Valley polarization of graphene via the saddle point

TL;DR

This paper tackles the challenge of achieving valley polarization in gapless graphene by proposing a dual-frequency, linearly polarized excitation that leverages a selection rule at the M-point saddle to generate valley-localized states. A THz envelope then displaces the M-point excitation into a low-energy K valley, with the sign of the THz pulse selecting between $K$ and $K^\ast$, enabling high valley polarization. Using both tight-binding simulations and ab initio TDDFT calculations, the authors show near-perfect valley polarization (up to $\eta \approx 0.9$) and reveal a THz-driven de-excitation mechanism that enhances valley contrast beyond what TB predicts. The approach provides a route to lightwave valleytronics in gapless Xenes and could extend to other graphene-based systems, offering a practical pathway for valley control without relying on a band gap or carrier-envelope phase stability.

Abstract

Graphene, and other members of the monolayer Xene family, represent an ideal materials platform for "valleytronics", the control of valley localized charge excitations. The absence of a gap in these semi-metals, however, precludes valley excitation by circularly polarized light pulses, sharply circumscribing the possibility of a lightwave valleytronics in these materials. Here we show that combining a deep ultraviolet linearly polarized light pulse with a THz envelope can induce highly valley polarized states in graphene. This dual frequency lightform operates by (i) the deep ultraviolet pulse activating a selection rule at the M saddle points and (ii) the THz pulse displacing the M point excitation to one of the low-energy K valleys. Employing both tight-binding and state-of-the-art time dependent density functional theory, we show that such a pulse results in a near perfect valley polarized excitation in graphene, thus providing a route via the saddle point to a lightwave valleytronics in the gapless Xene family.

Figures (5)

• Figure 1: Saddle point polarization in graphene. (a) The Brillouin zone of graphene with the three inequivalent M points labelled. A few cycle deep ultraviolet pulse tuned to the 4 eV M point gap, vector potential shown in panel (b), generates a charge excitation, panel (c). This charge excitation is strikingly inhomogeneous in momentum space, with the excitation dominant at one of the three inequivalent M points, panel (d).
• Figure 2: Valley polarization by double pumped light. By combining a deep ultraviolet pulse tuned to the M point gap with an orthogonal THz pulse whose amplitude satisfies $A/c = |{\bf K} - {\bf M_1}|$, vector potential shown in panel (a), the charge excitation created at $M_1$ by the deep ultraviolet pulse is shifted to one of the K valleys, panel (b), in which is shown the momentum resolved excitation after the pulse. The deep ultraviolet pulse is the same as that employed in Fig. \ref{['fig1']} and comparison of the momentum resolved excitations between the deep ultraviolet pulse acting alone, Fig. \ref{['fig1']}(d), and in combination with a THz envelope, panel (b), clearly shows the change induced by the THz component. Switching the sign of the THz pulse amplitude selects for either polarization at the K valley, panels (a,b), or the K$^\ast$ valley, panels (c,d).
• Figure 3: Optimizing valley polarization via the deep ultraviolet pulse component. (a) The valley polarization of graphene created by the dual frequency deep ultraviolet and THz pulse, shown as a function of the full width half maxima (FWHM) and amplitude ($A_0$) of the deep ultraviolet component. The THz component is held fixed to the form shown in Fig. \ref{['fig2']}(a). Regions of strong valley polarization can be seen to alternate with regions in which the valley polarization falls nearly to zero. Panels (b-e) display the momentum resolved excitation for four representative cases, as labelled in panel (a). The pulse parameters corresponding the Fig. \ref{['fig2']}(a,b) are also indicated as the point "(2b)".
• Figure 4: Variation of the valley polarization as a function of the duration of the THz pulse component. The charge excited by the THz component -- two lines of charge in the K-M direction at each valley -- depends on the THz electric field which, as the amplitude of this pulse component is fixed to $\bm{\mathrm{A}}_0 = (\bm{\mathrm{K}}-\bm{\mathrm{M}}_1)/c$, depends on the pulse duration. Reduction of the THz full width half maximum (FWHM) increases the THz electric field and excited charge, lowering the valley polarization, as shown in panel (a). The momentum resolved charge excitation for two representative pulses at the temporal limits of the pulse envelope, as labelled in panel (a), are shown in panels (b) and (c).
• Figure 5: Comparison between (i) tight-binding and (ii) time dependent density functional theory for the charge excitation induced by double pumped THz and deep ultraviolet light in gapless graphene. (a) Vector potential of a dual frequency laser pulse combining orthogonally polarized THz light (the Gaussian envelope) and a deep ultraviolet pulse tuned to the M point gap (shown also as the inset panel). (b,c) The charge excitation after the pulse calculated, respectively, with the tight-binding and time dependent density functional theory. While the principal result of charge excitation at the K$^\ast$ valley can be seen in both cases, the charge excitation generated by the THz component at the K valley -- clearly visible in the TB result -- is absent in the TD-DFT simulation.