PD Research Report for the 2016 year
Name（Research group） LIU Feng （Katsunori Wakabayashi research group, Graduate School ofScience and Technology）
Research Theme

Theoretical studies on electronic properties of atomically-thin materials

Research PeriodApril, 2016 ~ March, 2017

Research Results
In this year, we have published three papers include one on Physics Review Letters. We
also have one more paper submitted to Phys. Rev. B which is under the review process.
Here is the list of papers published from April, 2016 to March, 2017:
1. F. Liu and K. Wakabayashi, “Novel topological phase with a zero Berry curvature”,
Phys. Rev. Lett. 118, 076803 (2017).
2. F. Liu and K. Wakabayashi, “Numerical study of carbon nanotubes under circularlypolarized irradiation”, Appl. Phys. Express 9 085101 (2016), selected as spot light
3. H.-Y. Deng, F. Liu and K. Wakabayashi, “Optical excitation of surface plasma waves
without grating structures”, EPL 114 35002 (2016)
4. F. Liu and K. Wakabayashi, “Quadratic Dirac fermions in two-dimensional photoniccrystal”, under review of Phys. Rev. B
In this report, we focus on the results of the first three papers in the above list.
Result I:
Usually, topological materials are associated with
non-vanishing Berry curvatures, as Berry curvature is ageometric analogue of magnetic field in the momentum space.
However, inspired by the situation of Aharonov–Bohm effect,
where electrons are affected by the vector potential inspite of zero magnetic field, we have discovered a novel
nontrivial topological phase in 2D systems in the absenceof Berry curvature. 2 This novel topological phase is characterized by the Berryconnection, which is the geometric counterpart of vector
potential in the momentum space, and its integration overFig.1: schematic of 2D lattice model,
which shows nontrivial topological phasein the absence of Berry curvature when
|W|<|V|.

BZ yields the 2D Zak phase accompanying fractional wave
polarization in each direction. These fractional wave polarization manifests themselves
as doubly degenerate edge states with opposite parities.
This novel topological phase resides in a 2D square lattice model with Peierl’s
distortions on the basis of Su-Schrieffer-Heeger model, where the hoppings are classified
as intracellular and intercellular ones, receptively (Fig. 1). When the intracellular
hopping is smaller than the intercellular one, the system enters topological nontrivial

phase characterized by Zak phase (π, π) [as displayed by the inset of Fig.1]. The
discovery of this novel topological phase offers a new view point for designing
topological materials.
Result II:

By rolling graphene into a cylinder, one obtains theso-called carbon nanotube (CTN), which shares similarelectric and mechanical properties as graphene. Electronsin CNTs also hold the valley indices and it is suitable
to use CNTs as a platform for investigating the extractionof valley information. To obtain the valley information
explicitly, one needs to break the symmetry between twovalley indices K and K’. By shining the CNTs withcircularly-polarized light we have realized that theFig.2: carbon nanotube under
eigen wavefunctions of the CNT possess different valley circularly-polarized light, which
opposite valley indices on the top
indices on the top and bottom of the CNT (see the schematic possesses
and bottom of the carbon nanotube.
of Fig.2). More interesting, one can also choose which
valley index like K and K' to present on the top or bottom of the CNT by applying lightwith left or right polarization, which is useful for a light polarization sensor.
Why the polarizations of light can pick up the valley indices of wavefunctions? Thisis because that the polarized light breaks the both the time reversal and spatial inversion
symmetries of the CNT, which leads to the valley contrasting—K and K' points in the first
Brillouin zone are not symmetric anymore. The amplitude of applying light is about
1015W/m2 and its frequency is around 3eV, which are within the current reachability oftechnology.
Result III:Surface plasma waves (SPWs) are usually
discussed in the context of a metal in contact witha dielectric. However, they can also exist between
two metals. In this work we study these bimetallicwaves. We find that their dispersion curve always
cuts the light line, which allows direct optical
coupling without surface grating structures. We
propose practical schemes to excite them and theFig.3: Simulation shows that the plasmon between
two metals can be excited with high efficiency.
The inset displays the plasmon between twometals.

excitation efficiency is estimated. We also show thatthese waves can be much less lossy than conventional SPWs and their losses can besystematically controlled, a highly desirable attribute in applications. Figure 3 shows
the simulation result of transmission of plasmon between two metals, which displays highefficiency. The inset of Fig.3 displays the plasmon wave between two metal.