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\begin{document}
\title{Possible 400 K superconductivity of carbon nanotubes}
\author{C.Y. Yau\\              
         \\  Department of Physics
              \\    University of Cincinnati
            	  \\  Cincinnati, Ohio 45221\\[1em]}

\date{March 6, 2002 }
\maketitle
\begin{abstract}
     Room temperature superconductivity is a goal of scientists and 
engineers dealing with superconductors. As room temperature superconductivity 
is very important to electronic, levitation and national defense technology, 
achieving room temperature superconductivity can cause a big change to the 
world. Recently Zhao \textit{et al} [G.M. Zhao, Y.S. Wang,arXiv:cond-mat/0111268 v2
19 Nov 2001] has reported results of measurements of superconductivity of 
carbon nanotubes and yield a $T_{c}$ higher than room temperature. In this paper, I will review their results and the results 
published by other groups on same research field.
 \\[1em]
\end{abstract}

\pagebreak

\def\baselinestretch{1.1}

Superconductivity phenomenon accounts for disappearance of resistance and 
total expulsion of magnetic (so-called Meissner effect) at transition 
temperature $T_{c}$. Type I and type II superconductors behave differently 
under magnetic field. For type I, or low $T_{c}$ superconductor, the 
magnetic field is completely expelled from the inside when the temperature 
is higher than $T_{c}$. However for type II superconductors, or high
T$_{c}$ superconductors, they will have magnetic fields trapped inside and
will not expel them immediately when temperature is higher than $T_{c}$.
This is due to the flux pinning at the grain boundaries of high $T_{c}$ 
superconductors.Flux pinning makes the flow of supercurrent unimpeded and 
let the supercurrent flows for a temperature


\section{What is carbon nanotube}


Carbon nanotube (CNT) was first discovered by Sumio Iijima [1] in 1991. It 
is a tolled-up graphite sheets with caps on both ends. The tube is composed 
of hexagons of carbons on the tube with pentagons and heptagons (which are 
called ``defects'') on both ends. There are 3 types of structures of carbon 
nanotubes, viz. armchair, zigzag and chiral tubes. They have different 
electronics structures. Armchair tubes have zero bandgap and hence a metal, 
zigzag has a bandgap of 1.1 eV like silicon as a semiconductor, and chiral 
tubes have the bandgap between those two former tubes. Then the electronic 
properties of carbon nanotubes depend on the molecular structure of carbon 
nanotubes. The nanotubes can have several shells. And the structure is 
generally distinguished to be single-walled nanotube (SWNT) and multi-walled 
nanotubes (MWNT). SWNT is usually a defectless version of carbon nanotubes. 
In MWNT there are many cross-links or bonds between the shells, and the 
structure in MWNT is not always perfect. Hence a MWNT is usually called a 
defective nanotube.

\section{Proximity effect induced superconductivity of CNT}


Proximity induced superconducting behaviors of Single molecule SWNT and 
ropes of SWNTs are first reported by Kasumov [2] and the $T-{c}$ of CNT was 
recorded as < 1K for ropes (as shown in Fig. 2) and $\sim$ 0.4 K for single 
molecule of SWNT (as shown in Fig. 3). Proximity effect induced 
superconductivity makes use of S/N/S junction with the sample in the middle 
N layer, as shown in Fig 1. 

\begin{figure}[htb]

\centerline{\psfig{figure=fig1.ps,height=1.5in}}

\caption{\em{Proximity induced superconductivity measurement of ropes.}}

\end{figure}

\begin{figure}[htb]

\centerline{\psfig{figure=fig2.ps,height=1.5in}}

\caption{\em{R-T curve of proximity induced superconductivity ropes}}

\end{figure}



\begin{figure}[htb]

\centerline{\psfig{figure=fig3.ps,height=1.5in}}

\caption{\em{Arrangement of proximity induced superconductivity measurement of single SWNT.}}

\end{figure}

As the inter-tube Josephson tunneling (or coupling) effect can cause the 1D 
superconductor becomes 3D superconductor and increase the $T_{c}$, The 
$T_{c}$ of the rope may not be accurate and could be higher than the 
actually value of a single tube. Also the inset in Fig. 3 shows the hallmark 
of type I superconductor and this confirms why the $T_{c}$ of the samples 
are so low.

