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Tuning the Resonance in High Temperature Superconducting Terahertz Metamaterials
Hou-Tong Chen,∗Hao Yang, Ranjan Singh, John F. O’Hara, Abul
K. Azad, Stuart A. Trugman, Q. X. Jia, and Antoinette J. Taylor
MPA-CINT, MS K771, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
(Dated: September 10, 2010)
In this Letter we present resonance properties in terahertz metamaterials consisting of a split-ring resonator
array made from high temperature superconducting films. By varying the temperature, we observed efficient
metamaterial resonance switching and frequency tuning with some features not revealed before. The results
were well reproduced by numerical simulations of metamaterial resonance using the experimentally measured
complex conductivity of the superconducting film. We developed a theoretical model that explains the tun-
ing features, which takes into account the resistive resonance damping and additional split-ring inductance
contributed from both the real and imaginary parts of the temperature-dependent complex conductivity. The
theoretical model further predicted more efficient resonance switching and frequency shifting in metamaterials
consisting of a thinner superconducting split-ring resonator array, which were also verified in experiments.
PACS numbers: 78.67.Pt, 74.25.-q, 74.78.-w, 74.25.N-
Metamaterials consisting of metallic elements have enabled
a structurally scalable electrical and/or magnetic resonant re-
sponse, from which exotic electromagnetic phenomena absent
in natural materials have been observed [1]. Metals provide
high conductivity that is necessary to realize strong electri-
cal/magnetic metamaterial response [2, 3]. Metals, however,
play a negligible role in active/dynamical metamaterial reso-
nance switching and/or frequency tuning, which has been typ-
ically accomplished through the integration of metamaterials
with other natural materials (e.g. semiconductors) or devices,
and by the application of external stimuli [4–12]. It is essen-
tially the modification of the metamaterial embedded environ-
ment that contributes to such previously observed functional-
ities.
Recently, there has been increasing interest in supercon-
ducting metamaterials towards loss reduction [13–20]. Signif-
icant Joule losses have often prevented resonant metal meta-
materials from achieving proposed applications, particularly
in the optical frequency range.
perconducting materials possess superior conductivity than
metals at frequencies up to terahertz (THz), and therefore
it is expected that superconducting metamaterials will have
a lower loss than metal metamaterials. More interestingly,
superconductors exhibit tunable complex conductivity over a
wide range of values, through variation of temperature and ap-
plication of photoexcitation, electrical currents and magnetic
fields. Therefore, we would expect correspondingly tunable
metamaterials, which originate from the superconducting ma-
terials composing the metamaterial, in contrast to tuning the
metamaterial environment.
In fact, superconducting metamaterials have enabled dia-
magnetic response at very low frequencies, which may en-
able screening of static magnetic fields [21, 22]. In the mi-
crowave frequency range (∼10 GHz), left-handed supercon-
ducting transmission lines have been introduced and their tun-
ability has been realized with electrical currents or temper-
ature [13, 14]. Negative index metamaterials comprised of
niobium wires and split-ring resonators exhibited red-shifting
At low temperatures, su-
in resonance frequency (∼ 0.6%) when the temperature was
increased approaching the transition temperature Tc[17]. Fur-
ther experimental work has demonstrated tunability through
application of external dc or rf magnetic fields [16, 20].
At THz frequencies, low temperature superconductors may
be not suitable for metamaterial applications, since with a
smaller superconducting gap, Cooper pairs may be excited
and broken by THz photons, and therefore high temperature
superconductors (HTS) should be employed. In this Letter,
we present THz metamaterials based on electric split-ring
resonators (SRRs) made from epitaxial YBa2Cu3O7−δHTS
films. These metameterials exhibit temperature-dependent
resonance strength and frequency, which reveal some inter-
esting tuning features not previously observed. Finite-element
numericalsimulationsandtheoreticalmodelingareperformed
to understand the underlying tuning mechanism.
The epitaxial YBa2Cu3O7−δ(YBCO) films with δ = 0.05
were prepared using pulsed laser deposition on 500 µm thick
(100) LaAlO3(LAO) substrates. The transition temperature
was measured to be Tc=90 K. Square arrays of electric SRRs,
with the unit cell shown in the inset to Fig. 1(a), were fabri-
cated using conventional photolithographic methods and wet
chemical etching of the YBCO films. The YBCO SRRs have
a thickness of d = 180 nm or 50 nm, outer dimensions of
l = 36 µm, line width of w = 4 µm and gap size of g = 4 µm,
and the arrays have the periodicity of p = 46 µm. Terahertz
time-domain spectroscopy (THz-TDS) incorporated with a
continuous flow liquid helium cryostat was used to charac-
terize the YBCO films and metamaterials. Under normal inci-
dence, the THz transmission spectra were measured as a func-
tion of temperature, using an LAO substrate as the reference.
