Ultrafast Saddletronics

TL;DR

Ultrafast saddletronics demonstrates that linearly polarized light can selectively excite two of the three inequivalent $M$-point saddles in graphene, generating three possible saddle configurations and intrinsically current-carrying states. The authors combine π-band tight-binding calculations with ab initio real-time TD-DFT to reveal a simple geometric selection rule: the excitation probability scales with the projection of the light polarization onto the $M$-point momenta via $T(\omega) \\propto (\mathbf{M_i} \\cdot \\mathbf{A_0})^2 \, \\delta(2\varepsilon_M - \omega)$ with $\\varepsilon_M = 4$ eV, and a saddle current produces a detectable THz signal. This excitation is robust across sub-cycle and multi-cycle pulses, quantified by the saddle polarization $\\eta_M$ remaining near ±1 under wide parameter variation. Ab initio results confirm the tight-binding picture, showing zero excitation when the polarization is perpendicular to an $M$ point and maximal excitation when parallel. The work suggests a new ultrafast platform—saddletronics—for manipulating matter in graphene and Xenes, potentially enabling information processing on timescales faster than decoherence and extending to spinful and twisted systems.

Abstract

Low energy valleys in the band structure of 2d materials represent a potential route to the ultrafast writing of information in quantum matter by laser light, with excited charge at the K or K$^\ast$ valleys representing the fundamental states of 1 and 0. Here we demonstrate that a second electronic feature, the saddle point, is endowed with lightwave control over information states. Linearly polarized light is shown to excite 2 of the 3 inequivalent M point saddles in graphene, generating three possible excited configurations, with which of these are realised determined by the polarization vector direction. We show that saddle excitation is highly robust, with "saddle polarized" states created both in the sub-cycle strong field regime and the long time limit of extended multi-cycle pulses. Our findings, applicable to other members of the graphene family and Xenes such as stanene, point towards a rich and ultrafast light based manipulation of matter based on the saddle point.

Figures (5)

• Figure 1: Light-saddle coupling in graphene. For a deep ultraviolet light pulse tuned to the M point gap, there exists a profoundly anisotropic response to linearly polarized light. (a) Schematic illustration of excitation at the M point, with the saddle structure near M clearly visible. (b-d) The vector potential of three linearly polarized light pulses with the polarization vector indicated by the inset arrow, generates, (e-g), a momentum resolved charge excitation at 2 of the three inequivalent M points, with a complete absence of charge at the third, labelled $M_1$, $M_2$, and $M_3$ in (e-g). The polarization direction of saddle tuned light thus determines which configuration of 2 out of 3 inequivalent M points charge is excited at.
• Figure 2: Light induced "saddle current" in single layer graphene. Selective excitation of the three inequivalent saddle points is accompanied by a light-controlled current flow. (a) The total current as a function of the polarization vector of a linearly polarized pulse (other pulse parameters are identical to the waveforms presented in Fig. \ref{['fig1']}(a-c)). As is made clear by the inset panel, the direction of the induced current $\theta_J$ is exactly anti-parallel to the angle of the pulse polarization vector $\theta_L$. Underpinning this is a evolving distribution of the weight of the charge excitation between the three saddle points as the polarization vector changes, panel (b). Note that the total excited charge is identical for all pulses, with only its division between the three saddle points evolving with polarization direction.
• Figure 3: Light-saddle coupling map: saddle polarization explored over pulse parameters. (a) Saddle polarization, defined as the normed difference of the saddle charges at $M_1$ and $M_2$, $\eta_M = (Q_{M_1} - Q_{M_2})/(Q_{M_1} + Q_{M_2})$, is presented as a function of pulse duration and energy revealing that nearly perfect saddle polarization exists both for longer time pulses and in the ultrafast single cycle regime. The polarization vector is taken to be perpendicular to the $M_1$ special point, see Fig. \ref{['fig1']}(a). The vertical dashed line represents the current "world record" for a deep ultraviolet pulse of energy 4 eVgalli_generation_2019. (b-e) Momentum resolved excitation for three representative cases as indicated in panel (a). At long pulse duration the saddle excitation presents a highly localized excitation at the M points, that in the short pulse limit broadens around the M point, with reduction in amplitude of the excited charge. For both short and long times near complete saddle polarization is seen, with charge excited at $M_2$ and $M_3$ but not at $M_1$. The amplitude of the pulse employed here is 0.02 a.u., however similar findings are found for any sensible variation of light pulse amplitude.
• Figure 4: Density functional treatment of light-saddle coupling. Two principle cases of light-saddle coupling treated via time-dependent density functional theory: the polarization vector parallel and perpendicular to the crystal momenta of one of the M points. (a,b) M point gap tuned linearly polarized pulses with perpendicular and parallel polarization vector to the high symmetry point labelled $M_1$ in (c). These two pulses generate (c) zero charge excitation at $M_1$ and (d) predominant excitation at $M_1$ with $\sim 1/3$ reduced intensity at the two remaining M points.
• Figure 5: Polarization vector generating maximal coupling of linearly polarized light in graphene.. The excited charge at each crystal momentum $\bm{\mathrm{k}}$ is given by $Q \propto (\bm{\mathrm{u}}(\bm{\mathrm{k}}).\bm{\mathrm{A}}_0)^2 \delta (2\varepsilon_{\bm{\mathrm{k}}} - \omega)$, where $\bm{\mathrm{A}}_0$ is the polarization vector the linearly polarised light with energy equal to the gap at $\bm{\mathrm{k}}$, $2\varepsilon_{\bm{\mathrm{k}}}$ and the angle of vector $\bm{\mathrm{u}}(\bm{\mathrm{k}})$ is presented here as as a function of momentum $\bm{\mathrm{k}}$. When $\bm{\mathrm{A}}_0 \parallel \bm{\mathrm{u}}(\bm{\mathrm{k}})$ one evidently has maximal light-matter coupling at $\bm{\mathrm{k}}$. Note that $\bm{\mathrm{u}}(\bm{\mathrm{k}})$ changes slowly in the vicinity of the M points.