國家理論科學研究中心(南區)物理組

Highlights of recent research results:

During the years of 2005 and 2006, Prof. Lin, the coordinator, and his collaborators, has directed one of their research areas toward the life time calculations of the electrons in the nanotube systems. They employed the cutting-edge many-body technique to study the scattering rate of electrons in the nanotube and grapene. Their results are briefly summarized in the below.

The electron-electron ( e-e ) Coulomb interactions may play an important role in the many-particle properties, such as the electronic excitations and the electron lifetime. Due to the cylindrical symmetry, each carbon nanotube exhibits the decoupled electronic excitations of different angular momenta ( L 's). The low-frequency electronic excitations are only associated with the L= 0 mode which is central to the many-particle properties of free carriers near the Fermi level. Electrons could be excited from the occupied states to the unoccupied states by the Coulomb interaction or electromagnetic field. The excited free carriers further decay by the inelastic e-e scatterings.

A carbon nanotube can exhibit interesting excitation properties, since the transferred momentum ( q ) and angular momentum ( L ) of electrons are conserved on a cylindrical surface even in the presence of e-e interaction.

The sp 3 Slater-Koster tight-binding model and the random-phase approximation (RPA) are, respectively, used to study the magneto band structures and electronic excitations. The excitation spectra strongly depend on the magnitude and the direction of magnetic field, the transferred momentum, the temperature, the nanotube geometry, and the Zeeman splitting.

Fig. 1. The inelastic scattering rates of the (5,5) nanotube. They are calculated for the low energy states at T =300 K. Also shown in the inset are those of the conduction-band states from the intraband excitations.

 

When electrons are excited from occupied states to unoccupied states either by the Coulomb interactions or the electromagnetic field, they could further decay by the inelastic e-e scatterings. For metallic and moderate-gap carbon nanotubes at T =0, there exists the c → c interband deexcitations from the occupied conduction states to the unoccupied conduction states. The inverse electron lifetimes due to the Coulomb interactions were calculated by the self-energy in the previous our study. A simple relation between wave vector and decay rate is found to be absent. The lowest two conduction bands in moderate-gap carbon nanotubes have the vanishing decay rates, mainly owing to the absence of the low-frequency deexcitation channels.

 

The decay rates of the metallic carbon nanotubes at room temperature are shown in Fig. 1. Their dependence on the wavevector is sensitive. For the Fermi-momentum state, the interband excitations are the only deexcitation mechanism. The inverse lifetime, 1/ τ ( k F ),is about 50.9 meV (or τ~ 80 fs), as shown in Fig. 1. When the conduction-band states gradually deviate from the Fermi level, their decay rates grow (the solid curve). There are more vacant states at higher energies according to the Fermi-Dirac distribution function. Such states are responsible for the increase of 1/ τ with respect to | k-k F |. The ( k,c ) states, the k F state excepted, can be deexcited by the intraband and the interband excitations. The c → c intraband excitations dominate the decay processes except for these states very close to the Fermi level (the inset in Fig. 1, since they own the small-( q, ω de ) transfer, or correspond to the stronger screened response function. On the other hand, the v → v intraband excitations are the deexcitation channels of the valence-band states. Their decay rates drop with | k-k F | quickly (the dashed curve) because of the limitation of the electron distribution. 1/ τ 's are almost vanishing for the ( k,v ) states with energies lower than 4 k B T . Also noticed that 1/ τ ( k F ) depends on temperature linearly.

 

Fig. 2. The Coulomb decay rates of moderate-gap CNs for the first conduction bands. Also shown in the inset are those associated with positive decay energies.

 

Regarding the moderate-gap carbon nanotubes, the Coulomb scattering rates of the first conduction band are shown in Fig. 2 at room temperature. However, there is no simple relation between decay rate and wave vector, and 1/ τ declines quickly as k gradually deviates from the band-edge state. The k =0 state comes with the strongest decay rate. This state is deexcited to higher states under the negative energy transfer, but not the positive energy transfer (the inset in Fig. 2). For example, 1/ τ ( k =0 ,J =11 ,c ) of the (17,0) CN is about 3.25 meV ( τ ~ 1.23 ps). The decay rate of the band-edge state becomes faster with the increment of the nanotube radius. This result clearly illustrates that the increasing carrier density significantly enhances the intraband loss spectrum and thus the decay rate. Meanwhile 1/ τ ( k =0) exhibits the complicated temperature dependence, the composite behavior of linear and exponentional functions (not shown). As to other states, the decay rates under the negative energy transfer are comparable to those under the positive energy transfer.