We focus our attention on the metamaterial fundamen-
tal resonance (the so-called LC resonance) resulting from
the circulating currents excited by the incident THz electric
field [23]. In Fig. 1(a) we show the THz transmission ampli-
tude spectra for the 180 nm thick YBCO metamaterial sam-
ple at various temperatures. At temperatures far below Tc,
e.g. 10 K, the metamaterial exhibits the strongest resonance,
arXiv:1009.1640v1 [cond-mat.supr-con] 8 Sep 2010
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Temp (K):
100
84
80
78
75
70
60
10
0.2 0.40.6 0.8
Frequency (THz)
1.0
0
0.2
0.4
0.6
0.8
1.0
Transmission
0.0
0.2
0.4
0.6
0.8
Ttransmission minimum
204060
Temperature (K)
80100120140
0.56
0.58
0.60
Resonance frequency (THz)
(a)
Experiment
Simulation
Theory
(c)
(b)
Temperature (K)
σre
σim
4080120
0
2
4
6
×10 6 S/m
FIG. 1: (color online). (a) THz Transmission amplitude spectra of
the 180 nm thick YBCO metamaterial at various temperatures. (b)
Transmission minimum and (c) corresponding resonance frequency
as functions of temperature, from experiments, numerical simula-
tions, and theoretical calculations. Inset to (a) illustrates a micro-
scopic image of a single YBCO SRR, where the lighter colored area
is YBCO. Inset to (b) shows the real and imaginary parts of the com-
plex conductivity at 0.6 THz of an unpatterned 180 nm thick YBCO
film.
as indicated by the sharp THz transmission dip with a min-
imal transmission amplitude of 0.045 at 0.613 THz. This
strong resonance is almost the same as in a metamaterial sam-
ple where the YBCO SRRs was replaced by gold SRRs with
the same thickness and at the same temperature. As the tem-
perature increases, the resonance strength decreases, as seen
by the broadening and reduction in amplitude of the transmis-
sion dip. The resonance frequency experiences a red-shifting,
which reaches the lowest value of 0.564 THz near 80 K, re-
sulting in a frequency tuning of 8%. As the temperature fur-
ther increases, the resonance strength continues to decrease,
but the resonance frequency, on the other hand, shifts back
to higher frequencies. The temperature-dependent transmis-
sion minimum and the corresponding resonance frequency are
plotted in Figs. 1(b) and 1(c), respectively. The results show
that, at temperatures near 80 K, the transition of resonance
strength is fastest and the resonance frequency exhibits a dip,
not observed in previous work [17–20]. We can exclude the
LAO substrate as contributing to the metamaterial resonance
tuning, because the features in the temperature-dependent res-
onance in the YBCO metamaterial (see Fig. 1) were not ob-
served in a metamaterial sample where the YBCO was re-
placed by gold. In that gold SRR metamaterial sample, the
resonance frequency shifting was imperceptible, and the res-
onance strength only slightly decreased with increasing tem-
peratures. Additionally, through THz-TDS measurements, it
turns out that the dielectric constant of the LAO substrate only
exhibits a weak dependence on the temperature. Therefore, it
isthetemperature-dependentpropertiesofYBCOfilmthatare
responsible for the observed metamaterial resonance tuning.
The complex conductivity of YBCO film can be expressed
using the well-known two-fluid model [24]:
˜ σ(ω,T) =ne2
m∗
?
fn(T)
τ−1−iω+ifs(T)
ω
?
,
(1)
where fnand fsare fractions of normal (quasiparticle) and
superconducting (superfluid) carriers, respectively, with fn+
fs=1, n is the carrier density, m∗is the carrier effective mass,
and τ is the quasiparticle relaxation time. The real and imagi-
nary parts of the complex conductivity are then:
σre =
ne2
m∗
ne2
m∗
fn(T)τ
1+ω2τ2,
?fn(T)ωτ2
(2)
σim =
1+ω2τ2+fs(T)
ω
?
.
(3)
Using THz-TDS we experimentally measured the conduc-
tivity of an unpatterned 180 nm thick YBCO plain film. The
resultant real and imaginary parts of the complex conductivity
at 0.6 THz are plotted as functions of temperature in the inset
to Fig. 1(b). The real conductivity [Eq. (2)], which derives
from the Drude response of quasiparticles in Eq. (1), slowly
increases when temperature decreases across Tcto about 70 K.
It starts to decrease below 70 K, but not significantly, over
the temperatures we measured down to 50 K. In this temper-
ature range, ωτ ? 1 at the resonance frequency (∼ 0.6 THz),
the decreasing fn(T) may be compensated by the increasing
quasiparticle scattering time τ [25]. At temperatures above Tc,
theimaginaryconductivityisderivedfromtheDruderesponse
and is very small, since fs(T > Tc) = 0. As the temperature
decreases below Tc, the second term in Eq. (3) from the su-
perfluid Cooper pair state becomes non-zero and results in the
rapidly increasing imaginary conductivity, exceeding the real
conductivity below 80 K. Using these experimental values of
the YBCO complex conductivity at 0.6 THz, the metamaterial
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resonant response was simulated using commercially avail-
able finite-element simulation codes from COMSOL Multi-
physics. The simulated transmission minimum and the corre-
sponding frequency are plotted as functions of temperature in
Figs. 1(b) and 1(c), respectively, reproducing the experimental
results.
