landau levels (NL > 0), complete mode mixing in an effectively chaotic cavity produces an asymptotic saturation limit of F ≃1/4, consistent with RMT predictions for a chaotic scatterer. In contrast, the zeroth Landau level (NL = 0) converges to a limit of F = 1/3. We show that this distinct value has a microscopic origin in the sublattice polarization of the NL = 0 edge state. The generically mixed-sublattice localized states beneath the gate are strongly suppressed, confining transport to an effective single channel (N = 1). Complete mixing within this single channel yields a flat eigenvalue distribution and hence exactly F = 1/3, the same numerical value as pseudo-diffusive zero-field graphene transport, but arising here from single-channel RMT rather than Dirac-point evanescent mode physics. The F = 1/3 versus F = 1/4 crossover constitutes a Landau-level-resolved noise signature that is absent in conductance. It provides a direct discriminator between multi-channel chaotic mixing and single-channel transport in graphene QPCs, and offers quantitative benchmarks for experimental noise measurements.

Abstract

Graphene quantum point contacts (QPCs) in the quantum Hall regime host several 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 and thereby reveals microscopic mode partitioning, which conductance measurements cannot access. We develop a hybrid theoretical framework combining realistic tight-binding simulations of gate-defined graphene QPCs with random matrix theory (RMT) to predict shot noise and Fano factor signatures across different transport regimes. We validate the tight-binding model against experimental conductance maps of hBN-encapsulated graphene Hall bars. The model reproduces mode-selective transmission and identifies three distinct regimes: adiabatic propagation, sharp mode filtering, and multi-mode mixing driven by localized states beneath the split gate. Translating these microscopic transmission eigenvalue distributions into noise statistics via RMT, we find that the Fano factor exhibits a universal crossover as a function of the Landau level index. For higher Landau levels (NL > 0), complete mode mixing in an effectively chaotic cavity produces an asymptotic saturation limit of F ≃1/4, consistent with RMT predictions for a chaotic scatterer. In contrast, the zeroth Landau level (NL = 0) converges to a limit of F = 1/3. We show that this distinct value has a microscopic origin in the sublattice polarization of the NL = 0 edge state. The generically mixed-sublattice localized states beneath the gate are strongly suppressed, confining transport to an effective single channel (N = 1). Complete mixing within this single channel yields a flat eigenvalue distribution and hence exactly F = 1/3, the same numerical value as pseudo-diffusive zero-field graphene transport, but arising here from single-channel RMT rather than Dirac-point evanescent mode physics. The F = 1/3 versus F = 1/4 crossover constitutes a Landau-level-resolved noise signature that is absent in conductance. It provides a direct discriminator between multi-channel chaotic mixing and single-channel transport in graphene QPCs, and offers quantitative benchmarks for experimental noise measurements.

Abstract

Graphene quantum point contacts (QPCs) in the quantum Hall regime host several 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 and thereby reveals microscopic mode partitioning, which conductance measurements cannot access. We develop a hybrid theoretical framework combining realistic tight-binding simulations of gate-defined graphene QPCs with random matrix theory (RMT) to predict shot noise and Fano factor signatures across different transport regimes. We validate the tight-binding model against experimental conductance maps of hBN-encapsulated graphene Hall bars. The model reproduces mode-selective transmission and identifies three distinct regimes: adiabatic propagation, sharp mode filtering, and multi-mode mixing driven by localized states beneath the split gate. Translating these microscopic transmission eigenvalue distributions into noise statistics via RMT, we find that the Fano factor exhibits a universal crossover as a function of the Landau level index. For higher Landau levels (NL > 0), complete mode mixing in an effectively chaotic cavity produces an asymptotic saturation limit of F ≃1/4, consistent with RMT predictions for a chaotic scatterer. In contrast, the zeroth Landau level (NL = 0) converges to a limit of F = 1/3. We show that this distinct value has a microscopic origin in the sublattice polarization of the NL = 0 edge state. The generically mixed-sublattice localized states beneath the gate are strongly suppressed, confining transport to an effective single channel (N = 1). Complete mixing within this single channel yields a flat eigenvalue distribution and hence exactly F = 1/3, the same numerical value as pseudo-diffusive zero-field graphene transport, but arising here from single-channel RMT rather than Dirac-point evanescent mode physics. The F = 1/3 versus F = 1/4 crossover constitutes a Landau-level-resolved noise signature that is absent in conductance. It provides a direct discriminator between multi-channel chaotic mixing and single-channel transport in graphene QPCs, and offers quantitative benchmarks for experimental noise measurements.