Phason-driven temperature-dependent transport in moiré graphene

TL;DR

The study addresses the origin of temperature-dependent transport in moiré graphene, proposing that phason modes arising from moiré lattice reconstruction scatter electrons and dominate resistivity. It combines high-quality transport measurements in minimally twisted bilayer graphene with a continuum theory of moiré phonons and phasons and a semiclassical Boltzmann transport calculation that includes electron–phason coupling. The results reveal a robust linear-in-$T$ resistivity at intermediate temperatures, a low-$T$ $T^2$ regime attributed to phason scattering, and a strong modulation with band filling, indicating phasons as a principal mechanism shaping transport in moiré systems. This work highlights the intrinsic link between moiré lattice dynamics and electronic transport, with implications for tuning conductivity in vdW heterostructures through twist angle, band structure, and damping of collective modes.

Abstract

The electronic and vibrational properties of 2D materials are dramatically altered by the formation of a moiré superlattice. The lowest-energy phonon modes of the superlattice are two acoustic branches (called phasons) that describe the sliding motion of one layer with respect to the other. Considering their low-energy dispersion and damping, these modes may act as a significant source of scattering for electrons in moiré materials. Here, we investigate temperature-dependent electrical transport in minimally twisted bilayer graphene, a moiré system developing multiple weakly-dispersive electronic bands and a reconstructed lattice structure. We measure a linear-in-temperature resistivity across the band manyfold above $T\sim{10}$ K, preceded by a quadratic temperature dependence. While the linear-in-temperature resistivity is up to two orders of magnitude larger than in monolayer graphene, it is reduced (approximately by a factor of three) with respect to magic-angle twisted bilayer graphene. Moreover, it is modulated by the recursive band filling, with minima located close to the full filling of each band. Comparing our results with a semiclassical transport calculation, we show that the experimental trends are compatible with scattering processes mediated by longitudinal phasons, which dominate the resistivity over the contribution from conventional acoustic phonons of the monolayer. Our findings highlight the close relation between vibrational modes unique to moiré materials and carrier transport therein.

Figures (10)

• Figure 1: (a) Schematics of the studied device. (b) STM topographic image of a mTBG sample with top exposed surface; sample temperature and tip current are 78 K and 0.4 nA respectively. (c) Adhesion energy density (per graphene's unit cell) between the two layers of mTBG ($\theta=0.4^{\circ}$) in real space after relaxation; the model parameters are the shear and bulk modulus of graphene, $\mu = 9.57 \text{ eV/\AA}^{2}$ and $B = 12.82 \text{ eV/\AA}^{2}$, respectively, and the adhesion energy constant, $V = 0.89$ meV/Å$^{2}$ (see more details in the Supplemental Material supp). (d) Enlarged adhesion energy map corresponsing to a frozen longitudinal phason mode with wavevector $0.077$ nm$^{-1}$ along the $\Gamma-M$ axis of the moiré Brillouin zone. The color scale for the adhesion energy is the same in panel c and d. The scale bars are 100 nm in panels b, d, and 40 nm in c.
• Figure 2: (a) Resistivity of mTBG (black line, top panel) and Hall carrier density (red line, bottom panel) as a function of back-gate voltage. The Hall measurements are performed at a perpendicular magnetic field $B=0.24$ T. The vertical dashed gray lines are located at integer $n/n_s$ values. (b) Color maps of longitudinal resistivity (top) and Hall conductivity (bottom), as a function of band filling and magnetic field. The arrows indicate three representative conditions of rational values of flux quanta per superlattice unit cell. All data are acquired at $T=0.36$ K.
• Figure 3: (a) Resistivity and (b) Hall coefficient $R_H$ (measured at $B=0.25$ T) as a function of band filling and temperature (Log scale). (c) $\rho(T)$ at two representative values of band filling (see markers in panel a). Literature reference curves for 1.2°-TBG (gray dotted line) and monolayer graphene (MLG, light blue dotted line) are reported for comparison from Ref. polshyn2019large and Ref. wang2013one , respectively. (d) $\rho(T)$ at selected fillings within the first moiré band (black lines). The curves are offset by 0.3 k$\Omega$ for clarity. The solid red lines are linear fits. (e) Extracted $d\rho/dT$ from linear fits as a function of band filling. The shaded red area corresponds to $\pm$ one standard error from the fits.
• Figure 4: (a) Phonon bands of mTBG within the moiré Brillouin zone. The line styles and colors identify three groups of vibrational modes: in-phase phonons (gray dashed), optical moiré phonons (purple dotted), and phasons (purple continuous). The same code applies to contributions of these modes to $\rho_{e-ph}$ plotted in panels b, c and d. (b) Experimental T-dependent resistivity $\Delta\rho$ (open black circles) and computed resistivity $\rho_{e-ph}$ for carriers scattering off of in-phase phonons and phasons, as a function of band filling, at $T=8.6$ K. The model parameters are reported in the Supplemental Material supp. (c,d) Computed $\rho_{e-ph}$ for the longitudinal phason (solid) and transverse in-phase phonon (dashed) modes, as a function of $T$ at $n_s/4$ and $n_s/2$. The light blue and red lines are guides to the eye for the quadratic and linear-in-$T$ trends of the phason contribution. (e,f) $\Delta\rho$ as a function $T$, at $n_s/4$ and $n_s/2$. The light blue and red lines are quadratic and linear fits to the data, respectively, performed over different $T$ ranges. The y axis is the same in panels c-d, as also in panels e-f; the x axis is the same in panels c, d, e and f. (g) $\Delta\rho$ as a function of temperature at selected fillings within the first electronic band. The curves are offset by 0.3 k$\Omega$ for clarity. The light blue lines are quadratic fits to the data.
• Figure S1: (a) Electron bands at $\theta = 0.4^{\circ}$, where color distinguishes valleys. The panel on the right displays the total density of states in arbitrary units. (b) Fermi surfaces within the mBZ at three representative fillings: below, close to, and above the Lifshitz transition.