. The geometric inductance represents the conventional in-
ductance of the SRR loop and can be estimated  to be
H. In contrast, the additional inductance L
originates dominantly from the kinetic energy in supercon-
ducting carriers in the YBCO SRRs. This additional SRR in-
ductance can be calculated using the above derived YBCO
ﬁlm surface reactance X
and by considering the geometry
and dimensions of the YBCO SRR: L
Therefore, the total SRR inductance becomes L = L
In order to obtain the metamaterial resonance frequency using
Eq. (4), we estimate the SRR capacitance C
from the above estimated geometric inductance L
simulated resonance frequency ω
= 2π×0.62 THz assuming
perfect conducting SRRs (i.e. L
= 0 and R = 0 ). The cal-
culated temperature-dependent metamaterial resonance fre-
quency is plotted in Fig. 1(c) along with the experimental and
simulation results. Again, the theoretical result reproduces the
frequency tuning features, though the overall tuning range is
about half of the experimental and simulation data.
The above calculations show that the temperature-
dependent SRR resistance and additional inductance, due
to the temperature-dependent complex conductivity of the
YBCO ﬁlm, play an important role in the resonance switching
and frequency tuning. Eqs. (5) and (6) further reveal that, for
a ﬁxed value of the real conductivity, which is approximately
the case in our situation, the YBCO ﬁlm surface reactance,
and therefore the additional SRR inductance, reach the maxi-
mum value when the imaginary conductivity is approximately
equal to the real conductivity, and vice versa. This is consis-
tent with the experimental observations, where the metamate-
rial resonance frequency shifts to the lowest value when the
real and imaginary parts of the YBCO complex conductivity
cross each other.
The results in Fig. 2 suggest that metamaterials made from
thinner YBCO superconducting ﬁlms will have a lower res-
onance frequency, and will be more efﬁcient in resonance
switching and frequency tuning. In order to verify this pre-
diction, we fabricated and characterized a second metamate-
rial sample from 50 nm thick YBCO ﬁlm. The temperature-
dependent transmission spectra are shown in Fig. 3. The reso-
nance frequency at 20 K is measured to be 0.48 THz, which is
signiﬁcantly lower than that in the metamaterial sample from
180 nm thick YBCO ﬁlm. When temperature increases, the
resonance frequency continuously shifts to lower frequencies.
It becomes 0.31 THz at 78 K, achieving a tuning range of
35%. We did not observe the back shifting of resonance fre-
quency due to the high resistance at temperatures above 80 K,
which already completely damps the metamaterial resonance.
In conclusion, we have fabricated and characterized electric
SRR-based metamaterials from high temperature supercon-
ducting YBCO ﬁlms. We observed temperature induced meta-
material resonance switching and frequency tuning, which
can be reproduced by ﬁnite-element numerical simulations us-
ing the experimentally measured complex conductivity of the
YBCO ﬁlm. We found that both the temperature-dependent
real and imaginary parts of the complex conductivity of the
0.2 0.3 0.4 0.5 0.6 0.7
FIG. 3: (color online). Temperature-dependent THz Transmission
amplitude spectra of the 50 nm thick YBCO metamaterial.
superconducting ﬁlm have to be consistently considered in or-
der to achieve a correct interpretation. A theoretical model
has been developed, taking into account the SRR resistance
and additional inductance. Our modeling calculations were in
good agreement with experimental observations and numeri-
cal simulations, and further predicted more efﬁcient resonance
switching and frequency tuning with thinner YBCO metama-
terials, which was also veriﬁed in experiments. We expect
that such resonance tuning in superconducting metamaterials
could also be realized dynamically through application of op-
tical excitation, electrical currents, and/or magnetic ﬁelds. Al-
though high temperature superconducting metamaterials may
not be able to essentially address the loss issue at THz fre-
quencies and beyond, they should enable the development of
novel, multi-functional metamaterials.
We acknowledge support from the Los Alamos National
Laboratory LDRD Program. This work was performed,
in part, at the Center for Integrated Nanotechnologies, a
US Department of Energy, Ofﬁce of Basic Energy Sciences
Nanoscale Science Research Center operated jointly by Los
Alamos and Sandia National Laboratories. Los Alamos Na-
tional Laboratory, an afﬁrmative action/equal opportunity em-
ployer, is operated by Los Alamos National Security, LLC, for
the National Nuclear Security Administration of the US De-
partment of Energy under contract DE-AC52-06NA25396.
Electronic address: email@example.com
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