Electromechanical resonators as probes of the charge density wave transition at the nanoscale in NbSe2

Physical Review B - Condensed Matter and Materials Physics

Volumn 82, Issue 15, 2010, Pages

  Sengupta, Shamashis ^a   Solanki, Hari S ^a   Singh, Vibhor ^a   Dhara, Sajal ^a   Deshmukh, Mandar M ^a  

^a TATA INSTITUTE OF FUNDAMENTAL RESEARCH   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78149265565     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.82.155432     Document Type: Article

References (45)

1. G. Gruner, Density Waves in Solids (Perseus, Cambridge, MA, 2000).
2. D. E. Moncton, J. D. Axe, and F. J. DiSalvo, Phys. Rev. Lett. 34, 734 (1975). 10.1103/PhysRevLett.34.734
3. P. Monçeau, N. P. Ong, A. M. Portis, A. Meerschaut, and J. Rouxel, Phys. Rev. Lett. 37, 602 (1976). 10.1103/PhysRevLett.37.602
4. M. Barmatz, L. R. Testardi, and F. J. Di Salvo, Phys. Rev. B 12, 4367 (1975). 10.1103/PhysRevB.12.4367
5. S. V. Borisenko, A. A. Kordyuk, V. B. Zabolotnyy, D. S. Inosov, D. Evtushinsky, B. Büchner, A. N. Yaresko, A. Varykhalov, R. Follath, W. Eberhardt, L. Patthey, and H. Berger, Phys. Rev. Lett. 102, 166402 (2009). 10.1103/PhysRevLett.102.166402
6. J. A. Wilson, F. J. DiSalvo, and S. Mahajan, Adv. Phys. 24, 117 (1975). 10.1080/00018737500101391
7. A. H. Castro Neto, Phys. Rev. Lett. 86, 4382 (2001). 10.1103/PhysRevLett. 86.4382
8. M. D. Johannes and I. I. Mazin, Phys. Rev. B 77, 165135 (2008). 10.1103/PhysRevB.77.165135
9. A. Meerschaut and C. Deudon, Mater. Res. Bull. 36, 1721 (2001). 10.1016/S0025-5408(01)00646-8
10. E. Slot, M. A. Holst, H. S. J. van der Zant, and S. V. Zaitsev-Zotov, Phys. Rev. Lett. 93, 176602 (2004). 10.1103/PhysRevLett.93.176602
11. M. Calandra, I. I. Mazin, and F. Mauri, Phys. Rev. B 80, 241108 (R) (2009). 10.1103/PhysRevB.80.241108
12. R. F. Frindt, Phys. Rev. Lett. 28, 299 (1972) 10.1103/PhysRevLett.28.299
13. K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, Proc. Natl. Acad. Sci. U.S.A. 102, 10451 (2005) 10.1073/pnas.0502848102
14. N. E. Staley, J. Wu, P. Eklund, Y. Liu, L. Li, and Z. Xu, Phys. Rev. B 80, 184505 (2009). 10.1103/PhysRevB.80.184505
15. V. Sazonova, Y. Yaish, H. Ustunel, D. Roundy, T. A. Arias, and P. L. McEuen, Nature (London) 431, 284 (2004) 10.1038/nature02905
16. G. A. Steele, A. K. Huttel, B. Witkamp, M. Poot, H. B. Meerwaldt, L. P. Kouwenhoven, and H. S. J. van der Zant, Science 325, 1103 (2009) 10.1126/science.1176076
17. B. Lassagne, Y. Tarakanov, J. Kinaret, D. Garcia-Sanchez, and A. Bachtold, Science 325, 1107 (2009). 10.1126/science.1174290
18. X. L. Feng, R. He, P. Yang, and M. L. Roukes, Nano Lett. 7, 1953 (2007). 10.1021/nl0706695
19. H. S. Solanki, S. Sengupta, S. Dhara, V. Singh, S. Patil, R. Dhall, J. Parpia, A. Bhattacharya, and M. M. Deshmukh, Phys. Rev. B 81, 115459 (2010). 10.1103/PhysRevB.81.115459
20. J. S. Bunch, A. M. van der Zande, S. S. Verbridge, I. W. Frank, D. M. Tanenbaum, J. M. Parpia, H. G. Craighead, and P. L. McEuen, Science 315, 490 (2007) 10.1126/science.1136836
21. C. Chen, S. Rosenblatt, K. I. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. L. Stormer, T. F. Heinz, and J. Hone, Nat. Nanotechnol. 4, 861 (2009) 10.1038/nnano.2009.267
