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sition metal molecules, etc. ) can fill the innermost hollow cavities of nanotubes 25 and exhibit intriguing behaviors that are distinct from those of the corresponding bulk systems. 48,49 These distinct behaviors originate from the fact that the intermolecular spacings become compara- ble to the linear dimension of the nanoscale confining space. Therefore, the core tube deformation that breaks the cylindrical symmetry of the initial nanoscale com- partment will engender unique properties of intercalated molecules that are peculiar to the constrained condition in a radially corrugated space. 

Another interesting implication of our results is a pressure-driven change in the quantum transport proper- ties of π -electrons moving along the radially corrugated nanotube. It has been known that mobile electrons whose motion is confined to a two-dimensional curved thin layer behave differently from those on a conventional flat plane, because the geometric curvature of the layer effectively yields an electromagnetic field 50–52 that can affect low- energy excitations of the electrons. A quantitative exam- ination along with sophisticated atomistic simulations 53 should reveal novel MWNT applications based on radial corrugation. 

We have theoretically shown the presence of diverse radial corrugation modes in the cross section of MWNTs that shrink radially under irradiation. Using the contin- uum elastic approximation, we have established a phase diagram that enables a desired corrugation pattern to be obtained by tuning the innermost wall radius R and the total number of concentric walls N . We have also found that all corrugation patterns are classified into two de- formation phases between which there exists a significant 

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## V. CONCLUSION 

difference in the corrugation amplitude of the innermost wall of the nanotube. We believe that the results provide useful information for developing carbon-nanotube-based devices that utilize the nanoscale hollow cavity within the core of concentric carbon walls. 

We acknowledge M. Rahimi, K. Yakubo and T. Mikami for stimulating discussions and helpful comments. This study was supported by a Grant-in-Aid for Scientific Re- search from the MEXT, Japan. HS is thankful for the financial support provided by the Kazima Foundation and Hokkaido Gas Co., Ltd. SG acknowledges the sup- port of the Spanish Ministry of Science and Innovation through the Juan de la Cierva program. MA acknowl- edges the support of the European Research Council (FP7/2007-2013)/ERC grant agreement nr 240487 and the prize “ICREA Academia” funded by the Generali- tat de Catalunya. A part of the numerical simulations were carried out using the facilities of the Supercomputer Center, ISSP, University of Tokyo. 

In this Appendix, we derive the deformation energy U$_{M}$ of an elastic medium surrounding a MWNT. The mechanics of an elastic medium is governed by the 

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## Acknowledgement 

## Appendix A: Derivation of U M 

