Strong Asymmetric Charge Carrier Dependence in Inelastic Electron Tunneling Spectroscopy of Graphene Phonons

The observation of phonons in graphene by inelastic electron tunneling spectroscopy has been met with limited success in previous measurements arising from weak signals and other spectral features which inhibit a clear distinction between phonons and miscellaneous excitations. Utilizing a back-gated graphene device that allows adjusting the global charge carrier density, we introduce an averaging method where individual tunneling spectra at varying charge carrier density are combined into one representative spectrum. This method improves the signal for inelastic transitions while it suppresses dispersive spectral features. We thereby map the total graphene phonon density of states, in good agreement with density functional calculations. Unexpectedly, an abrupt change in the phonon intensity is observed when the graphene charge carrier type is switched through a variation of the back-gate electrode potential. This sudden variation in phonon intensity is asymmetric in the carrier type, depending on the sign of the tunneling bias.

Figure 1

Phonon spectroscopy of single layer graphene on an $h\text{−}\mathrm{BN}/{\mathrm{SiO}}_2$ field effect device. The $dI/dV$ spectra in (a) and $d^{2}I/d{V}^2$ data in (b)–(e) are the average of a series of spectra recorded over charge carrier concentrations, tuned by the back-gate electrode from $V_g=-40$ to $+40\mathrm{V}$. The inelastic transitions (1–5) are attributed to phonons in graphene and excitation (6) to an overtone. (c)–(e) Higher resolution portions of the $d^{2}I/d{V}^2$ spectra with increased averaging times. Symbols are experimental data, dashed lines show fits to single Lorentzian functions, and solid lines are the sum of the fits, except the blue dashed line in (c) connecting data symbols. Peak numbers refer to excitations in Table 1. A linear background was subtracted from $d^{2}I/d{V}^2$ spectra in (b)–(e).

Figure 2

(a) Phonon dispersion and (b) phonon DOS for single layer graphene obtained from density functional calculations. The observed phonon threshold energies are indicated by horizontal dashed lines with two experimentally determined standard deviations between lines.

Figure 3

Gate-voltage-dependent phonon spectroscopy of single layer graphene on $h\text{−}\mathrm{BN}/{\mathrm{SiO}}_2$. (a) $d^{2}I/d{V}^2$ gate map showing the asymmetry of the phonon intensity with sample tunneling bias $V_b$ and back-gate voltage $V_g$. The excitations $\hslash {\omega }_1$ to $\hslash {\omega }_6$ from Fig. 1 are indicated by the arrows. (b) $d^{2}I/d{V}^2$ data tracing the gate-dependent phonon intensity, using mode $\hslash {\omega }_6$ as an example. The peak height ratio between the outermost gate values around $\pm 40\mathrm{V}$ is $8.1\pm 0.9(+\hslash {\omega }_6)$ and $7.3\pm 0.6(-\hslash {\omega }_6)$. The uncertainties were derived from the standard error of $d^{2}I/d{V}^2$ values in the gate voltage range between $\pm (40\text{and}20)\mathrm{V}$. (c) $d^{2}I/d{V}^2$ gate map showing the asymmetry of the phonon excitations. The tip work function has been increased relatively to the measurement in (a) by adsorption of deuterium, resulting in a shift of the electron vs hole boundary to positive gate voltages in the gate map [29]. The intervals enclosed by arrows denote the regions where the $\hslash {\omega }_6$ mode is enhanced.