Complex conductance of ultrathin La₂₋xSrxCuO₄ films and heterostructures
We used atomic-layer molecular beam epitaxy to synthesize bilayers of a cuprate metal (La₁.₅₅Sr₀.₄₅CuO₄) and a cuprate insulator (La₂CuO₄), in which each layer is just one unit cells thick. We have studied the magnetic field and temperature dependence of the complex sheet conductance, σ(ω), of the...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2015
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irk-123456789-1282842018-01-08T03:03:41Z Complex conductance of ultrathin La₂₋xSrxCuO₄ films and heterostructures Gasparov, V.A. Božović, I. Свеpхпpоводимость, в том числе высокотемпеpатуpная We used atomic-layer molecular beam epitaxy to synthesize bilayers of a cuprate metal (La₁.₅₅Sr₀.₄₅CuO₄) and a cuprate insulator (La₂CuO₄), in which each layer is just one unit cells thick. We have studied the magnetic field and temperature dependence of the complex sheet conductance, σ(ω), of these films. Experiments have been carried out at frequencies between 2–50 MHz using the single-spiral coil technique. We found that: (i) the inductive response starts at ∆T = 3 K lower temperatures than Re σ(T), which in turn is characterized by a peak close to the transition, (ii) this shift is almost constant with magnetic field up to 14 mT; (iii) ∆T increases sharply up to 4 K at larger fields and becomes constant up to 8 T; (iv) the vortex diffusion constant D(T) is not linear with T at low temperatures as in the case of free vortices, but is rather exponential due to pinning of vortex cores, and (v) the dynamic Berezinski–Kosterlitz–Thouless (BKT) transition temperature occurs at the point where Y = (lω/ξ₊)² = 1. Our experimental results can be described well by the extended dynamic theory of the BKT transition and dynamics of bound vortex–antivortex pairs with short separation lengths. 2015 Article Complex conductance of ultrathin La₂₋xSrxCuO₄ films and heterostructures / V.A. Gasparov, I. Božović // Физика низких температур. — 2015. — Т. 41, № 12. — С. 1237–1242. — Бібліогр.: 34 назв. — англ. 0132-6414 PACS: 74.78.Fk, 74.72.Gh, 74.40.−n http://dspace.nbuv.gov.ua/handle/123456789/128284 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| topic |
Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная |
| spellingShingle |
Свеpхпpоводимость, в том числе высокотемпеpатуpная Свеpхпpоводимость, в том числе высокотемпеpатуpная Gasparov, V.A. Božović, I. Complex conductance of ultrathin La₂₋xSrxCuO₄ films and heterostructures Физика низких температур |
| description |
We used atomic-layer molecular beam epitaxy to synthesize bilayers of a cuprate metal (La₁.₅₅Sr₀.₄₅CuO₄)
and a cuprate insulator (La₂CuO₄), in which each layer is just one unit cells thick. We have studied the magnetic
field and temperature dependence of the complex sheet conductance, σ(ω), of these films. Experiments have
been carried out at frequencies between 2–50 MHz using the single-spiral coil technique. We found that: (i) the
inductive response starts at ∆T = 3 K lower temperatures than Re σ(T), which in turn is characterized by a peak
close to the transition, (ii) this shift is almost constant with magnetic field up to 14 mT; (iii) ∆T increases sharply
up to 4 K at larger fields and becomes constant up to 8 T; (iv) the vortex diffusion constant D(T) is not linear
with T at low temperatures as in the case of free vortices, but is rather exponential due to pinning of vortex cores,
and (v) the dynamic Berezinski–Kosterlitz–Thouless (BKT) transition temperature occurs at the point where
Y = (lω/ξ₊)²
= 1. Our experimental results can be described well by the extended dynamic theory of the BKT
transition and dynamics of bound vortex–antivortex pairs with short separation lengths. |
| format |
Article |
| author |
Gasparov, V.A. Božović, I. |
| author_facet |
Gasparov, V.A. Božović, I. |
| author_sort |
Gasparov, V.A. |
| title |
Complex conductance of ultrathin La₂₋xSrxCuO₄ films and heterostructures |
| title_short |
Complex conductance of ultrathin La₂₋xSrxCuO₄ films and heterostructures |
| title_full |
Complex conductance of ultrathin La₂₋xSrxCuO₄ films and heterostructures |
| title_fullStr |
Complex conductance of ultrathin La₂₋xSrxCuO₄ films and heterostructures |
| title_full_unstemmed |
