Longitudinal Nonreciprocal Charge Transport with Time Reversal Symmetry

Abstract

Longitudinal nonreciprocal charge transport is widely believed to require time-reversal symmetry breaking, either in magnetic materials or through external magnetic fields. Here, we show that longitudinal nonreciprocity can arise even in nonmagnetic conductors without magnetic fields through disorder-induced asymmetric scattering. Using a semiclassical Boltzmann framework, we develop a general theory in which skew-scattering and side-jump processes generate a nonlinear longitudinal current that remains finite even in time-reversal-symmetric systems. A systematic symmetry analysis identifies 42 point groups that permit this extrinsic mechanism. As a concrete realization, we demonstrate that Bernal-stacked bilayer graphene exhibits a large and gate-tunable longitudinal nonreciprocal response with a sizable nonreciprocity factor near its Lifshitz transition. These results establish disorder-driven asymmetric scattering as a general mechanism for bulk longitudinal nonreciprocal charge transport in crystalline conductors.

Figures (4)

• Figure 1: Longitudinal nonreciprocal transport without magnetic fields. (a) Schematic $I_{||}$–$V$ characteristics illustrating linear, nonlinear, and resulting nonreciprocal responses. A second-order contribution makes the forward and reverse currents unequal, producing a nonreciprocal current response. (b) Microscopic mechanism. In noncentrosymmetric systems, asymmetric impurity scattering mechanisms such as skew-scattering and side-jump generate a longitudinal current $\propto E^2$, even when time-reversal symmetry ($\mathcal{T}$) is preserved. The table summarizes known mechanisms for longitudinal nonlinear transport and shows that extrinsic scattering processes enable nonreciprocity in nonmagnetic materials.
• Figure 2: Bernal-stacked bilayer graphene (BLG) and its electronic properties. (a) Crystal structure of BLG showing the AB stacking and the relevant intra- and interlayer hopping processes. (b) Electronic band dispersion of BLG. (c) Berry curvature distribution of the first conduction band in momentum space, exhibiting pronounced hot spots near the $K$ and $K'$ valleys. The dashed hexagon indicates the first Brillouin zone with marked high-symmetry points. (d) Band structure near the $K$ valley, color-coded by the Berry curvature magnitude, together with the density of states. BLG parameters are discussed in Sec. S2 of the SM NCT_SM, and the onsite potential is $\Delta = 0.05$ eV.
• Figure 3: Linear and nonlinear conductivities in bilayer graphene in the $\mu$-$\Delta$ plane. (a) Density of states, showing van Hove singularities near the band edges. (b) Linear Drude conductivity $\sigma_{yy}=\sigma_{xx}$. (c) Nonlinear side-jump contribution $\sigma^{\rm NSJ}_{yyy}$. (d) Nonlinear skew-scattering contribution $\sigma^{\rm NSK}_{yyy}$. We considered $T=20$ K with model parameters identical to Fig. \ref{['fig2']}.
• Figure 4: Large longitudinal nonreciprocity in gated bilayer graphene. (a) Calculated nonreciprocity factor $\eta$ as a function of chemical potential $\mu$ and displacement field $D$. Strong nonreciprocity appears near the band edges, where linear conductivity is small and nonlinear conductivity is large. (b) Experimentally measured second-harmonic voltage $V^{2\omega}_{xx}$ versus first-harmonic voltage $V^{\omega}_{xx}$ for different displacement fields $D$, reproduced from Ref. Ahmed2025detecting. (c) Nonreciprocity factor $\eta$ extracted from the experimental data using Eq. \ref{['eq:NR_factor']}, reaching values larger than $\sim 30\%$, consistent with theory.