The Shapiro steps (ShSs) developing in sliding charge-density wave (CDW) under rf irradiation are considered in terms of the CDW travel in the periodic (washboard) potential. We demonstrate that treating the CDW as an inertialess object whose velocity is defined by the instantaneous voltage one can predict the positions of the ShSs in dc voltages for the given amplitude of rf voltage. Moreover, the approximation allows indicating the rf voltages at which the ShSs' magnitudes show maxima and minima. The only information necessary in advance is the I–V characteristic without rf irradiation and the cross-sectional area of the sample. Thus, one can recover the course of an I–V curve in average and the positions of ShSs on it, though not their forms.
References
1.
P.
Monceau
, “Electronic crystals: An experimental overview
,” Adv. Phys.
61
, 325
(2012
).2.
3.
S.
Brown
and A.
Zettl
, in Charge Density Wave Current Oscillations and Interference Effects, in Charge Density Waves in Solids
, edited by L. P.
Gor'kov
and G.
Grüner
(Elsevier
, Amsterdam, North-Holland
, 1989
), Vol. 25
, p. 223
.4.
R. E.
Thorne
, “Charge-density-wave conductors
,” Phys. Today
49
(5
), 42
(1996
).5.
T. L.
Adelman
, S.
Zaitsev-Zotov
, and R. E.
Thorne
, “Field-effect modulation of charge-density-wave transport in NbSe3 and TaS3
,” Phys. Rev. Lett.
74
, 5264
(1995
).6.
V. Ya.
Pokrovskii
, S. G.
Zybtsev
, M. V.
Nikitin
, I. G.
Gorlova
, V. F.
Nasretdinova
, and S. V.
Zaitsev-Zotov
, “High-frequency, ‘quantum’ and electromechanical effects in quasi-one-dimensional charge density wave conductors
,” Phys.-Usp.
56
, 29
–48
(2013
).7.
J. W.
Brill
, “Handbook of elastic properties of solids
,” in Liquids and Gases
, edited by M.
Levy
(Academic Press
, New York
, 2001
), Vol. 2
, Chap. 10, p. 143
.8.
C.
Day
, “Whiskers of tantalum trisulfide twist in response to an electric field
,” Phys. Today
60
(7
), 24
(2007
).9.
P. A.
Poltarak
, S. B.
Artemkina
, A. I.
Bulavchenko
, T. Y.
Podlipskaya
, and V. E.
Fedorov
, “Colloidal dispersions of tantalum trisulfide: Syntheses and characteristics
,” Russ. Chem. Bull.
64
, 1850
(2015
).10.
V. E.
Fedorov
, S. B.
Artemkina
et al, “Colloidal solutions of niobium trisulfide and niobium triselenide
,” J. Mater. Chem. C
2
, 5479
(2014
).11.
J. O.
Island
et al, “Electronics and optoelectronics of quasi-1D layered transition metal trichalcogenides
,” 2D Mater.
4
, 022003
(2017
).12.
H. S. J.
van der Zant
, O. C.
Mantel
, C.
Dekker
, J. E.
Mooij
, and C.
Traeholt
, “Thin film growth of the charge-density-wave oxide Rb0.30MoO3
,” Appl. Phys. Lett.
68
, 3823
(1996
).13.
D.
Dominko
, D.
Starešinić
, K.
Salamon
, K.
Biljaković
, A.
Tomeljak
et al, “Detection of charge density wave ground state in granular thin films of blue bronze K0.3MoO3 by femtosecond spectroscopy
,” J. Appl. Phys.
110
, 014907
(2011
).14.
G.
Liu
, S.
Rumyantsev
, M. A.
Bloodgood
, T. T.
Salguero
, and A. A.
Balandin
, “Low-frequency current fluctuations and sliding of the charge density waves in two-dimensional materials
,” Nano Lett.
18
, 3630
(2018
).15.
A. A.
Sinchenko
, P.
Lejay
, and P.
Monceau
, “Sliding charge-density wave in two-dimensional rare-earth tellurides
,” Phys. Rev. B
85
, 241104(R)
(2012
).16.
S. G.
Zybtsev
, V. Y.
Pokrovskii
, V. F.
Nasretdinova
, and S. V.