22. V. Singh, S. Sengupta, H. S. Solanki, R. Dhall, A. Allain, S. Dhara, P. Pant, and M. M. Deshmukh, Nanotechnology 21, 165204 (2010). 10.1088/0957-4484/ 21/16/165204
23. The amplitude of driving force experienced by the resonator is d C g d z V g dc V g ac, where C g is the gate capacitance.
24. V. Sazonova, Ph.D. thesis, Cornell University, 2006.
25. R. G. Knobel and A. N. Cleland, Appl. Phys. Lett. 81, 532 (2002). 10.1063/1.1493221
26. ) 2 + C g V g ac } V s d, where C g is the gate capacitance. ξ f 0 is the amplitude of vibration at resonant frequency f 0 and Q is the quality factor. Δ is an arbitrary phase factor and its origin is discussed in Refs.. V g ac, V s d ∼ 10 - 100 mV.
27. However, quasi-one-dimensional NbSe 3 shows significant gating, see T. L. Adelman, S. V. Zaitsev-Zotov, and R. E. Thorne, Phys. Rev. Lett. 74, 5264 (1995). 10.1103/PhysRevLett.74.5264
28. S. Sapmaz, Y. M. Blanter, L. Gurevich, and H. S. J. van der Zant, Phys. Rev. B 67, 235414 (2003). 10.1103/PhysRevB.67.235414
29. ) 2. α depends upon the device geometry but not on E.
30. I. Kozinsky, H. W. Postma, I. Bargatin, and M. L. Roukes, Appl. Phys. Lett. 88, 253101 (2006) 10.1063/1.2209211
31. Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, Nature (London) 458, 1001 (2009). 10.1038/nature07932
32. Cr, Au, and NbSe 2 (Ref.) have positive thermal-expansion coefficients. On heating from 28 to 40 K, they will expand, and the strain ε will reduce. If any correction due to thermal expansion is incorporated, then the estimate of change in E will be even greater than 10%.
33. M. H. Jericho, A. M. Simpson, and R. F. Frindt, Phys. Rev. B 22, 4907 (1980). 10.1103/PhysRevB.22.4907
34. M. S. Skolnick, S. Roth, and H. Alms, J. Phys. C 10, 2523 (1977). 10.1088/0022-3719/10/14/007
35. W. L. McMillan, Phys. Rev. B 12, 1187 (1975). 10.1103/PhysRevB.12.1187
36. See supplementary material at http://link.aps.org/supplemental/10.1103/ PhysRevB.82.155432 for resistance data on suspended devices and the variation in resonant frequency at temperatures much higher than the CDW transition.
37. P. Prelovsek and T. M. Rice, Phys. Rev. Lett. 51, 903 (1983). 10.1103/PhysRevLett.51.903
38. C. H. Chen, J. M. Gibson, and R. M. Fleming, Phys. Rev. Lett. 47, 723 (1981). 10.1103/PhysRevLett.47.723
39. D. J. Eaglesham, S. McKernan, and J. W. Steeds, J. Phys. C 18, L27 (1985). 10.1088/0022-3719/18/1/005
40. H. Ibach and H. Luth, Solid-State Physics (Springer-Verlag, Berlin, 2003).
41. Plot of d G d q versus temperature for Device 1 [corresponding to Fig.] is provided in Ref.. The reduction in d G d q with increase in temperature across the CDW transition is evident in this device also. However, the abruptness of the phase transition is not as clear in this data as in Fig. (for Device 2). From the appearance of the plot, if we assume that the phase transition is occurring around 27.2 K, then, a power-law fit gives a critical exponent of 0.57 ± 0.21.
42. W. Rehwald, Adv. Phys. 22, 721 (1973). 10.1080/00018737300101379
43. Charge Density Waves in Solids: Proceedings of the International Conference, edited by, Gy. Hutiray, and, J. Solyom, (Springer-Verlag, Berlin, 1985), Chap. 5.
44. H. Mutka, Phys. Rev. B 28, 2855 (1983). 10.1103/PhysRevB.28.2855
45. O. Sezerman, A. M. Simpson, and M. H. Jericho, Solid State Commun. 36, 737 (1980). 10.1016/0038-1098(80)90001-0