Complex conductance of ultrathin La₂₋xSrxCuO₄ films and heterostructures |
| title_sort |
complex conductance of ultrathin la₂₋xsrxcuo₄ films and heterostructures |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2015 |
| topic_facet |
Свеpхпpоводимость, в том числе высокотемпеpатуpная |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/128284 |
| citation_txt |
Complex conductance of ultrathin La₂₋xSrxCuO₄ films and heterostructures / V.A. Gasparov, I. Božović // Физика низких температур. — 2015. — Т. 41, № 12. — С. 1237–1242. — Бібліогр.: 34 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT gasparovva complexconductanceofultrathinla2xsrxcuo4filmsandheterostructures AT bozovici complexconductanceofultrathinla2xsrxcuo4filmsandheterostructures |
| first_indexed |
2025-07-09T08:46:58Z |
| last_indexed |
2025-07-09T08:46:58Z |
| _version_ |
1837158442625662976 |
| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 12, pp. 1237–1242
Complex conductance of ultrathin La2–xSrxCuO4 films
and heterostructures
V.A. Gasparov
Institute of Solid State Physics RAS, Chernogolovka, Moscow district 142432, Russia
E-mail: vgasparo7@gmail.com
I. Božović
Brookhaven National Laboratory, Upton, NY 11973, USA
Applied Physics Department, Yale University, New Haven CT 06520, USA
Received June 11, 2015, published online Oсtober 23, 2015
We used atomic-layer molecular beam epitaxy to synthesize bilayers of a cuprate metal (La1.55Sr0.45CuO4)
and a cuprate insulator (La2CuO4), in which each layer is just one unit cells thick. We have studied the magnetic
field and temperature dependence of the complex sheet conductance, σ(ω), of these films. Experiments have
been carried out at frequencies between 2–50 MHz using the single-spiral coil technique. We found that: (i) the
inductive response starts at ∆T = 3 K lower temperatures than Re σ(T), which in turn is characterized by a peak
close to the transition, (ii) this shift is almost constant with magnetic field up to 14 mT; (iii) ∆T increases sharply
up to 4 K at larger fields and becomes constant up to 8 T; (iv) the vortex diffusion constant D(T) is not linear
with T at low temperatures as in the case of free vortices, but is rather exponential due to pinning of vortex cores,
and (v) the dynamic Berezinski–Kosterlitz–Thouless (BKT) transition temperature occurs at the point where
Y = (lω/ξ+)2 = 1. Our experimental results can be described well by the extended dynamic theory of the BKT
transition and dynamics of bound vortex–antivortex pairs with short separation lengths.
PACS: 74.78.Fk Multilayers, superlattices, heterostructures;
74.72.Gh Hole-doped;
74.40.−n Fluctuation phenomena.
Keywords: superconducting heterostructures, high-frequency conductivity, Berezinski–Kosterlitz–Thouless tran-
sition.
Ultrathin films of high-temperature superconductors
have been studied intensely, with numerous attempts to
observe the Berezinski–Kosterlitz–Thouless (BKT) transi-
tion [1–19]. For example, a few unit-cell (UC) thick
YBa2Cu3O7–x (YBCO) films sandwiched between semi-
conducting or insulating layers have broader resistive tran-
sitions than thicker ones, which have been attributed to the
BKT physics [4–6]. The same explanation was proposed for
the observation of nonlinear current-versus-voltage (I–V)
characteristics in YBCO, BiSrCaCuO, and TlBaCaCuO
single crystals and thin films (see Ref. 7 and references
therein). This has been a matter of substantial debate,
though. For example, Repaci et al. [8] found the I–V char-
acteristics to be ohmic even in 1 UC thick YBCO films at
temperatures below the critical temperature (Tc), indicating
the absence of the BKT transition. Subsequently, however,
it was shown that at low currents the addition of current
noise can turn nonlinear I–V curves into ohmic behavior [9].
Thus, it is easy to confuse nonlinear I–V tails generated by
noise with non-ohmic tails expected from the BKT transi-
tion. Moreover, it was recently shown that the size effects
may radically alter the I–V curves of superconducting
films [10] so that they mimic the dc BKT behavior. Thus,
it is important to understand that nonlinear I–V character-
izes per se cannot prove the occurrence of the BKT transi-
tion; one needs to see a concurrent sharp drop in the super-
fluid density.
