1. Atomic Structural Response to External Strain for AGNRs Wenfu Liao & Guanghui Zhou KITPC Program—Molecular Junctions Supported by NSFC under Grant No. 10974052

2. CONTET I. Background II. Bond Variation for AGNRs under Uniaxial Strain III. Summary

3. I. Backgroud  Gapless  Zero band mass  Electron-hole symmetry  Pair creation  Chiral (Pseudospin)  Berry phase  No back-scattering tight-binding electron energy dispersion of graphene

4. Material for Novel Devices? 1. Typical speed 2. Huge current density 3. Large mean free path (high conductivity) 4. Large phase coherence lengths (coherent electronic circuits) 5. Easily cutting the sheet into nanoribbons (nanoscaled molecular electronic devices) 6. Strong field effect (metallic FET) 7. Ballistic transport up to room temperature 8. High-strength composites 9. Spin-valve, spin-qubit and hydrogen storage

5. Open and/or tune an energy gap ?! — gap engineering (manipulation) 1. Finite size graphene nanoribbons—GNRs i. quasi-1D nature (a new type of quantum wires) i. quasi-1D nature (a new type of quantum wires) ii. similar to carbon nanotubes (CNTs) ii. similar to carbon nanotubes (CNTs) iii. building blocks for nanoelectronic devices iii. building blocks for nanoelectronic devices 2. Disorders (defects, impurity, …) 3. External fields (EM-field, etc.)

6. 4. Multi-layers 5. Mechanically 5. Mechanically !?— “strain engineering ” Strain, even if it does not generate gaps, can also introduce strong anisotropies in the atomic structure and charge transport that can be used for applications ! Among all these methods, strain may be one of the most competitive candidates to exercise due to its continuous tunability and easiness performance even at nano- scale.

7. (1) Single-walled CNTs under strain

8. Small band-gap semiconducting (or quasimetallic) nanotubes exhibit the largest resistance changes and piezoresistive gauge factors under axial strains.

9. Maki et al, Nano Lett. 7, 890 (2007) Photoluminescence Measurement

10. (2) Graphene under strain

13. Nano. Lett. 10, 3486 (2010)

14. Appl. Phys. Lett. 98, 023112 (2011)

15. Band gap as a function of strain for AGNR with different width Band gap as a function of strain for ZGNR with different width Questions: 1.Variation of atomic structure, bond length and angle? 2.What is the distribution of the applied strain? Which part of bonds afford the force mostly? 3.Nanomechanical detector (sensor) design?

17. AC-strain ZZ-strain II. Bond variation for AGNRs under a strain

18. Band distribution for supercells of asymmetric 6- and 8-AGNR

19. Band distribution for supercell of symmetric 7-AGNR

20. Table of bond lengths for 6-, 7- and 8-AGNR 1.AC-strain is mostly afforded by the central region bonds while ZZ-strain is afforded by the edge region ones. 2.AC-strain elongates all bond while ZZ-strain only elongates most bond but a small part of bond lengths are compressed.

21. Isosurface charge density for optimized supercells

22. Percentage of varied bonds for N-AGNRs under a strain 1.Asymmetric 2n-AGNRs show 2n types of bonds, while symmetric (4n+1)/(4n+3)-AGNRs present only (3n+1)/(3n+2) types of bonds. 2.(4n+1)/(4n+3)-AGNRs trend to be more stable/unstable against strain as n increases, among which the narrowest 7-AGNR is the most stable one against external strain. N-AGNRs can be classified into 3 types according to their structural response to a strain: symmetric 2n-, asymmetric (4n+1)- and (4n+3)-AGNRs. After doing a large amount of calculations for many AGNRs we conclude a general rule.

23. Symmetric AGNRs are better building block for electronic circuits and devices for stability consideration, while asymmetric ones may be useful in electromechanical nanodevices, such as force sensor, etc.

24. 1. Strained GNRs — detailed relation between atomic and electronic structures? 2. Electron level explain for bond variation. 3. Predicted atomic and electronic structures can be observed experimentally? 4. Strained GNRs can used to design the nano- electromechanical devices and opto- electronic devices? III. Summary

25. Thanks for your attention !!!