Artificial honeycomb lattices
for
electrons, atoms
and photons
韩佳星
宋祺
杨灿
娄伟坚
李晓晴
刘孟超
目录：
• 一、人工蜂巢模型的背景
• 二、实现人工蜂巢模型的方法
– 1.电子
– 2.光子
– 3.原子和离子
– 4.Hubbard模型
– 5....
三、总结
一、人工蜂巢模型的背景
• 1. 石墨烯
• 2. 传统固体材料的局限性
• 3. 人工蜂巢模型的意义
几种人工蜂巢模型
四种制造人造石墨烯：
a.砷化镓异质结的表
面SEM纳米图案
b.分子石墨烯系统
c.冷原子的光学晶格
d.利用光学感应方法
制造的光子的蜂巢晶
体
二、实现人工蜂巢模型的方法-电子
– 1.调制电子能带结构
二、实现人工蜂巢模型的方法-电子
– 2.金属电极沉积技术
二、实现人工蜂巢模型的方法-电子
– 3.基于STM的分子操纵
二、实现人工蜂巢模型的方法-电子
– 3.基于STM的分子操纵
二、实现人工蜂巢模型的方法-电子
– 3.基于STM的分子操纵
二、实现人工蜂巢模型的方法-光子
• 光学蜂巢晶格结构
• 光子晶体
二、实现人工蜂巢模型的方法-光子
• 制造光学晶体的方法：
– 1. 光学诱导法
二、实现人工蜂巢模型的方法-光子
– 1.光学诱导法
二、实现人工蜂巢模型的方法-光子
• 制造光学晶体的方法：
– 2.费米光刻法
二、实现人工蜂巢模型的方法-光子
• 二维光子晶体模型：
二、实现人工蜂巢模型的方法-光子
• 二维光子晶体模型：
二、实现人工蜂巢模型的方法-光子
二、实现人工蜂巢模型的方法-光子
二、实现人工蜂巢模型的方法-光子
二、实现人工蜂巢模型的方法-原子离子
• 冷原子的光学晶格实现方法：
二、实现人工蜂巢模型的方法-原子离子
• 装载Bose子
二、实现人工蜂巢模型的方法-原子离子
二、实现人工蜂巢模型的方法-原子离子
二、实现人工蜂巢模型的方法-原子离子
• 装载Fermi子
二、实现人工蜂巢模型的方法-原子离子
二、实现人工蜂巢模型的方法-原子离子
二、实现人工蜂巢模型的方法-原子离子
Hubbard Model
• The first component is the hopping
integral. The hopping integral is
typically represented by the letter t,
because it represents the kinetic
energy of electrons hopping
between atoms.
• The second term in the Hubbard
model is then the on-site repulsion,
typically represented by the letter U,
because it represents the potential
energy arising from the charges on
the electrons.
From: http://cyrill.slezak.co.at/thesis/node11.html
Split Band
In the strongly correlated or ‘atomic’ U/t >> 1 limit the Fermi–
Hubbard model displays two bands, which are split by the repulsive
interaction energy U arising from having two fermions with
antiparallel spin on the same site. In the atomic limit it is therefore
natural to expect a gapped collective mode in which particles
belonging to the lower Hubbard band are cooperatively promoted
to the upper Hubbard band.
From: http://www.nature.com/nnano/journal/v4/n3/fig_tab/nnano.2009.31_F1.html
Artificial Honeycomb Lattice
The sample used in this study was the host of a
2DEG in a 25-nm-wide, one-side modulationdoped Al0.1Ga0.9As/GaAs quantum well.
The artificial honeycomb lattice extended over a
100-μm–by–100-μm square region with a lattice
constant a ~ 130 nm
From: Singha, A. et al. Two-dimensional Mott–Hubbard electrons in an
artificial honeycomb lattice. Science 332, 1176–1179 (2011).
Light Scattering Experiment
ωL, ωS labels the incident (scattered) photon
energy and is the tilt angle.
The relevant electronic process that contributes
to the Raman scattering cross section. The initial
state is labeled by |1>, the final state by |2>, and
the intermediate state with one hole and an
extra electron is labeled by |n>. The final excited
state is separated from the ground state by the
Hubbard charge gap U; that is, by the energy
cost of having two antiparallel spin electrons on
the same site. In the intermediate state, we have
also depicted the absorbed (at frequency ωL)
and emitted (at frequency ωS) photons.
In this experiments, the strongly correlated
regime U >> t is achieved when B quenches the
hopping amplitude t and increases the
interaction energy U.
From: Singha, A. et al. Two-dimensional Mott–Hubbard electrons in
an artificial honeycomb lattice. Science 332, 1176–1179 (2011).
三、总结
• 1. 人工蜂巢模型的优势
• 2. 几种方法：
– a.电子
– b.光子
– c.原子离子
– d.Hubbard模型
四、参考文献
•
•
•
•
•
•
•
•
•
1.Marco Polini. et al. Artificial honeycomb lattices for electrons, atoms and
photons.Nature nanotechnology.
2.Tarruell. et al.Creating, moving and merging Dirac points with a Fermi gas in a
tunable honeycomb lattice. Nature.
3.Soltan-Panahi. et al. Multi-component quantum gases in spin-dependent hexagonal
lattices. Nature Phys.
4.S. Bittner. et al. Extremal transmission through a microwave photonic crystal and
the observation of edge statesin a rectangular Dirac billiard.Physical Review B.
5.S. Bittner. et al. Observation of a Dirac point in microwave experiments with a
photonic crystal modeling graphene.Physical Review B.
6.Or Peleg. et al. Conical Diffraction and Gap Solitons in Honeycomb Photonic
Lattices.Physical Review Letters.
7.Marco Gibertini. et al. Engineering articial graphene in a two-dimensional electron
gas.Physical Review B.
8.L. Esak. et al. Superlattice and Negative Differential Conductivity in
Semiconductors.Communication.
9.Kenjiro K. et al. Designer Dirac fermions and topological phases in molecular
graphene.Lett.
谢谢