Further, it was noted that a precondition [8] for the
BKT transition to occur in a superconductor, i.e., that the
sample size Ls < λeff, where λeff = 2λ2/d is the effective
(Pearl) penetration depth and d is the film thickness, is not
satisfied even in 1 UC thick YBCO films [11]. Next, Davis
© V.A. Gasparov and I. Božović, 2015
V.A. Gasparov and I. Božović
et al. [13] made a detailed comparison of the experimental
data taken from YBCO films [12] with the BKT theory and
found disagreement, which was attributed to inhomogenei-
ty and vortex pinning. Finally, Rogers et al. [14] measured
low-frequency noise in ultrathin Bi2Sr2CaCu2O8 films and
reported absence of thermally activated vortices and BKT
transition, again attributing this to vortex pinning. Hence, it
is still controversial not only whether the true BKT transi-
tion has been observed in cuprates so far, but even whether
it can occur at all in superconducting films.
On the other side, Minnhagen [15] suggested that alt-
hough the usual BKT transition is not present when
Ls > λeff, it is still possible to observe at high frequencies
the BKT-like response from the bound pairs such that the
vortex separation length r < λeff. According to the BKT
theory extended to finite frequencies [15–17], higher-
frequency currents largely probe vortex–antivortex pairs of
smaller separations. At high frequency, the electromagnet-
ic response of a 2D superconductor is dominated by those
bound pairs that have r ~ lω, where lω = (14D/ω)1/2 is the
vortex diffusion length and D is the vortex diffusion con-
stant. Using the Bardeen–Stephen formula for free vortices,
2 2 22 /( )GL B nD e k T d= ξ π σ [18], at ω ≥ 10 MHz we esti-
mate that lω < 1 µm, which is much less than λeff ~ 40 µm
as found in 1 UC thick YBCO films. This implies that it
should be possible to detect the response of vortex–anti-
vortex pairs with short separation lengths at radio (rf) and
microwave (µW) frequencies in ultrathin cuprate films,
even though the usual BKT transition is not seen in dc and
low-frequency measurements.
Recently, we reported the frequency and temperature
dependences of the complex sheet conductance, σ(ω,T), of
1 to 3 UC thick YBCO films sandwiched between semi-
conducting Pr0.6Y0.4Ba2Cu3O7–x layers [7,19], and in bi-
layers of a cuprate metal, La1.55Sr0.45CuO4 (LSCO) and
a cuprate insulator, La2CuO4 (LCO), in the frequency
range 0.023 MHz < ω < 50 MHz [20,21]. In these samples,
as the frequency is increased, we observed a significant
increase of Tc. A maximum in Re σ(T) near Tc and a jump
in superfluid density were observed as well, and moreover
the scaling of the jump with the frequency and temperature
was found to be very close to the theoretical prediction.
The superfluid jump was suppressed in a small magnetic
field, the magnitude of which increased with the frequen-
cy. Vortex pinning with thermally activated vortex diffu-
sion constant was observed in these samples, but it did not
destroy the vortex–antivortex pairs with short separation
lengths. The results reviewed below indicate that such bi-
layers are a very good 2D model system for studying the
physics of the dynamic BKT transition.
Experimental
We have grown bilayer LSCO/LCO films in a unique
atomic-layer-by-layer molecular beam epitaxy (ALL-MBE)
system [22] that incorporates in situ surface science tools
such as time-of-flight ion scattering and recoil spectrosco-
py (TOF-ISARS) and reflection high-energy electron dif-
fraction (RHEED). ALL-MBE enables synthesis of atomi-
cally smooth films as well as of multilayers with perfect
interfaces [23,24]. Typical surface roughness determined
from atomic force microscopy (AFM) data is 0.2–0.5 nm,
less than 1 UC height which in LSCO is 1.3 nm. The films
were grown on single-crystal LaSrAlO4 substrates polished
perpendicular to the [001] crystal direction, so that the c
axis of LSCO was normal to the film surface. The micro-
structure, growth mechanism of LSCO/LCO films, and their
superconducting properties have been reported before [23,24].
