Enhanced electron-phonon coupling in graphene with periodically distorted lattice

Electron-phonon coupling directly determines the stability of cooperative order in solids, including superconductivity, charge, and spin density waves. Therefore, the ability to enhance or reduce electron-phonon coupling by optical driving may open up new possibilities to steer materials' functionalities, potentially at high speeds. Here, we explore the response of bilayer graphene to dynamical modulation of the lattice, achieved by driving optically active in-plane bond stretching vibrations with femtosecond midinfrared pulses. The driven state is studied by two different ultrafast spectroscopic techniques. First, terahertz time-domain spectroscopy reveals that the Drude scattering rate decreases upon driving. Second, the relaxation rate of hot quasiparticles, as measured by time- and angle-resolved photoemission spectroscopy, increases. These two independent observations are quantitatively consistent with one another and can be explained by a transient threefold enhancement of the electron-phonon coupling constant. The findings reported here provide useful perspective for related experiments, which reported the enhancement of superconductivity in alkali-doped fullerites when a similar phonon mode was driven.

Figure 1

The effects of resonant excitation of the in-plane $E_{1u}$ mode in bilayer graphene (the atomic motions are indicated by red arrows) are investigated with (a) terahertz time-domain spectroscopy and (b) time- and angle-resolved photoemission spectroscopy.

Figure 2

(a) An increase of the electron-phonon coupling constant ${\lambda }_{\text{e-ph}}$ is predicted to enhance the scattering time and thus reduce the width of the Drude peak in the real part of the optical conductivity. (b) Transmitted electric THz field without pump (blue) and pump-induced changes of the field at the peak of the pump-probe signal for ${\lambda }_{\text{pump}}=6.1\mu \mathrm{m}$. (c) Pump-induced changes of the real part of the optical conductivity as a function of energy for different pump wavelengths in the midinfrared, together with Drude fits. (d) Drude scattering time (left axis) and electron-phonon coupling constant (right axis) as a function of pump wavelength. The red(blue)-shaded area indicates the increase in ${\tau }_{\text{D}}$ due to heating (an enhanced ${\lambda }_{\text{e-ph}}$). The black dashed line indicates the equilibrium value of ${\tau }_{\text{D}}$.

Figure 3

(a) Expected increase of the energy-resolved relaxation rate due to a pump-induced enhancement of ${\lambda }_{\text{e-ph}}$. (b) Momentum-integrated photocurrent measured along the $\mathrm{\Gamma }K$ direction in the vicinity of the $K$ point as a function of pump-probe delay after excitation at ${\lambda }_{\text{pump}}=6.3\mu \mathrm{m}$. These experiments were performed at 30 K with energy and temporal resolutions of 600 meV and 100 fs, respectively. (c) Lineouts at constant energy (here, $E=0.43\mathrm{eV}$) are fitted with an exponential decay to obtain the energy-dependent relaxation time $\tau$. (d) Relaxation rate $1/\left(2\tau \right)$ as a function of energy for different pump wavelengths in the midinfrared. For ${\lambda }_{\text{pump}}=6.3$ and 7.3 $\mu \mathrm{m}$ (at resonance with the $E_{1u}$ phonon) the energy-integrated relaxation rate is enhanced, indicating an increase of the electron-phonon coupling constant ${\lambda }_{\text{e-ph}}$.

Figure 4

(a) Momentum-integrated photocurrent as a function of energy at negative delay (black) and at the peak of the pump-probe signal for ${\lambda }_{\text{pump}}=6.3\mu \mathrm{m}$ (on resonance, blue) and ${\lambda }_{\text{pump}}=9\mu \mathrm{m}$ (off resonance, red), together with Fermi-Dirac fits. (b) Electronic temperature as a function of pump-probe delay for ${\lambda }_{\text{pump}}=6.3\mu \mathrm{m}$ (blue) and ${\lambda }_{\text{pump}}=9\mu \mathrm{m}$ (red), together with double-exponential fits. Black lines illustrate the difference in the fast time constant between on- and off-resonance excitation. (c) Electronic peak temperature and (d) fast relaxation time as a function of pump wavelength (data points), together with a simulation based on a two-temperature model (green lines). The width of the green lines represents the experimental uncertainty in ${\lambda }_{\text{e-ph}}$.