1
Vol.:(0123456789)
Scientific Reports
| (2021) 11:16181
|
https://doi.org/10.1038/s41598-021-95530-5
www.nature.com/scientificreports
Supercapacitance
and superinductance of
TiN
and NbTiN films in the vicinity
of superconductor‑to‑insulator
transition
A. Yu. Mironov
1
, D. M. Silevitch
3
, S. V. Postolova
1
, M. V. Burdastyh
1,2
, T. Proslier
4
,
T. I. Baturina
1
, T. F. Rosenbaum
3
& V. M. Vinokur
5,6
*
We investigate the low‑temperature complex impedance of disordered insulating thin TiN and NbTiN
films in the frequency region 400
Hz–1 MHz in close proximity to the superconductor–insulator
transition (SIT). The frequency, temperature, and magnetic field dependencies of the real and
imaginary parts of the impedance indicate that in full accord with the theoretical predictions and
earlier observations, the films acquire self
‑induced electronic granularity and become effectively
random arrays of superconducting granules coupled via Josephson links. Accordingly, the inductive
component of the response is due to superconducting droplets, while the capacitive component
results from the effective Josephson junctions capacitances. The impedance crosses over from
capacitive to inductive behavior as films go across the transition.
As early as in 1978, Gerard ‘t Hooft in his brilliant
work
1
illustrated an absolute quark confinement as a dual anal-
ogy to absolute disappearance of the resistance in superconductors and termed the resulting extreme opposite to
the superconducting state a “superinsulator.” A gauge theory of the Josephson junction arrays (JJA)
2
predicted
the ground state dual to superconductivity and coined independently the same name for this phase possessing
an infinite resistance. Finally, the
work
3
independently rediscovered this phase arising as a result of the duality
of the uncertainty principle for Cooper pairs, named it again a superinsulator, and reported an experimental
evidence of a superinsulating state in TiN films. A comprehensive gauge theory of the superinsulating
state
4
rests
on the gauge field theory that revealed the topological nature of the superconductor–insulator transition (SIT)
5
and on generalization of the technique
of
2
onto finite temperatures. The superinsulating state, a mirror opposite
twin of superconductivity, appears at the insulating side of the
SIT
2
,
3
and is an exemplary manifestation of the
electric–magnetic
duality
6
extended onto a quantum realm.
The superinsulating properties, in particular, its infinite resistance, are an implication of the formation of the
magnetic monopole Bose
condensate
7
, a mirror twin of Cooper pairs condensate in superconductors, emerging
at the insulating side of the SIT. Monopole Bose condensate squeezes electric field lines connecting the charges of
the Cooper couple, i.e. a Cooper pair–anti-Cooper pair duo, into the Polyakov’s electric strings. Polyakovs strings
confine the motion of charges making them
immobile
4
, hence resulting in the infinite resistance. Small electric
fields,
E
<
E
c1
, where
E
c1
is a lower critical field, do not penetrate superinsulators. This can be viewed as an elec
-
tric analogue of the Meissner effect; the corresponding dielectric permeability is zero,
ε
=
0
8
. If the separation
between the constituent charges of a Cooper couple is small enough, the couple does not feel an immobilizing
binding action of the connecting Polyakov’s string in an analogue to the asymptotic freedom phenomenon in
OPEN
1
Rzhanov Institute of Semiconductor Physics SB RAS, 13 Lavrentjev Avenue, Novosibirsk,
Russia 630090.
2
Novosibirsk State University, Pirogova str. 2, Novosibirsk, Russia
630090.
3
Division of Physics,
Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA
91125, USA.
4
Institut de
Recherches sur les lois Fundamentales de L’univers, Commissariat de L’énergie Atomique et aux Énergies
Renouvelables-Saclay, Gif
-sur-Yvette, France.
5
Terra Quantum AG, St. Gallerstrasse 16A, 9400
Rorschach,
Switzerland.
6
Physics Department, City College of the City University of New York, 160 Convent Ave, New York,
NY 10031, USA.
*
email: vmvinokour@gmail.com
2
Vol:.(1234567890)
Scientific Reports
| (2021) 11:16181 |
https://doi.org/10.1038/s41598-021-95530-5
www.nature.com/scientificreports/
particle physics. Therefore, in a sufficiently small superinsulating system the motion of charges is not impeded,
and the system behaves like a metal.
At intermediate fields,
E
c1
<
E
<
E
th
, the Polyakov strings enter the superinsulator which, if large enough to
accommodate the strained strings, shows an infinite resistance. Finally, at the threshold field
E
=
E
th
, Polyakov
strings break down and the superinsulator turns into a standard insulator demonstrating thermally activated
resistance. These dc electric properties of superinsulators have been experimentally investigated in detail
in
8
and showed an excellent agreement with the theoretical predictions. At the same time, the ac properties of the
superinsulating state, especially on approach to the SIT, remain unexplored.