We have used a contactless, single-coil inductance tech-
nique [25,26] to measure the absolute value of magnetic
field penetration depth, λ(T), in superconducting thin film
samples. This technique, originally proposed by Gasparov
and Oganesyan [25] and improved in [26], has the same
advantages as the two-coil technique [27–30], while it has
much higher sensitivity to the variations of λ(T), etc. [26].
This technique was extensively used for the study of the
λ(T) dependence for YBCO, ZrB12, and MgB2 single crys-
tals and thin films [31,32].
In this rf technique, we measure the change of mutual
inductance, ∆M, between a film and a one-layer pancake
coil with diameter 1 mm. This coil is located in the prox-
imity of the film and connected in parallel to a capacitor C.
The LC circuit is driven by a TE 1000 RF Vector Imped-
ance Analyzer operating at 0.5–150 MHz, with a high fre-
quency stability of 1 Hz. An impedance meter (VM-508
TESLA) operating at 2–30 MHz, with a high frequency
stability of 10 Hz, was used as well. The film is placed in
vacuum, at a small distance (~ 0.1 mm) above the coil; this
allows the sample temperature to vary from room tempera-
ture down to 1.2 K. The instrument measures the imped-
ance as a function of frequency, which is scanned near the
resonant one. Thus we determine the resonance frequency
and the impedance (at resonance) as a function of the tem-
perature. Since in our bilayer films the superconducting
layer thickness d = 0.2–0.5 nm << λ , the change in the
complex mutual inductance of the coil, M(T), that occurs
because of the superconducting transition in the film, may
be written as [26]
( ) ( )
( )
( )
2
0
0 0
0
Re 1 .
1 2 cot /h
M x dxf
M T L i
f T x d
∞ = − = − πµ + λ
λ∫
(1)
Here
[ ]
21
1
0
( ) e ( ) ( )
N
hx
m
M x r m R J x r m r
−
−
=
= + ∆ + ∆
∑ (2)
is the self-inductance of the coil without the sample, x is
the wave number in the xy plane, h is the sample-coil dis-
tance, r is the internal radius of the one-layer spiral coil, ∆r
is the spacing between adjacent turns of the coil, d is the
1238 Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 12
Complex conductance of ultrathin La2–xSrxCuO4 films and heterostructures
film thickness, and µ0 is the free-space permeability. The
range of values of x giving the dominant contribution to
M(x) is very small, on the order of the inverse of the inter-
nal diameter of the coil (~0.25 mm). In the London regime,
mainly the inductive part of the coil impedance is changed
during the superconducting transition. This change is de-
tected as a change of the frequency f(T) and converted into
the variation of λ(Τ) using Eqs. (1) and (2), where
–12
0 1 0( / ( )l i i = ωµ σ − ωµ λ (3)
is a complex length. Here σ1 is the real part of the film
conductivity, 1
1( ) ( ) [ ( , ), , ]kT T i L T −σ ω = σ ω − ω ω , where
σ1(ω,T) is the dissipative component of the sheet conduct-
ance and 2
0( ), /kL T dω = µ λ is the sheet kinetic inductance.
By replacing σ1 = 0 and keeping in mind that d << λ , we
obtain the final expression for the variation of the mutual
inductance between the coil and the film:
0
2
0
( )Re
2
dM xM dx
x
∞πµ
≈ −
λ ∫ , (4)
2
0 1
0
( )Im
2
dM xM dx
x
∞
≈ πµ ωσ ∫ . (5)
The change of the imaginary part of M with temperature
can be determined [26] from the real part of the LC circuit
impedance Re Z(T), by means of the equation
( )
( ) ( )
( ) 2
3 2
0 0
1 1 1Im
Re Re2
f T
M T
Z T f Zf T C
= − π
.
(6)
Here f0 and Re Z0 are the resonant frequency and the im-
pedance of the LC circuit above Tc.
We have also used two-coil mutual inductance technique.
In these experiments, the film is clamped between two
axially symmetric coils of the average radius 1 mm. The
in-phase and quadrature components of the voltage at the
receiving coil, in response to an ac current in the drive coil,
are detected by conventional lock-in techniques [27–30].
For our films with d << λ the in-phase signal is roughly
proportional to the mutual inductance between the drive
and pick-up coils: ( ) 2
0 2 /( )M T M Rd≈ λ , while the quad-
rature signal is proportional to the imaginary part of M(T),
where M0 is the mutual inductance between the coils with-
out the film, d is the film thickness, and R is the effective
radius of the coils.