\begin{figure}[htb]

\centerline{\psfig{figure=fig4.ps,height=2in,}}

\caption{\em{R-T curve of single molecule of SWNT. The inset shows the H-T curve indicates a type I superconductor behavior of single molecule of SWNT.}}

\end{figure}

Kasumov's results were further confirmed by Morpurgo's group [3]. Kasumov
[4] also confirmed his result was not due to the superconducting contact
pads by introducing defects in nanotubes by electron irradiation during $R-T$ 
measurement and caused an increase of 41 ohm in resistance after irradiation. 
Tang's group [5] reported a $T_{c}< 20$ K of individual single molecule of
SWNT by Meissner effect and showed that SWNT could be a type I superconductor. 
Kociak \textit{et al} [6] reported a $T_{c}$ of 0.2 which matches the 
result of 0.4 K of Kasumov's group.

\section{400 K or more superconductivity of carbon nanotubes}

In November 2001, Zhao et al [7] reported a larger than 400 $T_{c}$ of 
multi-walled carbon nanotubes. The arrangement of the R-T measurement is 
shown in Fig 5.

\begin{figure}[htb]

\centerline{\psfig{figure=fig5.ps,height=1.5in}}

\caption{\em{Suspended arrangement for R-T measurement of rope of MWNTs with silver contact.}}

\end{figure}

The reported R-T results as shown in Fig. 6 fits an insulating behavior of 
semiconductors. However, after eliminating the signals of insulators, the 
sample shows a resistance drop like an inhomogeneous superconductor, as 
shown in Fig. 7.

\begin{figure}[htb]

\centerline{\psfig{figure=fig6.ps,height=2in}}

\caption{\em{R-T curve of sample showing the insulating behavior.}}

\end{figure}


\begin{figure}[htb]

\centerline{\psfig{figure=fig7.ps,height=2in}}

\caption{\em{After eliminating the signals of insulators, the curve shows a resistance drop similar to inhomogeneous superconductors with $T_{c,mid}$ $\sim$ 650 K}}

\end{figure}

Zhao also measured the remnant magnetic field of the sample with increasing
temperatures. And they found the $T_{c}$ $\sim$ 400 K as shown in 
Fig. 8, consistent with the data shown in the $R-T$ curve. If the sample is 
ferromagnetic, the curve will drop very quickly instead of slowly. Then this 
eliminates the possibility of the ferromagnetic properties of samples. The 
remnant magnetization would probably totally disappeared at $\sim$ 800K. The 
$T_{c}$ at 400 K is supposed by the group to be the accepted result for the 
sample. However, the $T_{c}$ is too high for many scientists to accept. A 
question normally arises: will there be any unknown effect causing this big 
change?

\begin{figure}[htb]

\centerline{\psfig{figure=fig8.ps,height=2in}}

\caption{\em{Measurement of remnant magnetization with increasing temperature. If the sample is ferromagnetic, the trend of the curve will go like the bold solid line that the M$_{r}$ will drop quickly.}}

\end{figure}

\section{Conclusion}
The data of proximity-induced superconductivity cannot prove the nanotubes 
are superconductors. Josephson tunneling effect will eliminate the 1D nature 
of nanotubes and convert it into 3D nature and this can bring forth a much 
higher $T_{c}$. Kausmov's data are undeniable, but we will question: will
there be any unknown effects causing this big change? Further experiments 
will be highly encouraged to confirm the results.

\begin{thebibliography}{99}
\bibitem{refA} S.\ Ijima,  Nature\ {\bf 354}, 56(1991)
\bibitem{refB} A.\ Yu. Kasumov et al, Science\ {\bf 284}, 1508(1999)
\bibitem{refC} A.F.\ Morpurgo ,et al,Science\ {\bf 286}, 263(1999)
\bibitem{refD} A.\ Yu. Kasumov, TNT 2001, September 3-7, Segovia-Spain    
\bibitem{refE} Z.K.\ Tang, et al. Science {\bf 292}, 2462(2001)
\bibitem{refF} M.\ Kociac, et al, Phys. Rev. Lett. \ {\bf 86}, 2416(2001)
\bibitem{refG} G.M.\ Zhao, Y.S.\ Wang, arXiv:cond-mat/0111268 v2 19 Nov 2001

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