 

Fig. 3. (a) The Coulomb decay rates of narrow-gap CNs for the first conduction bands. (b) Those associated with positive decay energies and (c) correspond to the interband c→v dacay.

 

1/ τ of the lowest conduction band of moderate-gap (12,0) nanotube is depicted in Fig. 3(a) at room temperature. There is no simple relation between 1/ τ and wave vector. The decay rate exhibit a weak oscillator, an increase and then a decline, at small k and almost remains unchanged at others. It is contributed unequally from the positive ω de and the negative intraband deexcitations and the positive ω de interband deexcitations. For example, the band-edge state is deexcited to the conduction-band state under the negative intraband intraband transfer and the valence-band state under the negative intraband intraband transfer, but not the positive ω de intraband transfer. The decay rate of this state is about 200 meV ( τ ~ 20 fs) for the (12,0) CN. 1/ τ with the positive ω de intraband transfer quickly becomes large from zero as k grows from k =0 [Fig. 3(b)], and it is the same with the decay rate arising from the negative intraband intraband transfer when k >3 10 5 /cm. On the other hand, the interband decay occurs at the sufficiently high decay energy ( ω de > E g ) so that it is much slower than the intraband decay [Fig. 3(c)]. The ratio of 1/ τ between the former and the latter is about 10 2 . The initial ( k,c ) state is principally deexcited to the final ( k,v ) state in the vicinity of k =0; therefore, the decay energy generally becomes large as initial k grows. When the initial state deviate from k =0, the increasing ω de clearly reduce the number of deexcitation channels and thus the decay rate.

 

The above-mentioned results are essential for the nanotube physics and applications. We find a good comparison with the experimental deexcitation rate, which is an evidence of the predominant contribution from interelectron Coulomb interaction and gives credibility to the applied RPA approximation. The photoelectron spectroscopy, the absorption spectroscopy, and the fluorescence spectroscopy could be employed to investigate the lifetimes or the decay rates of electrons. In some respect, they serve as an important vehicle to the theoretical predictions of metallic and moderate-gap carbon nanotubes . As to the narrow-gap carbon nanotubes, the predicted results require further experimental examinations.

 

Other research results:

1. Structure of step surfaces and nanocluster :

Prof. F. C. Chuang has been focusing on the atomic structure of vicinal surfaces and nanoclusters, and electron transport behavior in nanowires.

The determination of atomic structure of crystalline surfaces is a long-standing problem in surface science. In order to solve this problem theoretically, they have developed a genetic algorithm coupled with the silicon empirical potential to search for the low energy surface structures. These structures are further optimized using first-principle calculations. The STM images of the selected structures are calculated in order to be compared with the experimental data. We have successfully applied this method to several high-index surfaces [e.g. Si(105), Si(114), Si(337), and Si(103)], and continue to study more interesting vicinal semiconductor surfaces.

Atomic clusters, nanoclusters, or nanoparticles, regarded as a phase of matter, have been studied not only for their interesting physical and chemical properties but also for their future applications. These nanoclusters can form uniform arrays or nanowires on semiconductor surfaces. The detailed structural study of nanoclusters in the free space and on semiconductor surfaces is a first step to make the dream of nano-machines feasible. Three systems have been studied. They are the static and dynamical properties of Sn clusters in free space, the structural and electronic properties of Al clusters in free space, and the Si magic clusters formed upon Si(111) 7x7 reconstruction surfaces.