We used a two-stage Gifford–McMahon cryocooler
from ULVAC technologies Inc., with a UR4K03 cold head
combined with a C10 compressor, running on 60 Hz power.
We customized it by adding a thermal damping system that
we have developed, providing temperature stabilization to
sub-mK level in the entire region of 3 K < T < 300 K [33].
For temperature control, a heater driven by a commercial
temperature controller (Lake Shore 340) is mounted on the
sample stage. The sample with sapphire holder was mount-
ed either horizontally or vertically. A copper solenoid coil
placed on the top of the cryocooler head allowed us to ap-
ply a small magnetic field (~100 G) either perpendicular
or parallel to the film surface. Additional measurements
have been done in a superconducting magnet with fields
up to 9 T.
Results
The inversion from M(T) in single-coil technique to
λ(T) and σ(T) is simple compared to the more familiar
two-coil mutual inductance technique [27–30]. Calculating
the integrals in Eqs. (4) and (5), one gets the values of
Re M(T) and Im M(T) at a fixed temperature. Thus we get
λ(T) and finally the kinetic inductance of the film,
1 2
0( ) /kL T d− = µ λ , and the high-frequency conductivity,
σ(ω,T), shown in Figs. 1 and 2.
We found that 1( )kL T− fits well over a wide temperature
range to a parabolic dependence [34]: 1 1( ) (0)k kL T L− −= ×
2[1 ( / ) ]coT T× − , shown as thin solid lines in Fig. 1. The
mean-field transition temperature, Tco, determined by ex-
trapolation of the parabolic dependence of ( )1
kL T− to 0, is
larger than the onset point of the experimental ( )1
kL T−
transitions by 4 K, while it is the same as the onset point of
ωRe σ(T). We emphasize that this quadratic equation fits
the data below a characteristic temperature that we denote
as dc
BKTT , which is lower than BKTT ω , the position of the
peak in ω Re σ(T).
In Fig. 3 we show the values of 1( )kL T− and ω Re σ(T)
of a metal–insulator (M–I) bilayer film with a higher Tc,
measured at different frequencies, 8 MHz < ω < 51 MHz,
in single-coil inductance experiments. One can notice
Fig. 1. (Color online) Temperature dependences of 1( )kL T− and
(Re )Tω σ for bilayer film at 8 MHz and different magnetic
fields perpendicular to the film surface: B = 0; 0.0014; 0.0023;
0.003; 0.006; 0.013; 0.019; 0.036; 0.1; 0.2; 0.4; 0.6; 1.0; 1.5; 2.0;
3.4; 4.6; 5.2; 6.0; 7.0 T. The solid lines are quadratic fits to
1( )kL T− below TBKT at different magnetic fields. Also shown is
the theoretical BKT function (dashed line).
Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 12 1239
V.A. Gasparov and I. Božović
a large frequency dependence of Tc — the temperature at
which the superconducting transition onsets becomes ap-
parent, is continuously increases with ω up to 51 MHz, in
both ( )1
kL T− and ω Re σ(T). Apart from this, we also ob-
served a small difference, ∆T = 0.22 K, in the onsets
Re M(T) and Ιm M(T), for low-frequency data as well,
from two-coil mutual inductance data taken at 23 kHz.
Analysis and discussion
In order to see whether this assumption about the BKT
transition is correct, in Fig. 1 we plot the theoretical BKT
function 1( )kL T− (the dashed straight line) derived from the
universal relationship:
( )
2
1
2
0 0
32
/12.3 [nH·K]
dc
dc dcB BKT
k BKT BKT
k TL T T− π
= =
φ µ
(7)
predicted by the BKT theory [11].
Notice however, that this theoretical dependence (Eq. (7))
is valid for the dc case. The observed high-frequency re-
sponse is dominated by the pairs with the vortex separation
length r ~ lω ~ ω–1/2 and therefore BKTT ω must increase with
the frequency. This is why the critical temperature deter-
mined from the intercept of the dashed theoretical line with
the experimental 1( )kL T− curve is lower then BKTT ω . Note
also that there is some uncertainty about the exact thick-
ness of the superconducting fluid in the LSCO/LCO bi-
layer films [24].
