We present systematic measurements of the mechanical properties of few unit cell (UC) thick exfoliated crystals of a high-Tc cuprate superconductor Bi2Sr2CaCu2O8+δ. We determine the elastic properties of these crystals by deformation using an atomic force microscope at room temperature. With the spatial measurements of local compliance and their detailed modeling, we independently determine the Young's modulus of rigidity and the prestress. The Young's modulus of rigidity is found to be in the range of 22 GPa–30 GPa for flakes with a thickness from ∼5 UC to 18 UC. The prestress spreads over the range of 5 MPa–46 MPa, indicating a run-to-run variation during the exfoliation process. The determination of Young's modulus of rigidity for thin flakes is further verified from the recently reported buckling technique.
References
1.
D.
Akinwande
, N.
Petrone
, and J.
Hone
, Nat. Commun.
5
, 5678
(2014
).2.
A.
Castellanos-Gomez
, V.
Singh
, H. S. J.
van der Zant
, and G. A.
Steele
, Ann. Phys.
527
(1-2
), 27
–44
(2015
).3.
V.
Singh
, S. J.
Bosman
, B. H.
Schneider
, Y. M.
Blanter
, A.
Castellanos-Gomez
, and G. A.
Steele
, Nat. Nanotechnol.
9
(10
), 820
–824
(2014
).4.
P.
Weber
, J.
Güttinger
, A.
Noury
, J.
Vergara-Cruz
, and A.
Bachtold
, Nat. Commun.
7
, 12496
(2016
).5.
M.
Will
, M.
Hamer
, M.
Müller
, A.
Noury
, P.
Weber
, A.
Bachtold
, R. V.
Gorbachev
, C.
Stampfer
, and J.
Güttinger
, Nano Lett.
17
(10
), 5950
–5955
(2017
).6.
S. K.
Sahu
, J.
Vaidya
, F.
Schmidt
, D.
Jangade
, A.
Thamizhavel
, G.
Steele
, M. M.
Deshmukh
, and V.
Singh
, 2D Mater.
6
(2
), 025027
(2019
).7.
V.
Singh
, O.
Shevchuk
, Y. M.
Blanter
, and G. A.
Steele
, Phys. Rev. B
93
(24
), 245407
(2016
).8.
D.
Davidovikj
, F.
Alijani
, S. J.
Cartamil-Bueno
, H. S. J.
van der Zant
, M.
Amabili
, and P. G.
Steeneken
, Nat. Commun.
8
(1
), 1253
(2017
).9.
C.
Binek
, Sci. Rep.
7
(1
), 4906
(2017
).10.
M.
Poot
and H. S. J.
van der Zant
, Appl. Phys. Lett.
92
(6
), 063111
(2008
).11.
S.
Sengupta
, H.
Solanki
, V.
Singh
, S.
Dhara
, and M.
Deshmukh
, Phys. Rev. B
82
(15
), 155432
(2010
).12.
C.
Lee
, X.
Wei
, J. W.
Kysar
, and J.
Hone
, Science
321
(5887
), 385
–388
(2008
).13.
A.
Castellanos-Gomez
, M.
Poot
, G. A.
Steele
, H. S. J.
van der Zant
, N.
Agraït
, and G.
Rubio-Bollinger
, Adv. Mater.
24
(6
), 772
–775
(2012
).14.
A.
Falin
, Q.
Cai
, E. J. G.
Santos
, D.
Scullion
, D.
Qian
, R.
Zhang
, Z.
Yang
, S.
Huang
, K.
Watanabe
, T.
Taniguchi
, M. R.
Barnett
, Y.
Chen
, R. S.
Ruoff
, and L. H.
Li
, Nat. Commun.
8
, 15815
(2017
).15.
K.
Liu
, Q.
Yan
, M.
Chen
, W.
Fan
, Y.
Sun
, J.
Suh
, D.
Fu
, S.
Lee
, J.
Zhou
, S.
Tongay
, J.
Ji
, J. B.
Neaton
, and J.
Wu
, Nano Lett.
14
(9
), 5097
–5103
(2014
).16.
Y.
Huang
, E.
Sutter
, N. N.
Shi
, J.
Zheng
, T.
Yang
, D.
Englund
, H.-J.
Gao
, and P.
Sutter
, ACS Nano
9
(11
), 10612
–10620
(2015
).17.
E.
Sterpetti
, J.
Biscaras
, A.
Erb
, and A.