 

2 . Electronic transport behavior in the nanowire

Prof. F. C. Chuang also studied electronic transport properties in the nanowire. The continuous miniaturization in the electronics industry has reached the limit in which the interconnection of the devices in a reliable and controllable way is particularly challenging. Fervent strides are underway in the preparation of nanoscale wires for molecular and nanoelectronics applications: such wires can operate both as nanoscale devices and as interconnects. Silicon nanowires (SiNW) offer, in addition to their appeal as building blocks for nanoscale electronics, the benefit of simple fabrication techniques compatible with the currently well-developed silicon technology. The current growth methods can yield wires with diameters ranging from several tens of nanometers down to 1 nm. These SiNWs are usually crystalline with only a few axis orientations observed and have a prismatic shape bounded by facets that are parallel to the wire axis. Motivated by the STM experiments of Ma et al.[ D. D. D. Ma et. al., Science 2003 , 299 , 1874.], we have developed a combined GA-DFT procedure to search for the structure of [110] passivated silicon nanowires (SiNWs) up to 60 atoms per unit cell. We have reported our result in Nano Letters.

 

3. Ab initio calculations of nanotube

In Prof. C. Y. Yang's research project, ab initiocalculations will be employed to study the physical properties of a variety of nano-scale materials. He will explore the possibility of using the fullerene C 60 molecules to store hydrogen molecules. A recent experiment has given this idea a boost. Its potential applications are tremendous. He will also examine the role of the BN nanotube as a “nano-cable”, inside which various materials are shielded and protected from outside interference. Interaction between bio-chemical molecules and carbon nanotubes will be investigated, probing the use of the carbon nanotube as a tool for sensing and manipulating biological processes. Finally, transport properties are studied for systems with nanotubes or molecules connected between two electrodes. With magnetic impurities encapsulated or doped, spin-dependent transport should be apparent and spintronic applications should not be far off. The use of molecules should also lead to further development in molecular electronics.

 

4.Impurity in graphene system

Prof. D. H. Lin has established the Friedel theorem for the relativistic spin-1/2 system. The results would be important in studying the 2D graphene system, the structure of neutron star, and the application in controlling a spin bus (a controllable coupler of many qubits).

 

5 . Numerical calculations in molecule system

Prof. J. Y. Hsu has carried out the scheme for the numerical calculation in nanosystem. He has employed the tight-bind molecule junction to model the system, whose results can be applied to the study of quantum transport. This field has been high on the agenda of devices for molecule computers.

 

Outlines of Activities:

In addition to the annual budget funded by NCTS, 0.5 million NTD for the year of 2005, the focus group also received the half amount of NCTS fund from the Cheng Kung University. The budget was mostly spent on supporting the activities of eight mini-workshops and biweekly seminars held during the year, and the programs for one foreign visiting physicist from China and three visiting scholars from the nearby universities and colleges. To share the resource with the nearby university scholars and promote their interactions, two mini-workshops were taken place in NCCU, and one in NSYSU. According to our record, each mini workshop attracted at least 60 persons to attend.

Besides, in order to enhance the research capacity in condensed matter physics of southern Taiwan, we realized that the attitude of young Ph.D. students or post doctors can be one of major factors. To this end, three workshops were organized specially for them to present the works, where the purpose for exchange of mutual experience in physics and formation of peer pressure were achieved.

Frequent mini-workshops can keep group members' enthusiasm for research from dying away. Due to a large demand on the number of talks, we have also invited many domestic researchers from other regions. Thus the extension of the interaction and possible collaborations between local member and other regions researchers is established.

The contents of workshop presentations include both the theoretical and experimental works. The topics of the talks included spin Hall effect, electronic, magnetic, optical properties of quantum dot, wire, well, nanotubes, graphene, surface structure of nanomaterials, and electron transport behaviors in nanosystems. The various techniques were presented by the experienced scholars, from whom the young participants should benefit. All the invited speakers came from different regions of our country. The informations about the workshops can be found in http://www.ncts.ncku.edu.tw/phys/phys.php?name=intro.htm

 

Visitors and their performances:

In this year, we have an international visitor, Prof. Zhao Jijun from Dalin University of Technology in China, and he has been working on the nano-material and nanotube ropes by using the first-principal calculations. During his visiting period, he has provide some suggestions and pointed out some directions of research of nanotue physics.