Another test for BKTT ω can be made by analyzing the on-
set points of strong dependences of 1( )kL T− and ω Re σ(T)
on the frequency. A central quantity in the dynamic de-
scription of BKT transition is the frequency-dependent
complex dielectric function ε(ω) which describes the re-
sponse of a 2D superconductor to an external time-de-
pendent field. The measured 1( )kL T− is renormalized from
the value 1
0 ( )kL T− in the absence of vortices: 1
0 ( ) (/ )kk LL T T− =
0/ Re [ 1/ ( )]s sn n= = ε ω .
After Refs. 3 and 11, one can derive the following rela-
tion in the high-frequency limit:
1( ) ( 1)
Re 2 ln
kL T Y
Y Y
− π −
=
ω σ
, (8)
where 2( / )Y l +
ω= ξ , lω = 14D/ω1/2 is the vortex diffusion
length and D is the vortex diffusion constant. Both real and
imaginary part of the 1/ε(ω) are directly related to Y(T) [3].
Using the 1( )kL T− and ω Re σ(T) data from Figs. 1 and 2,
we solved Eq. (1) for Y(T) and in Fig. 4 plotted Y versus
1/ 1/( )BKTT T− curves. Here BKTT ω is a temperature where
Y = 1.
The qualitative explanation of the Y(T) dependence
shown in Fig. 4 is as follows. By probing the system at
Fig. 2. (Color online) Temperature dependences of ω Re σ(T) at
the same magnetic fields as in Fig. 1.
Fig. 3. (Color online) Temperature dependences of 1( )kL T− and
ωRe σ(T) for a LSCO/LCO bilayer film with a higher Tc, meas-
ured by the single-coil inductance technique at 8.8–50.8 MHz.
Fig. 4. (Color online) Temperature dependences of Y = (lω /ξ
+)2
at different magnetic fields perpendicular to the film face, B = 0;
0.0014; 0.0023; 0.003; 0.006; 0.013; 0.019; 0.036; 0.1; 0.2; 0.4;
0.6; 1.0; 1.5; 2.0; 3.4; 4.6; 5.2; 6.0; 7.0 T. Inset shows the Y ver-
sus TBKT/T dependences for LSCO/LCO heterostructure and
1 unit cell thick YBCO film [7].
1240 Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 12
Complex conductance of ultrathin La2–xSrxCuO4 films and heterostructures
finite frequencies, the observed bound-pair response is
dominated by those pairs with r ~ lω. At temperatures be-
low dc
BKTT , the dissipation is proportional to the number of
such vortex–antivortex pairs [11,15]. This number grows
gradually with temperature up to BKTT ω . On the high-
temperature side, Re σ decreases with increasing tempera-
ture since Re 1/ fnσ ∝ µ, where nf is the density of free
vortices and µ is the vortex mobility [11]. Dissipation is
the largest when the correlation length ξ+(T), i.e., the aver-
age distance between thermally induced free vortices
above BKTT ω , becomes equal to lω, which determines the
BKT transition temperature at a given frequency, BKTT ω .
This transition temperature is determined as the point at
which Y = 1 (corresponding to the maximum of ω Re σ(T)
curve) and is frequency-dependent due to r ~ lω relation.
From the Y(T) data on the low-temperature side (Fig. 4),
we found that the vortex diffusion constant D(T) is not
linear with T at low-temperature range as is the case for
free vortices [11]. Rather, the data can be fitted with an ex-
ponential dependence 0 0 exp / 1/ 1 ,( ) ( )/B BKTD T D E k T T ω = −
which can be attributed to pinning of vortex cores [11].
The pinning energy, E0/kB = 52 K, decreases with H down
to 16 K for H = 0.2 T and then is almost H-independent for
H > 0.2 T. On the high-temperature side, the Y(T) curves
deviate from the exponential form due to temperature de-
pendence of ξ+(T) but they collapse onto a single curve for
H < 0.2 T, indicating that the temperature dependence of
ξ+(T) is the same for these fields. The Abrikosov vortex
lattice parameter 1/2
0 ext/( )va H= φ (1.02·10–5 cm at 0.2 T)
is the scale limiting the formation of vortex–antivortex pairs
in a magnetic field [13]. We can estimate the field Hext
which destroys the vortex pair unbinding from the follow-
ing relation: lω ~ av. Apparently, this is the reason why the
Y(T) curves deviate from the single one for H > 0.2 T, due
to the destruction of the dynamic BKT transition by the
magnetic field.
