
Secondary plasmon resonance in graphene nanostructures
Yang Li, Hong Zhang, Da-Wei Yan, Hai-Feng Yin, Xin-Lu Cheng
Front. Phys. ›› 2015, Vol. 10 ›› Issue (1) : 103101.
Secondary plasmon resonance in graphene nanostructures
The plasmon characteristics of two graphene nanostructures are studied using time-dependent density functional theory (TDDFT). The absorption spectrum has two main bands, which result from π and σ + π plasmon resonances. At low energies, the Fourier transform of the induced charge density maps exhibits anomalous behavior, with a π phase change in the charge density maps in the plane of the graphene and those in the plane 0.3 Å from the graphene. The charge density fluctuations close to the plane of the graphene are much smaller than those above and beneath the graphene plane. However, this phenomenon disappears at higher energies. By analyzing the electronic properties, we may conclude that the restoring force for the plasmon in the plane of the graphene does not result from fixed positive ions, but rather the Coulomb interactions with the plasmonic oscillations away from the plane of the graphene, which extend in the surface-normal direction. The collective oscillation in the graphene plane results in a forced vibration. Accordingly, the low-energy plasmon in the graphene can be split into two components: a normal component, which corresponds to direct feedback of the external perturbation, and a secondary component, which corresponds to feedback of the Coulombic interaction with the normal component.
time-dependent density functional theory (TDDFT) / graphene nanostructure / plasmon / induced charge
Fig.1 Schematics of the superconducting qubits and circuit diagram used in this work for a Controlled-CPHASE-SWAP (CCZS) gate. (a) Sketch of the device with three transmon qubits of tunable frequencies. Eeach qubit contains a SQUID (superconducting quantum interference device) ring whose magnetic flux can be varied by a current flowing on a on-chip flux line nearby (not shown), which in turn changes the qubit’s frequency. Each qubit is equipped with its own flux line, control line, and readout resonator (not shown) as widely used in the transmon-based superconducting quantum circuits. Adjacent qubits are coupled and share a common feedline for dispersive readout. (b) Schematics of our scheme decomposing a Fredkin-like CCZS gate into a sequence of three iSWAP operations (marked as ×) between adjacent qubits. Each iSWAP operation represents a coherent |
Tab.1 List of states after each step of the iSWAP gate. |
Initial state | After first | After | After last |
---|---|---|---|
Fig.4 Generation and benchmarking of a three-qubit GHZ state using our Fredkin-like CCZS gate. (a) The measured populations associated with the state of |
Fig.5 Demonstration of a controlled three-qubit iSWAP operation with an arbitrary angle. The populations of the |
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