This summer, three scholars, Prof. C. P. Chang from, Prof C. H. Lin and Prof. R. B. Chen from nearby universities have jointed the short-term visit program.

During this period, Prof Chang has been working on electronic properties of the AA- and ABC-stacked few-layer graphites in the presence of an electric field, perpendicular to the layers through the tight-binding method. He found that the electronic properties are closely related to the geometric structure and the field strength. In the presence of an electric field or not, the band structure of the AA-stacked few-layer graphites exhibit the linear behaviors near the Fermi energy. The interlayer interactions and electric field lead to the shifts in the Fermi momenta and the state energies. The ABC-stacked few-layer graphites are characterized by the complicated low-energy band structure due to the stacking effects, where the electric field has a great influence on the changes in the state energy and the subband spacing, the opening of a band gap, the production of the oscillating bands, and the increase of the band-edge states. As a result, two different kinds of structure, whose positions and heights are modulated by the electric field, are found in the density of states (DOS) in contrast to the featureless DOS in the AA systems.

Prof. C. H. Lin has investigated the wrapping conformations of a polymer on the nanoparticle surface. Under the assumption of invariant length for each polymer segment, they obtain a set of analytic equations describing the conformation with a minimum free energy. In addition to some numerical solutions for the conformations of the polymer chain on cylindrical and ellipsoidal surfaces, the content was extended by including the energy distributions for different shaped cores, the effect of the position of the initially anchored point of a polymer on its final wrapping length, and the dependence of the wrapping length on the size of a spherical core. The better initially anchored position is found to be near the belly region of an ellipsoidal core and the dewrapping of a polymer is apt to occur at the distant place from the belly. The study also reveals that it seems there is an optimum size for the wrapping core.

Prof. R. B. Chen, has studied energy loss spectra of finite carbon nanotubes. The tight-binding model and the gradient approximation are, respectively, used to calculate electronic states and energy loss spectra. Electronic states would depend on the geometric structure, they are modulated by an electric field, a magnetic field, which accounts for the characteristic of the loss function. The loss function from the and electrons was also analyized.

 

Group achievements:

During the program period, one of active participants, Prof. Chung had established intensive collaboration with Prof. M. -F. Lin. His research results of nanotube were fruitful, and this year he has successfully obtained his professorship in the Tainan University of Technology. Other four frequent student participants, Dr. J.-J. Cai, C-W Chiu, C. -L. Lu, and J. H. Ho have received their Ph. D degrees under the supervision of Prof. Lin , and been employed as postdoctors by Academic Sinica, or NCKU.

Other two faculty members, D. H. Lin in NSYSU and in T. S. Li in Kun Shan University are also applying for the associate and full professorship in their institutes, respectively. Their promotions are in our expectations.

 

International Conference Participation:

By the support of NCTS, Prof. R. B. Chen has attended the 16 th International Conference on Electronic Properties of Two-Dimensional Systems, held in Albuquerque, New Mexico at the Hyatt Regency Hotel from July 10 to 15, 2005. He presented the paper with the title “ Electronic and optical properties of finite carbon nanotubes in a static Electric field”. In his talk, he addressed upon the electronic and optical properties of the quantum-size features of finite carbon nanotubes. The discrete electronic states in the presence of a static electric field are calculated by using the tight-binding method including the curvature effects. Electronic properties are significantly affected by the magnitude and the direction of the electric field, and the geometric structure (radius, length; chirality). The electric field can lead to the complete energy-gap modulation. The optical excitation spectra exhibit absorption peaks, which directly reflect the characteristics of electronic properties. The absorption frequency, the number of absorption peaks, and the spectral intensity are very sensitive to the change in the electric field. There are more absorption peaks when the electric field is in (or almostly) parallel with the cross-section plane. The optical measurements could be compared with the theoretically predicted absorption spectra and electronic properties.

 

Committee members:

Min-Fa Lin (coordinator) Nat'l Cheng Kung Univ.
C. P. Chang Tainan Univ. of Technology
R. B. Chen Nat'l Kaohsiung Marine Univ.
Yan-Chr Tsai Nat'l Chung Cheng Univ.