Proceedings of International Conference on Physics in ... - KEK

IV-characteristics conductance
Figure 4: (upper) DC current. (lower left) IVcharacteristics.
(lower right) Conductance.
Especially, in a circularly polarized light, a gap opens at
the Dirac point [7]. This has an important physical consequence
since a gap <strong>of</strong> a 2+1 dimensional Dirac electron
is related to parity anomaly and is detectable through transport
measurements, i.e., the Hall effect. In 2+1 dimensions,
the Hall conductivity can be written as a momentum integral
<strong>of</strong> the Berry curvature (∼ Chern density) over the
Brillouin zone. This is known as the TKNN formula[32],
and is know extended to ac-driven transport via the Floquet
picture (∼ Furry picture) [7]
σxy(Aac) = e 2
∫
dk
(2π) d
∑
fα(k) [ ∇k × Aα(k) ]
. (10)
z
α
Here, Aα(k) ≡ −i⟨⟨Φα(k)|∇ k |Φα(k)⟩⟩ is the photoinduced
artificial gauge field. In the Floquet picture, the
Green’s function incorporates the effect <strong>of</strong> photon absorption
and emission (Fig. 3 (a)), and Hall conductivity is
given by the bubble diagram in the non-interacting case,
which is nothing but the parity anomaly diagram. The
photo-induced Berry curvature shown in Fig. 3 (c) acts as
an artificial magnetic field and becomes finite when the circularly
poralized light is introduced.
The current in the presence <strong>of</strong> circularly poralized light
in a graphene ribbon attached to two electrodes is plotted
in Fig. 4. The calculation has been done by combining the
Keldysh green’s function method with the Floquet picture.
The Hall current, which is originally absent, increases as
the strength <strong>of</strong> light becomes stronger. The numerical result
supports our understanding <strong>of</strong> the photovotaic Hall effect
obtain by the extended TKNN formula (eqn.(10)).
We would like to acknowledge Naoto Tsuji, Martin Eckstein
and Philipp Werner for enlighting discussions. It is
a pleasure to thank Gerald Dunne for illuminating discussions
during PIF2010.
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