Electronic transport in BN-encasulated graphene limited by remote phonon scattering

Abstract

We study the impact of BN's phonons on the electrical resistivity of hBN-encapsulated graphene. While encapsulation yields high-mobility devices, the surrounding BN itself introduces remote scattering from polar optical phonons, whose role in standard resistivity measurements remains unclear. We combine high-quality transport experiments with ab initio calculations including a proper treatment of dynamically screened remote interactions. We demonstrate that hBN's out-of-plane phonons strongly influence resistivity between 150 K and room temperature, whereas higher-energy LO modes and intrinsic graphene phonons alone cannot explain the observed trends. The coupling between electrons and the BN's phonons becomes more pronounced at low carrier densities due to reduced screening. Our findings establish that remote phonon scattering fundamentally limits transport in encapsulated graphene, solving a longstanding debate.

Figures (4)

• Figure 1: (a) Schematic illustration of the Hall bar device using an hBN/graphene/hBN stack. (b) Raman spectrum (averaged over the whole area between the contacts 1 to 4) taken with a 532 nm wavelength exitation and showing the characteristic peaks of graphene/h-BN heterostructures. (c) Longitudinal conductivity $\sigma = \sigma_{xx}$ as a function of gate voltage ($V_g$) in the temperature range $10$-$300$ K. $V_{\rm CNP}$ is the reference charge neutrality point voltage, and $n_{g}$ is the carrier density. (d) Different models of the gate voltage dependence of conductivity for a representative carrier mobility of $40{,}000\,\text{cm}^2\text{/Vs}$. Magenta dashed line: one carrier model. Green dash-dotted line: phenomenological model accounting for a residual charge density $n_0 = 10^{11}\,\text{cm}^{-2}$. Solid lines: thermally activated carriers at $0$, $50$, $150$, and $300$ K, (black, blue, orange, and brown respectively) for a disorder with potential fluctuationsPhysRevB.84.115442 of $35 \,\text{meV}$ (which gives $n_0(0\,\text{K}) \simeq 0.74\,\times 10^{11}\,\text{cm}^{-2}$ and $n_0(300\,\text{K}) \simeq 2.08\,\times 10^{11}\,\text{cm}^{-2}$). The inset of (d) shows the same experimental data as (c) for electron doping ($n_g>0$) on a log-log scale.
• Figure 2: Analysis of the resistivity of BN-encapsulated graphene. The columns correspond to experimental measurements with hole doping ('Exp. holes') , electron doping ('Exp. electrons') and ab initio calculations ('Theory') considering 20 BN layers on each side of graphene. Each column has its own color scale. Calculations are performed for electron doping, but due to enforced electron-hole symmetry the theory compares to both experiments. First row shows $\rho$ as a function of $T$. The contribution from acoustic phonons alone is represented as a dash-dotted line ('Ac. only'). Second row shows $\rho^{-1}_{\rm opt}= \left( \rho-\rho_0-\rho_{\rm ac}\right)^{-1}$ in semi-logarithmic scale as a function of $1/T$, see text. Last row shows the extracted electronic coupling to BN's ZO phonons, in units of $C_0 \approx 15.2$ eV$^{-1}$ ps$^{-1}$. In the first 2 rows, we also plot the resistivity for isolated graphene as a dashed line ('Iso. Gr.'). The grey shading represents its variations with doping level accounting also for impurity-induced residual resistivity. .
• Figure 3: Slope of the acoustic phonons' linear contribution to the resistivity as a function of Fermi level. The slope is extracted from experiments by linear regression on the resistivity between $50$ and $150$ K, for both electron ('electrons' --- red circles) and hole ('holes' --- blue circles) doping type. The result from ab initio calculations, performed at the GW level, is represented as a constant line ('theory, ab initio' --- dashed line). The same fitting procedure is then applied to the theoretical resistivity calculations, where the acoustic coupling is reduced by $17\%$ ('theory fitted' --- green dots). This consistently shows good agreement with experimental data in a significant range of Fermi levels.
• Figure 4: Gate dependent carrier density, $n_{\textrm{H}}$, determined using the Hall voltage every 50 K, and $n_{\textrm{g}}$ calculated with a capacitive model with $C_{\textrm{g}} = 10^{-4}$ F.m$^{-2}$. The gray area is where $n_{\rm{H}} \neq n_{\rm{g}}$, while the blue and red ones are for regions where it can be safely stated that only one type of carrier contributes to transport.