To gain an insight into the expected ac behavior of the systems in the critical vicinity of the SIT, let us
recall that in the critical vicinity of the SIT, the films acquire a self-induced granularity, i.e., becomes and array
of superconducting granules connected by Josephson
links
3
. Next, we note that because of this self-induced
granular structure, the local superconducting gap remains finite even at the very transition (although the global
superconductivity, of course, disappears). Hence such a system is pretty much like an array of
capacitors
9
con
-
necting inductive elements, see Supplementary Information (SI). This implies that on approach to the SIT from
the superconducting side, when the electron path length diverges, an increase in the inductance and a decrease
in the capacitance of the system will be observed. This conclusion is consistent with the expected decrease in
static dielectric
permeability
8
on approach to the SIT. Accordingly, further movement into the insulating side of
the junction should increase the capacitance of the entire system.
Here we report the results of low-temperature measurements of the complex ac impedance in disordered
insulating thin TiN and NbTiN films in a close proximity to the SIT. We demonstrate that as the applied mag
-
netic field or change in the normal sheet resistance drive the films across the SIT, the character of the systems’
response crosses over from the highly inductive to highly capacitive behavior expected for the superconductor-
to-superinsulator transition.
Sample preparation
The ac transport measurements are taken on the thin TiN and NbTiN films grown by the atomic layer deposi-
tion (ALD) technique as best technique for growing thin
films
10
,
11
. The fabrication technique is described in
detail
in
3
,
12
. For growing TiN films we used
TiCl
4
, and
NH
3
as gaseous reactants. To grow NbTiN films we used
NbCl
5
additionally. For changing the stoichiometry of NbTiN films, we used а variation of the ratio of
TiCl
4
/
NbCl
5
cycles during the
growth
13
. The TiN films were deposited on the
SiO
2
substrate. The superconducting
properties of the ultrathin NbTiN films were optimized by utilizing the AlN buffer layers grown on top of the
Si
substrate
14
. The thickness of TiN films is
d
=
3.6
nm and the thickness of the NbTiN films is
d
=
10
nm. The
film structure inspection by the high resolution transmission electron microscope (HRTEM) shows that the film
is smooth, continuous, and uniform, and does not have pinholes. Figure 1a presenting a HRTEM image of the
TiN film displays the polycrystalline structure with densely packed crystallites. The HRTEM image of NbTiN
films display the same structure and are described
in
12
. The crystallites are densely packed and they have dif-
ferent orientations. The boundaries between crystallites are atomically thin. The size distribution of crystallites
together with the best fits by Gaussian and log-normal distributions giving average values 4.9 nm and 4.8 nm,
respectively, is shown in Fig. 1b. Note the asymmetry of the histogram. The diffraction images of NbTiN films
are similar to those of TiN films, see Fig. 1c, and are presented
in
12
. The analysis of the diffraction data reveals
that the both TiN and NbTiN crystallites have the same rock-salt crystal structure. Using the Vegard’s law, we
find that the NbTiN film are solid solution of NbN and TiN taken in a ratio of approximately 7:3 for the sample
U
12
, while samples N1, N2, N3 have NbN to TiN ratio approximately equal to 2:1. We patterned the TiN and
NbTiN films into the configuration shown in Fig. 1d by standard UV lithography and plasma etching. Such a
configuration allows for combined measurements of the dc resistance and ac complex impedance. Additionally
on TiN mesastructure was manufactured of the 100 nm thick gold electrodes separated by the 50
μ
m by usual
thermal evaporated technic (see Fig. 1e). For NbTiN samples we use the same mesastructure without gold elec-
trodes, but measurements were taken only between the contacts 1 and 5–6. The distance between the contacts
was 2.5 mm. Resistivity measurements were performed at sub-Kelvin temperatures in helium dilution refrigera-
tors. In order to drive our TiN film with thickness 3.6 nm across the SIT we employ the controlled oxidation in
the air at
T
=
600
◦
K which results in an increase of the sheet resistance at room temperature. Note that etching
usually gives a more predictable result than oxidation. However, in the case of very thin films (
d
<
4
nm), the
required etching time is less than 0.5 s, which significantly complicates the procedure for obtaining films close
to the superconductor–insulator transition. In the case of NbTiN films, we used the plasma etching procedure
for obtaining samples N1 and N2 from N3. The thicknesses of U and N1 samples are 10 nm, the thicknesses of
N2 and N3 samples are indistinguishable and equal approximately to 9 nm.
Results
Temperature dependencies of the resistance per square,
R
(
T
)
, are shown in Fig.
2
and plotted in a log–log scale
spanning the window over four decades in temperature.
The evolution of
R
(
T
)
for a representative TiN film across the superconductor-to-insulator transition is
shown in Fig.
2
a. The initial film is a superconductor. After heating, See Supplementary Information (SI), it
becomes an insulator. The strength of the insulating behavior depends on the distance between electrodes. As
demonstrated
in
4
superinsulating properties develop in full power only in the systems which are large enough
to accommodate fully strained Polyakov’s electric strings confining the free motion of Cooper pairs. Therefore,
decreasing the distance between electrodes, i.e., decreasing the system’s effective size, suppresses its superinsulat-
ing properties as has been indeed observed experimentally in NbTiN
films
8
,
15
.