Another test for BKTT ω can be made by analyzing the on-
set points of strong dependences of 1( )kL T− and ω Re σ(T)
on the magnetic field perpendicular to the film surface,
which we denote as Hc2(T). As one can see from Fig. 5, the
onset point for 1( )kL T− is shifted downwards with respect to
the onset of ω Re σ(T) by a nearly constant value of about
4 K. This Hc2(T) dependence is rather peculiar. It follows
that there are three “critical” temperatures, (i) the mean-
field value Tc0 = 20.9 K, (ii) BKTT ω = 19 K, and (iii) H
BKTT =
= 16 K due to the destruction of the BKT transition by the
magnetic field. This is clear from the log Hc2 vs T plot
shown on the right-hand side in Fig. 5. We can see the
break in the slope of Hc2(T) inferred from 1( )kL T− which is
absent in Hc2(T) determined from ω Re σ(T).
Figures 6(a) and (b) show similar two-step behavior of
Hc2(T) observed in one-unit-cell-thick YBa2Cu3O7–x films
sandwiched between semiconducting Pr0.6Y0.4Ba2Cu3O7–x
layers [7]. Here we plot the Hc2(T) data from Re M(T) and
Im M(T) curves, showing almost the same difference in Tc
(3 K).
Conclusions
In conclusion, we have studied the dependences of the real
and the imaginary parts of complex sheet conductance, σ(ω),
on the magnetic field and temperature, in LSCO/LCO bi-
layer films as well as in one-unit-cell-thick YBCO films
sandwiched between semiconducting Pr0.6Y0.4Ba2Cu3O7–x
layers. Our rf measurements on these films showed three
key features: (i) a steep jump in 1( )kL T− , (ii) a maximum in
ω Re σ(T), and (iii) a systematic downward shift of the Tc
onset point of 1( )kL T− curves compared to the transition
onset of ω Re σ(T) curves. Magnetic field H > 0.2 T re-
moves the steep jump of 1( )kL T− but it does not change the
temperature shift. Although the first two features are in
agreement with the dynamic BKT model, independence of
the shift on the magnetic field is rather surprising.
Fig. 5. (Color online) (a) Hc2(T) determined as the onsets of 1( )kL T− and Re σ(T) field dependences. The solid lines indicate the tempe-
rature dependences according to the WHH model. (b) Hc2(T) curves present the same data on the log scale. The solid lines are guide to
the eye.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 12 1241
V.A. Gasparov and I. Božović
Acknowledgments
We are grateful to V.F. Gantmakher and R. Huguenin
for helpful discussions. We would like to thank S. Zlobin
for experimental aid. This work was supported in part by
the Russian Academy of Sciences Program “Quantum
mesoscopic and nonhomogeneous systems” and RFFI
grant 12-02-00171. The work at Brookhaven National La-
boratory was supported by the U.S. Department of Energy,
Basic Energy Sciences, Materials Sciences and Engineer-
ing Division.
1. J.M. Kosterlitz and D.J. Thouless, J. Phys. C 6, 1181 (1973);
Prog. Low Temp. Phys. B 7, 373 (1978).
2. M. Rasolt, T. Edis, and Z. Tesanovic, Phys. Rev. Lett. 66,
2927 (1991).
3. P. Minnhagen and P. Olsson, Phys. Rev. B 45, 5722 (1992).
4. T. Terashima, K. Shimura, Y. Bando, Y. Matsuda, A. Fujiyama,
and S. Komiyama., Phys. Rev. Lett. 67, 1362 (1991).
5. C. Kwon, Qi Li, X.X. Xi, S. Bhattacharya, C. Doughty, T.
Venkatesan, H. Zhang, J.W. Lynn, J.L. Peng, Z.Y. Li, N.D.
Spencer, and K. Feldman, Appl. Phys. Lett. 62, 1289 (1993).
6. M.Z. Cieplak, S. Guha, S. Vadlamannati, T. Giebultowicz,
and P. Lindenfeld, Phys. Rev. B 50, 12876 (1994).
7. V.A. Gasparov, G.E. Tsydynzhapov, I.E. Batov, and Qi Li,
J. Low Temp. Phys. 139, 49 (2005).
8. J.M. Repaci, C. Kwon, Qi Li, X. Jiang, T. Venkatessan, R.E.
Glover, III, C.J. Lobb, and R.S. Newrock, Phys. Rev. B 54,
9674 (1996).
