Ultrafast Dynamics of Massive Dirac Fermions in Bilayer Graphene

Bilayer graphene is a highly promising material for electronic and optoelectronic applications since it is supporting massive Dirac fermions with a tunable band gap. However, no consistent picture of the gap’s effect on the optical and transport behavior has emerged so far, and it has been proposed that the insulating nature of the gap could be compromised by unavoidable structural defects, by topological in-gap states, or that the electronic structure could be altogether changed by many-body effects. Here, we directly follow the excited carriers in bilayer graphene on a femtosecond time scale, using ultrafast time- and angle-resolved photoemission. We find a behavior consistent with a single-particle band gap. Compared to monolayer graphene, the existence of this band gap leads to an increased carrier lifetime in the minimum of the lowest conduction band. This is in sharp contrast to the second substate of the conduction band, in which the excited electrons decay through fast, phonon-assisted interband transitions.

Figure 1

Ultrafast ARPES measurements of bilayer graphene: (a) Normalized photoemission intensity integrated above the Fermi level. Vertical dashed lines mark the times of the dispersion snapshots in (g)–(j). (b)–(e) Diagrams of ultrafast processes and relaxation dynamics involving optical pumping (straight arrows), electron scattering (curled arrows), optical (vertical blue wiggled arrows), and acoustic (green wiggled arrows) phonon scattering. Filled (open) circles signify electrons (holes). (f) Spectrum before the arrival of the pump pulse with the inset showing the acquisition direction for all data ($\overline{\mathrm{\Gamma }}–\overline{K}$). (g)–(j) ARPES difference spectra obtained by subtracting the spectrum in (f) from the spectrum taken at the given time. A pump laser fluence of $F=1.0\mathrm{mJ}/{\mathrm{cm}}^2$ was used. The dashed parabolic bands are the result of a tight binding calculation and have been added as a guide to the eye.

Figure 2

Disentangling the dynamics in the bilayer bands: (a),(e) Photoemission intensity integrated between the dashed lines in (b) and (f) as a function of binding energy. Markers correspond to data points at the given time delay, and lines are integrated intensity from simulated photoemission data with the given temperatures. (b),(f) Experimental photoemssion data at the peak excitation signal at time $t=40\mathrm{fs}$. (c),(g) Simulated data at the given temperature taking the experimental resolution into account. (d),(h) Simulated data without resolution broadening. The vertical dashed lines in (a) and (e) and the horizontal dashed lines in (d) and (h) mark the onset energy of the two conduction bands. The data in (a)–(d) correspond to a fluence of $1.0\mathrm{mJ}/{\mathrm{cm}}^2$ while the data in (e)–(h) correspond to $3.5\mathrm{mJ}/{\mathrm{cm}}^2$.

Figure 3

Comparing the relaxation dynamics of massive and massless Dirac Fermions: (a) Spectrum before the arrival of the pump pulse and (b)–(d) difference spectra at selected time delays for BLG. (f)–(i) Corresponding data for MLG. Dispersion lines from tight binding models have been added as guide to the eye. (e),(j),(k) Normalized photoemission intensity binned over the boxes in (b)–(d) for (e) BLG and (g)–(i) for (j) MLG. The time traces in (e) and (j) have been labeled with a number according to the box numbers, and the given time constants are results of single exponential fits to the corresponding trace. The error bar on these fits amounts to $\pm 20\mathrm{fs}$. (k) Integrated intensity in box 1 for both BLG and MLG. Lines correspond to double-exponential function fits with the given time constants. The fluence is $0.6\mathrm{mJ}/{\mathrm{cm}}^2$ for all data presented here. (l),(m) Sketch of the relaxation dynamics involving hot electrons (red spheres), holes (yellow spheres), and phonon emission (wiggled arrows) around the Dirac point for (l) massive Dirac Fermions and (m) massless Dirac Fermions.