Lorentzian-Gaussian Analysis of Gate-Tunable Quantum Transport in an hBN-Encapsulated Monolayer Graphene Nano-Device

This study fabricates an hBN-encapsulated monolayer graphene nano-device and uses Lorentzian-Gaussian fitting of its gate-dependent four-probe resistance to extract quantitative metrics describing the charge neutrality peak. Method papers provide best practices for graphene device fabrication, however fewer works connect these procedures to quantitative resistance-peak metrics that can be compared across hBN-MLG-hBN devices; the specific question addressed here is whether such metrics are reproducible and physically interpretable enough to serve as a comparative measure of fabrication quality. The stack was assembled by mechanical exfoliation and dry-transfer, patterned into a Hall-bar geometry with Cr/Pd/Au edge contacts, and measured in a four-probe lock-in configuration at 4 K while sweeping the silicon back gate. The device exhibited a clear resistance maximum rising from a background of 0.4-1.0 kΩ to 4.6-4.7 kΩ. After smoothing and second-order baseline subtraction, the peak was fit with both line shapes, yielding a peak center of −3.5382 V, a Lorentzian FWHM of 2.6528 V, and a Gaussian FWHM of 2.8663 V. Converting the gate voltage axis to carrier density using the 300 nm oxide gate dielectric gives a residual doping of ≈2.5 × 1011 cm−2 and a charge-inhomogeneity width of ≈1.9 × 1011 cm−2, both roughly four orders of magnitude larger than the thermal scale at 4 K. This establishes that the observed peak width is disorder-limited rather than thermally limited, and therefore that the width is a legitimate descriptor of fabrication quality. The contribution of this work is methodological: a fully scripted peak-metric procedure, reported together with the sensitivity of each metric to the smoothing and baseline choices is identified, which can be applied unchanged to future hBN-MLG-hBN devices.