Quantum Transport Spectroscopy of Pseudomagnetic Field in Graphene

TL;DR

This work addresses detecting strain-induced pseudomagnetic fields in graphene via bulk quantum transport. The authors demonstrate that nonuniform strain yields a pseudomagnetic field $B_{pm}$ that splits valley-resolved Landau quantization under an external field $B$, producing beating in Shubnikov–de Haas oscillations. They establish universal scaling laws, $n_c ∝ B^2$ and $ν_c ∝ B$, and extract $B_{pm}$ down to millitesla scales, corresponding to strain gradients on the order of $10^3$ m$^{-1}$ and local strains near $10^{-3}$. This quantum-oscillation spectroscopy thus provides a robust tool to map and harness strain-induced gauge fields in Dirac materials, with implications for strain-tunable valleytronics and straintronic devices.

Abstract

Nonuniform strain in graphene acts as a valley-dependent gauge field, generating pseudomagnetic fields (PMFs) that mimic real magnetic fields but preserve global time-reversal symmetry. While local probes have visualized such fields, their quantitative detection via macroscopic transport has remained elusive. Here, we demonstrate that high-mobility graphene exhibits distinct beating patterns in Shubnikov-de Haas oscillations, arising from valley-resolved Landau quantization under different effective magnetic fields. Systematic analysis of these beats reveals universal quadratic and linear scaling of the node carrier density and Landau level filling factor with the applied magnetic field, enabling the extraction of PMFs as small as a few millitesla. Our results establish quantum oscillation spectroscopy as a robust and broadly applicable probe of strain-induced gauge fields in Dirac materials, opening avenues for mechanically tunable valleytronic and straintronic devices.

Figures (8)

• Figure 1: Device structure and amplitude modulation of quantum oscillation. (a) Top panel: Schematic of the graphite/hBN/graphene/hBN/graphite dual-gated Hall bar device. Bottom panel: Optical image of the device. The scale bar is $3~\mathrm{\mu m}$. (b) Plot of longitudinal magnetoresistance $R_{xx}(B)$ as a function of carrier density $n$ at finite magnetic field $B = 0.2$ T. (d) Plot of $\delta R_{xx}(B)$ versus $n$ in the presence of $B = 0.2$ T after removal of a smooth background. The regions marked by dashed ellipses in (b) and (c) mark nodes in the quantum oscillations.
• Figure 2: Magnetic field dependent modulation of the beating nodes. (a) Plot of residual ${\delta R_{xx}}$ as a function of $n$ at different values of $B$ ranging from $\mathrm{0.22~T ~to~ 0.4~T}$ (indicated by the colorbar on the top). Each plot has been vertically offset by 0.8Ω for clarity. (b) Plot of the node positions ln(${n_c}$) as a function of magnetic field ln($B$). The black dashed line shows the linear fit to the data with a slope of $\sim 1.99 \pm 0.06$, implying that $n_c \propto B^2$.
• Figure 3: Strain-induced pseudomagnetic field and the origin of beating in Shubnikov--de Haas oscillations. (a) Schematic Landau level (LL) structure in single-layer graphene for the two valleys, $K$ and $K'$, under an external magnetic field $B$ in the absence of pseudomagnetic field ($B_{\mathrm{pm}} = 0$); both valleys are degenerate. (b) Calculated normalized DOS for $K$, $K'$, and their combined contribution for $B = 0.2~\mathrm{T}$ and $B_{\mathrm{pm}} = 0$, showing conventional periodic SdH oscillations with no amplitude modulation. (c) Under a finite pseudomagnetic field $B_{\mathrm{pm}}$, charge carriers in the two valleys experience opposite effective fields $B_{\mathrm{eff}}^{K,K'} = B \pm B_{\mathrm{pm}}$, breaking valley degeneracy and inducing a relative phase shift between their LL spectra. (d) Calculated normalized DOS for $B = 0.2~\mathrm{T}$ and $B_{\mathrm{pm}} = 13.4~\mathrm{mT}$ showing clear amplitude modulation (beating) arising from valley interference between the shifted quantization ladders. The DOS plots in panels (b) and (d) are vertically offset for clarity. A constant LL broadening of $\sim 1$ meV has been used in all calculations.
• Figure 4: Extraction of $B_{pm}$ from Fourier spectrum. (a) Plot of $R_{xx}$ versus $n$ measured at $B=0.32$ T. (b) Fourier spectrum of the data in panel (a) showing the two Fourier peaks $f_1$ and $f_2$.
• Figure S1: Device characterization. Plot of $R_{xx}$ as a function of $V_{bg}$, measured at $T = 20~\mathrm{mK}$ and $B = 0~\mathrm{T}$ (pink open circles). The black line represents a fit to Eq. \ref{['eg: S1']}.