Ultrafast Band-Gap Renormalization in Bilayer Graphene

Abstract

We demonstrate, by femtosecond time- and angle-resolved photoemission spectroscopy, that photoinduced interlayer charge transfer in a heterostructure consisting of Bernal-stacked bilayer graphene and a single atomic layer of silver on 6H-SiC(0001) transiently modulates the intrinsic potential landscape across the silver-graphene interface. This acts as an ultrafast optoelectronic gate that drives momentum-dependent band renormalizations, resulting in a transient band-gap opening on femtosecond timescales. Simultaneously, the photogenerated hot-carrier population enhances electronic screening, leading to subsequent closing of the band-gap beyond the thermal equilibrium value. These findings reveal two different mechanisms for photoinduced, reversible control of the electronic band structure in bilayer graphene -- interlayer charge transfer and hot-carrier-enhanced screening -- providing a general framework for the ultrafast control of electronic properties in graphene-based heterostructures. This opens up novel pathways for the realization of ultrafast optoelectronic devices and the exploration of correlated quantum phases in bilayer graphene under non-equilibrium conditions.

Figures (8)

• Figure 1: Structural and electronic properties of Bernal-stacked BLG / MLAg / 6H-SiC(0001). (A) Illustration of the tr-ARPES experiment used in this study and the crystalline structure of the sample with MLAg intercalated between 6H-SiC and BLG. The sample is photoexcited with pump pulses ($\hbar\omega_\mathrm{pump} = 3.1eV$) at an incident fluence of $4.5mJ\per cm\squared$. Time-delayed probe pulses ($\hbar\omega_\mathrm{probe} = 22.1eV$) generate photoelectrons, which are detected in a hemispherical photoelectron analyzer. (B) Unit cell of BLG: The bottom layer shows the two carbon atoms of the sublattices of a graphene layer and the associated $p_z$ orbitals on dimer and non-dimer sites. The parameter $\gamma_1$ reflects the hopping between $p_z$ orbitals on dimer sites. The presence of an intrinsic $U$ creates a gradient in the carrier density across the two layers. (C) Hexagonal Brillouin zones and three-dimensional representation of the tight-binding valence band structures of BLG McCannPhysicalReviewLetters2006McCannPhysicalReviewB2006McCannReportsOnProgressInPhysics2013 and MLAg in the $\mathrm{Ag}_{(1)}$ phase RosenzweigPhysicalReviewB2020. The red lines indicate the directions along which the photoemission spectra were measured. (D) Tight-binding model of the electronic band structures of BLG and MLAg in the $\mathrm{Ag}_{(1)}$ phase along selected high-symmetry directions. The right panel shows a close-up of the BLG band structure near the CNP with the spectral signatures for $\gamma_1$, $U$ and $U_\mathrm{g}$ indicated.
• Figure 2: Non-equilibrium carrier and interlayer charge transfer dynamics. (A) Equilibrium photoemission spectrum (left) of BLG at $\mathrm{K}_\mathrm{G}$ and differential photoemission spectrum (right) at $t - t_0 = 100fs$, both superimposed with the equilibrium tight-binding band structure. The momentum cut is oriented perpendicular to the $\mathrm{\Gamma}$--$\mathrm{K}_\mathrm{G}$ direction and is highlighted in red in Fig.\ref{['fig:struct_electronic_prop']}C, with $k_\parallel$ denoting the electron wave vector parallel to the sample surface. The redistribution of spectral weight below $\mu_\mathrm{e}$ indicates a rigid upshift of the $\pi$ bands toward lower binding energies, as indicated by the arrows. Direction of the band shifts in panels A and D is referenced to the equilibrium $\mu_\mathrm{e}$. (B) Integrated photoemission intensities from regions of interest R1--R3, indicated in panel A, as a function of pump--probe delay. (C) Electronic temperature $T_\mathrm{e}$ as a function of pump--probe delay. Solid lines in panels B and C represent multi-exponential fits to the experimental data (Supplementary Materials). The two time constants, $\tau_\mathrm{oe}$ and $\tau_\mathrm{ae}$, characterize the carrier--lattice thermalization process. (D) Equilibrium photoemission spectrum (left) of MLAg at $\mathrm{K}_\mathrm{Ag}$ and differential photoemission spectrum (right) at $t - t_0 = 100fs$. The momentum cut is oriented perpendicular to the $\Gamma$--$K_\mathrm{Ag}$ direction and is highlighted in blue in Fig. \ref{['fig:struct_electronic_prop']}C. Redistribution of spectral weight below $\mu_\mathrm{e}$ indicates a rigid downshift of the valence band toward higher binding energies, as indicated by the arrows. (E) Rigid band shifts $\Delta E$ in BLG and MLAg and the change in the built-in potential across the MLAg--BLG interface, $\Delta\varphi_\mathrm{bi}$, as a function of pump--probe delay. The scale on the right axis of the graph indicates the transferred charge density $n_\mathrm{ICT}$, determined from $\Delta\varphi_\mathrm{bi}$. The red and blue solid lines are exponential fits to the experimental data (Supplementary Materials). The black solid line, representing $\Delta\varphi_\mathrm{bi}$, is obtained by subtracting the corresponding fits. (F) Energy-band diagrams of MLAg (left) and BLG (right), illustrating the ICT-induced rigid band shifts in both BLG and MLAg, and the resulting $\Delta\varphi_\mathrm{bi}$.
