Fishbone resonance structure in the attosecond transient absorption spectrum of graphene

We investigate the attosecond transient absorption spectrum (ATAS) of graphene by numerically solving four-band density-matrix equations, which demonstrates apparent ``fishbone'' resonance structures. To gain insight into these interesting structures, we exploit a simplified model that considers only electrons $\mathrm{\ensuremath{\Gamma}}$ and $\mathrm{M}$ points in Brillouin zone. With help this model, can analytically express ATAS as sum zeroth- first-order Bessel functions variables strength frequency infrared pump field well effective mass at points. Lorentzian Fano line shapes are addressed. The fishbone structure consists periodic V-shaped be explained functions, its tilt angle is solely determined laser. periodicity originates from dependence on time delay between probe lasers. Compared with numerical results, our analytical theory qualitatively or even quantitatively predict fringes structures ATAS.