Shukla
, Nat. Commun.
8
(1
), 2060
(2017
).18.
M.
Liao
, Y.
Zhu
, J.
Zhang
, R.
Zhong
, J.
Schneeloch
, G.
Gu
, K.
Jiang
, D.
Zhang
, X.
Ma
, and Q.-K.
Xue
, Nano Lett.
18
(9
), 5660
–5665
(2018
).19.
L.
Sihan
, H.
Yusheng
, W.
Chongde
, and S.
Zhaohui
, Supercond. Sci. Technol.
2
(2
), 145
–148
(1989
).20.
O.-M.
Nes
, M.
Castro
, M.
Slaski
, T.
Laegreid
, K.
Fossheim
, N.
Motohira
, and K.
Kitazawa
, Supercond. Sci. Technol.
4
(1S
), S388
–S390
(1991
).21.
C. M.
Stafford
, C.
Harrison
, K. L.
Beers
, A.
Karim
, E. J.
Amis
, M. R.
VanLandingham
, H.-C.
Kim
, W.
Volksen
, R. D.
Miller
, and E. E.
Simonyi
, Nat. Mater.
3
(8
), 545
(2004
).22.
A.
Jindal
, D. A.
Jangade
, N.
Kumar
, J.
Vaidya
, I.
Das
, R.
Bapat
, J.
Parmar
, B. A.
Chalke
, A.
Thamizhavel
, and M. M.
Deshmukh
, Sci. Rep.
7
(1
), 3295
(2017
).23.
A.
Castellanos-Gomez
, M.
Buscema
, R.
Molenaar
, V.
Singh
, L.
Janssen
, H. S. J.
van der Zant
, and G. A.
Steele
, 2D Mater.
1
(1
), 011002
(2014
).24.
D.
Norouzi
, M. M.
Müller
, and M.
Deserno
, Phys. Rev. E
74
(6
), 061914
(2006
).25.
J. E.
Sader
, J. W. M.
Chon
, and P.
Mulvaney
, Rev. Sci. Instrum.
70
(10
), 3967
–3969
(1999
).26.
S.
Timoshenko
and S.
Woinowsky-Krieger
, Theory of Plates and Shells
(McGraw-Hill
, 1959
).27.
M.
Radmacher
, M.
Fritz
, J. P.
Cleveland
, D. A.
Walters
, and P. K.
Hansma
, Langmuir
10
(10
), 3809
–3814
(1994
).28.
L. D.
Landau
, L. P.
Pitaevskii
, A. M.
Kosevich
, and E. M.
Lifshitz
, Theory of Elasticity
(Pergamon Press
, 1986
).29.
R. E.
Miller
and V. B.
Shenoy
, Nanotechnology
11
(3
), 139
–147
(2000
).30.
N.
Iguiniz
, R.
Frisenda
, R.
Bratschitsch
, and A.
Castellanos-Gomez
, Adv. Mater.
31
(10
), 1807150
(2019
).31.
D. J.
Bishop
, A. P.
Ramirez
, P. L.
Gammel
, B.
Batlogg
, E. A.
Rietman
, R. J.
Cava
, and A. J.
Millis
, Phys. Rev. B
36
(4
), 2408
(1987
).32.
L.
Song
, L.
Ci
, H.
Lu
, P. B.
Sorokin
, C.
Jin
, J.
Ni
, A. G.
Kvashnin
, D. G.
Kvashnin
, J.
Lou
, B. I.
Yakobson
, and P. M.
Ajayan
, Nano Lett.
10
(8
), 3209
–3215
(2010
).33.
A. A.
Griffiths
, Philos. Trans. R. Soc. London Ser. A
221
, 163
(1921
).34.
A.
Zandiatashbar
, G.-H.
Lee
, S. J.
An
, S.
Lee
, N.
Mathew
, M.
Terrones
, T.
Hayashi
, C. R.
Picu
, J.
Hone
, and N.
Koratkar
, Nat. Commun.
5
, 3186
(2014
).35.
G.
Lopez-Polin
, C.
Gomez-Navarro
, V.
Parente
, F.
Guinea
, M. I.
Katsnelson
, F.
Perez-Murano
, and J.
Gomez-Herrero
, Nat. Phys.
11
(1
), 26
–31
(2015
).36.
M.
Poot
and H. S. J.
van der Zant
, Phys. Rep.
511
(5
), 273
–335
(2012
).© 2019 Author(s).
2019
Author(s)
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