but it cannot explain the experimental data (fig.
The mechanism of the HHG should depend on
the ratio between the Rabi frequency and the
bandgap. Because graphene is a gapless material
(Eg = 0), the condition of the semimetal regime
(Eg/2ℏ ≤ WR0) can be achieved even with a weak
field excitation. As a control study, we performed
an HHG experiment and theoretical calculation
on monolayer MoS2 (fig. S6) (29), which is an
atomically thin material with honeycomb lattice
structure like graphene but with a finite bandgap
(exciton resonance ~1.85 eV). We set the excitation photon energy and intensity to be the same
as those used in the experiments and calculations for graphene. The intensity of the seventh-harmonic radiation monotonically decreases with
increasing ellipticity of the laser, and the perpendicular component to the major axis (Iy) is small
(Fig. 4D). The calculated curves in Fig. 4E for
Eg = 1.85 eV, which corresponds to Eg/2ℏ > WR0,
reproduce the experimental data for monolayer
MoS2. This indicates that at the current excita-
tion strength, the mechanism of HHG in mono-
layer MoS2 is not in the semimetal regime. The
calculation for monolayer MoS2 assumes the
band structure with a bandgap of 1.85 eV and
parabolic dispersions of the valence and conduc-
tion bands with the same form factor as graphene
(29). The comparative study of HHG in monolayer
graphene and monolayer MoS2 reveals that the
mechanism of HHG in solids depends on the
bandgap of the material. In the limit of a small
bandgap or large Rabi frequency, the mechanism
is in the semimetal regime, and the unique el-
lipticity dependence of HHG appears. We also
showed the universality of the ellipticity depen-
dence of HHG for different order harmonics.
The HH spectra in Fig. 2 show that not only the
seventh but also the ninth harmonic is enhanced
with elliptically polarized excitation. The ellip-
ticity dependence for the fifth harmonic is shown
in fig. S7 (29). It should be noted that not the
linear energy dispersion but the zero-gap prop-
erty of graphene plays an important role in HHG,
because we found that the unique ellipticity
dependence appears in the calculation even when
a parabolic band structure is assumed. The sim-
ilar nature is expected to appear in narrow bandgap
semiconductors such as InSb. Our experimen-
tal findings and good agreement with the theo-
retical calculation strongly suggest that the fully
quantum mechanical model that we have devel-
oped provides an appropriate model of HHG in
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This work was supported by a Grant-in-Aid for Scientific Research
(A) (grant 26247052). N. Y. was supported by a Japan Society
for the Promotion of Science fellowship (grant 16J10537).
Materials and Methods
Figs. S1 to S7
10 February 2017; accepted 25 April 2017
738 19 MAY 2017 • VOL 356 ISSUE 6339 sciencemag.org SCIENCE
Fig. 4. Ellipticity dependence of HH radiation from graphene and monolayer MoS2. (A) Illustration
of polarization configuration of the pump beam and HH radiation. (B) Normalized intensities of
the seventh-harmonic radiation from graphene as a function of laser ellipticity. (C) Theoretical
results reproducing the experimental data in (B). (D and E) The same data set as (B) and (C) for