Phonon-Pump Extreme-Ultraviolet-Photoemission Probe in Graphene: Anomalous Heating of Dirac Carriers by Lattice Deformation

We modulate the atomic structure of bilayer graphene by driving its lattice at resonance with the in-plane $E_{1u}$ lattice vibration at $6.3\mu \mathrm{m}$. Using time- and angle-resolved photoemission spectroscopy (tr-ARPES) with extreme-ultraviolet (XUV) pulses, we measure the response of the Dirac electrons near the $K$ point. We observe that lattice modulation causes anomalous carrier dynamics, with the Dirac electrons reaching lower peak temperatures and relaxing at faster rate compared to when the excitation is applied away from the phonon resonance or in monolayer samples. Frozen phonon calculations predict dramatic band structure changes when the $E_{1u}$ vibration is driven, which we use to explain the anomalous dynamics observed in the experiment.

Figure 1

(a) Sketch of the tr-ARPES experiment. The MIR-pump pulse (red, light grey) at normal incidence resonantly excites the in-plane $E_{1u}$ lattice vibration in bilayer graphene. A collinear XUV-probe pulse (blue, dark grey) ejects photoelectrons that pass through a hemispherical analyzer and impinge on a two-dimensional detector. (b) Equilibrium band structure for hydrogen-intercalated monolayer (ML) and bilayer (BL) graphene measured with HeII$\alpha$ radiation for a cut through the $K$ point perpendicular to the $\mathrm{\Gamma }K$ direction (see inset).

Figure 2

Snapshots of the electronic structure along the $\mathrm{\Gamma }K$ direction (see inset) of bilayer graphene for different pump-probe delays (upper panel) together with the corresponding pump-probe signal (lower panel). The excitation wavelength was $6.3\mu \mathrm{m}$ in resonance with the in-plane $E_{1u}$ lattice vibration. The fluence was $F=0.26\mathrm{mJ}/{\mathrm{cm}}^2$.

Figure 3

(a) Momentum-integrated photocurrent from Fig. 2 as a function of energy and pump-probe delay in the vicinity of the Fermi level. (b) Width of the Fermi-Dirac distribution as a function of pump-probe delay (data points). The continuous line is a fit including an error function for the rising edge and the sum of two exponentials to describe the decay. (c) Dependence of the peak electronic temperature, obtained by deconvolving the peak Fermi width with the experimental energy resolution (see Supplemental Material [20]), on excitation wavelength for constant excitation fluence of $0.26\mathrm{mJ}/{\mathrm{cm}}^2$. (d) Dependence of the fast relaxation time ${\tau }_1$ on excitation wavelength for constant excitation fluence of $0.26\mathrm{mJ}/{\mathrm{cm}}^2$. The corresponding data for monolayer graphene for fluences between 0.26 and $0.8\mathrm{mJ}/{\mathrm{cm}}^2$ is shown in black for direct comparison. Continuous lines in (c) and (d) are guides to the eye. Dashed lines in (c) and (d) show the Fano line shape of the phonon in the real part of the optical conductivity $\mathrm{\Delta }{\sigma }_1$ from [14].

Figure 4

(a) Sketch of the excitation due to electric field acceleration (green, light grey) and band structure shift (blue, dark grey). The field polarization lies along $k_y$ ($\mathrm{\Gamma }M$). The displacement of the atoms in real space leads to a corresponding displacement of the Dirac cone in momentum space along $k_x$ ($\mathrm{\Gamma }K$). The combined effect results in a complicated sloshing motion of the electrons that depends on the relative phase and amplitudes of the electric field acceleration and the band structure displacement, respectively. (b) Density functional theory calculations of the electronic structure around the $K$ point in the vicinity of the Fermi level for different lattice distortions of 0%, 2%, and 3% of the equilibrium lattice constant along the $E_{1u}$ mode coordinate.