• Figure 3: Ultrafast band renormalization in BLG. (A) Differential photoemission spectra at $t - t_0 = 100fs$ (left) and $250fs$ (right) of BLG at $\mathrm{K}_\mathrm{G}$. The comparison of the spectra reveals a delayed buildup of in-gap spectral weight between the $\pi_0$ and $\pi_0^\ast$ bands, as well as a delayed buildup of spectral weight below the $\pi_1$ band. (B, C) Transient differential EDCs for two distinct momentum regions of interest R1 (B) and R2 (C) marked in panel A. Relevant band energies are indicated. The arrows indicate the directions of the band renormalizations in panel B and the rigid band shift in panel C associated with the observed redistributions of spectral weight. (D) Equilibrium photoemission spectrum measured with higher energy resolution ($\Delta E_\mathrm{res}\approx 190meV$) compared to all other spectra shown. It enables to spectrally resolve the splitting of the $\pi_0$ and $\pi_1$ bands. The spectrum is superimposed with an EDC at $k_\parallel - \mathrm{K}_\mathrm{G}\approx 0.17\per\angstrom$. The equilibrium interlayer potential asymmetry $U$, which can be determined from the $\pi_0$--$\pi_0^*$ splitting around CNP at $\mathrm{K}_\mathrm{G}$ is indicated. (E) Changes in the $\pi_0$ band binding energies $\Delta E$ as a function of pump--probe delay for different momentum regions of interest R3--R5 indicated in panel D. The binding energies have been determined from fits to EDCs (Supplementary Materials). The changes in band energies for R3 and R4 have been vertically offset for clarity. (F) Interlayer potential asymmetry $U$ as a function of pump--probe delay calculated by subtraction of the R5 transient from the R3 transient in panel E. Solid lines are guides to the eye. Here, red (blue) coloring indicates gap opening (closing) with respect to equilibrium as depicted by the insets.
• Figure 4: Single-back-gate model and non-equilibrium dielectric response of BLG. (A) Tight-binding band structure of the $\pi_0$ and $\pi_0^\ast$ bands, calculated before photoexcitation (dashed line) and for an increased interlayer potential asymmetry of $\Delta U = 100meV$ (solid line) at $t - t_0 = 100fs$. The band structure for $\Delta U = 100meV$ was shifted by $\Delta E_\mathrm{G} = -50meV$ to lower binding energies to account for the ICT-induced rigid band shift. For the $\pi_0$ band near $\mathrm{K}_\mathrm{G}$, the band shifts due to $\Delta U$ and $\Delta E_\mathrm{G}$ almost completely compensate each other, leading to a virtually absent spectral redistribution in the differential photoemission spectrum. (B) Transient dynamics of $U$ determined from the experiment ($U_\mathrm{exp}$) compared to the result of the single-back-gate model ($U_\mathrm{mod}$). (C) Differential photoemission spectra at $t - t_0 = 100fs$ in the $\pi^\ast$-band region superimposed with the tight-binding band structure. The region of interest R2, marked by the blue line, includes the energy range above $\mu_\mathrm{e}$, where carrier cooling is only possible by acoustic phonon emission (green arrow). The energy region R1 includes in addition the energy range above $\mu_\mathrm{e}$, where carrier cooling is dominated by optical phonon emission (yellow arrow) YanPhysicalReviewB2008MalicPhysicalReviewB2011. The initial photoabsorption process using $\hbar\omega = 3.1eV$ pump pulses (see black arrow) generates a nascent carrier distribution at $E-\mu_\mathrm{e}\approx1.1eV$. (D) Comparison of the time dependence of the relative permittivity $\varepsilon_\mathrm{r, eff}$ and the momentum-integrated photoemission intensities $I$ in regions R1 and R2 marked in panel C.
• Figure S1: Interlayer potential asymmetry of BLG. Equilibrium photoemission spectra at $\mathrm{K}_\mathrm{G}$. The EDC near and within the band-gap region was fitted using a sigmoid function to determine the band-edge energy at $\mathrm{K}_\mathrm{G}$ of the $\pi_0$ band. The interlayer potential asymmetry $U$ was approximated by twice the energy difference between bandedge and charge neutrality point (CNP), corresponding to the doping level of $600meV$ relative to $\mu_\mathrm{e}$, and the $\pi_0$-band edge, i.e., $U \approx 2 (E_{\pi_0} - E_\mathrm{CNP})\approx 300meV$.