Zaitsev-Zotov
, “Gigahertz-range synchronization at room temperature and other features of charge-density wave transport in the quasi-one-dimensional conductor NbS3
,” Appl. Phys. Lett.
94
, 152112
(2009
).17.
S. G.
Zybtsev
, V. Y.
Pokrovskii
, V. F.
Nasretdinova
, S. V.
Zaitsev-Zotov
, V. V.
Pavlovskiy
, A. B.
Odobesco
, W. W.
Pai
, M.-W.
Chu
, Y. G.
Lin
, E.
Zupanič
, H. J. P.
van Midden
, S.
Šturm
, E.
Tchernychova
, A.
Prodan
, J. C.
Bennett
, I. R.
Mukhamedshin
, O. V.
Chernysheva
, A. P.
Menushenkov
, V. B.
Loginov
, B. A.
Loginov
, A. N.
Titov
, and M.
Abdel-Hafiez
, “NbS3—A unique quasi one-dimensional conductor with three charge density wave transitions
,” Phys. Rev. B
95
, 035110
(2017
).18.
S. G.
Zybtsev
, V. Y.
Pokrovskii
, S. V.
Zaitsev-Zotov
, and V. F.
Nasretdinova
, “Growth, crystal structure and transport properties of one-dimensional conductors NbS3
,” Physica B
407
, 1696
–1699
(2012
).19.
S. G.
Zybtsev
, S. A.
Nikonov
, and V. Y.
Pokrovskii
, “Spontaneous phase slippage and CDW synchronization near the Peierls transition
,” Phys. Rev. B
102
, 235415
(2020
).20.
S. G.
Zybtsev
, V. Y.
Pokrovskii
, V. F.
Nasretdinova
, S. V.
Zaitsev-Zotov
, E.
Zupanič
, M.
van Midden
, and W. W.
Pai
, “The ultra-high-TP charge-density wave in the monoclinic phase of NbS3
,” J. Alloys Compd.
854
, 157098
(2021
).21.
D.
Reagor
, S.
Sridhar
, M.
Maki
, and G.
Grüner
, “Inertial charge-density-wave dynamics in (TaSe4)2I
,” Phys. Rev B
32
, 8445
(1985
).22.
A.
Zettl and G. Grüner
, “Phase coherence in the current-carrying charge-density-wave state: Ac-dc coupling experiments in NbSe3
,” Phys. Rev. B
29
, 755
(1984
).23.
R. E.
Thorne
, W. G.
Lyons
, J. W.
Lyding
, J. R.
Tucker
, and J.
Bardeen
, “Charge-density-wave transport in quasi-one-dimensional conductors. II. Ac-dc interference phenomena
,” Phys. Rev. B
35
, 6360
(1987
).24.
S.
Shapiro
, A.
Janus
, and S.
Holly
, “Effect of microwaves on Josephson currents in superconducting tunneling
,” Rev. Mod. Phys.
36
, 223
(1964
).25.
S. G.
Zybtsev
, S. A.
Nikonov
, V. Ya.
Pokrovskii
, V. V.
Pavlovskiy
, and D.
Starešinić
, “Step-by-step advancement of the charge-density wave in the rf-synchronized modes and oscillations of the width of Shapiro steps with respect to the rf power applied
,” Phys. Rev. B
101
, 115425
(2020
).27.
Under rf irradiation the instantaneous voltage at each V value varies from V+√2Vrf to V−√2Vrf. Therefore for consideration of the curves in Fig. 1 the range of Vdc is to be by √2Vrf wider in both directions.
28.
We consider the half-period in which the signs of Vdc and rf voltage coincide as the first one. During the second half-period the signs are opposite.
29.
While δx1 is positive, δx2 is typically negative or zero.25 Therefore, the total CDW displacement in 1/f time interval, δx1+δx2, equals |δx1|-|δx2|, while the total travel, |δx1|+|δx2|, equals δx1-δx2.
30.
In principle, Vdc can be calculated for an arbitrary Vrf, so that the polyline can be made smooth.
31.
S. A.
Nikonov
, S. G.
Zybtsev
, and V. Y.
Pokrovskii
, “RF Mixing with sliding charge-density waves
,” Appl. Phys. Lett.
(to be published).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
2021
Author(s)
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