9. M.C. Sullivan, T. Frederiksen, J.M. Repaci, D.R. Strachan,
R.A. Ott, and C.J. Lobb, Phys. Rev. B 70, 140503(R) (2004).
10. A. Gurevich and V.M. Vinokur, Phys. Rev. Lett. 100,
227007 (2008).
11. M.R. Beasley, J.E. Mooij, and T.P. Orlando, Phys. Rev. Lett.
42, 1165 (1979).
12. A.T. Fiory, A.F. Hebard, P.M. Mankiewich, and R.E.
Howard, Phys. Rev. Lett. 61, 19 (1988).
13. L.C. Davis, M.R. Beasley, and D.J. Scalapino, Phys. Rev. B
42, 99 (1990).
14. C.T. Rogers, K.E. Myers, J.N. Eckstein, and I. Božović,
Phys. Rev. Lett. 69, 160 (1992).
15. P. Minnhagen, Rev. Mod. Phys. 59, 1001 (1987).
16. V. Ambegaokar, B.I. Halperin, D.R. Nelson, and E.D. Siggia,
Phys. Rev. Lett. 40, 783 (1978); Phys. Rev. B 21, 1806 (1980).
17. B.J. Halperin and D.R. Nelson, J. Low Temp. Phys. 36, 599
(1979).
18. J. Bardeen and M.J. Stephen, Phys. Rev. 140, A1197 (1965).
19. V. Gasparov, E. Zhukova, A. Voronkov, B. Gorshunov, and
Qi Li, J. Phys.: Conf. Ser. 150, 052058 (2009).
20. V.A. Gasparov and I. Božović, Phys. Rev. B 86, 094523 (2012).
21. V.A. Gasparov, Xi He, G. Dubuis, D. Pavuna, N.D. Kusch,
E.B. Yagubskii, J.A. Schlueter, and I. Božović, Int. J. Mod.
Phys. B 29, 1542012 (2015).
22. I. Božović, IEEE Trans. Appl. Supercond. 11, 2686 (2001).
23. A. Gozar, G. Logvenov, L. Fitting Kourkoutis, A.T. Bollinger,
L.A. Giannuzzi, D.A. Muller, and I. Božović, Nature 455,
782 (2008).
24. G. Logvenov, A. Gozar, and I. Božović, Science 326, 699 (2009).
25. V.A. Gasparov and A.P. Oganesyan, Physica C 178, 445
(1991).
26. A. Gauzzi, J. Le Cochec, G. Lamura, B.J. Jönsson, V.A.
Gasparov, F.R. Ladan, Placais, P.A. Probst, D. Pavuna, and
J. Bok, Rev. Sci. Instrum. 71, 2147 (2000).
27. A.T. Fiory, A.F. Hebard, P.M. Mankiewich, and R.E. Howard,
Appl. Phys. Lett. 52, 2165 (1988).
28. J.L. Jeanneret, G.A. Gavilano, A. Racine, C. Leemann, and
P. Martinoli, Appl. Phys. Lett. 55, 2336 (1989).
29. J.H. Claassen, Appl. Phys. Lett. 82, 601 (2003).
30. S.J. Turneaure, A.A. Pesetski, and T.R. Lemberger, J. Appl.
Phys. 83, 4334 (1998).
31. V. Gasparov, I. Sheikin, and S. Otani, Physica C 178, 449
(1991).
32. V.A. Gasparov, N.S. Sidorov, and I.I. Zver’kova, Phys. Rev.
B 73, 094510 (2006).
33. G. Dubuis, Xi He, and I. Božović, Rev. Sci. Instrum. 85,
103902 (2014).
34. M. Tinkham, Introduction to Superconductivity, McGraw
Hill, New York (1996), 2nd ed., p. 381.
Fig. 6. (Color online) (a) Hc2(T) determined as the onsets of Re M(T) and Im M(T) field dependences for 1 UC YBCO film. (b) The
same data, on the log scale. The solid lines are guides to the eye.
1242 Low Temperature Physics/Fizika Nizkikh Temperatur, 2015, v. 41, No. 12
Experimental
Results
Analysis and discussion
Conclusions
Acknowledgments
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