The measured real conductivity of the YBCO film reveals
less than 20% change over the temperature range from 60 K to
90 K, where the resonance strength experiences a fast change
and the resonance shifts its frequency. This variation of real
conductivity cannot solely cause the observed large metama-
terial resonance switching and frequency tuning. Both the real
and imaginary parts of the complex conductivity have to be
considered for the metamaterial resonance. The imaginary
conductivity, which is due to the superfluid carriers and causes
no loss, becomes dominant at low temperatures, and it is re-
sponsible for the enhancement in resonance strength.
The resonance frequency is determined by the effective
capacitance, C, inductance, L, and resistance, R, in the
SRRs [26]:
ω2
0=
1
LC−R2
4L2.
(4)
It has been shown that the kinetic inductance, which repre-
sents the kinetic energy storage in free electrons in metals, or
Cooper pairs in superconductors, plays an important role in
determining the metamaterial resonance frequency [17, 27].
This effect underpins the red-shifting of the resonance fre-
quency in niobium metal superconducting metamaterials op-
erating near 10 GHz as the temperature increases and ap-
proaches Tc[17]. However, the back blue-shifting, shown in
Fig. 1(c) between ∼80 K and Tc, was not observed in nio-
bium, and the model proposed in that work would not explain
this effect when only the superfluid state (i.e. imaginary con-
ductivity) was considered [17].
Here we consider a more general situation that the SRRs
are fabricated from a conducting film (YBCO film in our case)
with a complex conductivity ˜ σ and thickness d. Such an un-
patterned plain film can be modeled as a lumped impedance
in an equivalent transmission line. By equating the (multi-
ple) reflections or transmissions from the film and the trans-
mission line model, this complex surface impedance (or sheet
impedance with units of Ω/square) of the unpatterned film can
be derived as:
˜ZS= RS−iXS= Z0n3+i˜ n2cot(˜βd)
˜ n2
2−n2
3
,
(5)
where the tildes over the variables indicate complex values,
Z0=377 Ω is the vacuum intrinsic impedance, n3=√εLAO=
4.8istheLAOsubstraterefractiveindex, ˜ n2=?i˜ σ/ε0ωisthe
complex propagation constant where c0is the light velocity
in vacuum. Both ˜ n2and˜β can be calculated from the experi-
mental complex conductivity near the metamaterial resonance
frequency. When n3?|˜ n2|, which is valid in our case, Eq. (5)
complex refractive index of the film, and˜β = ˜ n2ω/c0is the
can be further simplified as:
˜ZS= iZ0
˜ n2cot(˜βd).
(6)
From Eqs. (5) and (6), it is obvious that both the finite real
and imaginary parts of the film refractive index ˜ n2, and there-
fore the finite real and imaginary parts of the complex con-
ductivity ˜ σ, contribute to the film surface resistance RSand
reactance XS. They are plotted in Fig. 2 for the 180 nm thick
YBCO film as functions of temperature, and are also calcu-
lated for a 50 nm thick YBCO film assuming its complex con-
ductivity does not depend on the film thickness.
The YBCO SRR array resistance R (SRR reactance X is
zero at resonance) can be obtained by considering the nonuni-
form distribution of currents in a unit cell [28]: R∼= [(A−
g)/w]RS, where A = 64 µm is the median circumference of
the (small) current loop. When temperature increases, the in-
creasing SRR resistance R accounts for the resonance damp-
ing and therefore the increasing transmission minimum. If we
model the SRR array as a lumped resistor R in the transmis-
sion line [29], we can calculate the resonance transmission as
afunctionoftemperature, whichisplottedinFig.1(b)andsat-
isfyingly reproduces the experimental and simulated results.
In order to correctly interpret the temperature-dependent
resonance frequency shifting, additional inductance in SRRs
has to be taken into account besides the geometric inductance
0
12
Surface impedance (Ω/square)
4060 80100120 140
0
2
4
6
Temperature (K)
(b)
(a)
18
6
50 nm
180 nm
50 nm
180 nm
RS
XS
24
FIG. 2: (color online). Complex surface impedance of the 180 nm
thick unpatterned YBCO superconducting film calculated using the
experimental complex conductivity at 0.6 THz. (a) Surface resis-
tance RS, and (b) surface reactance XS. The dashed curves are for an
assumed 50 nm thick YBCO film.
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4
LG. The geometric inductance represents the conventional in-
ductance of the SRR loop and can be estimated [30] to be
LG∼= 4×10−11H. In contrast, the additional inductance LS
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 XSand by considering the geometry
and dimensions of the YBCO SRR: LS∼= [(A−g)/w](XS/ω).
Therefore, the total SRR inductance becomes L = LG+LS.
In order to obtain the metamaterial resonance frequency using
Eq. (4), we estimate the SRR capacitance C∼= 1.5×10−15F,
from the above estimated geometric inductance LGand the
simulated resonance frequency ω0=2π×0.62 THz assuming
perfect conducting SRRs (i.e. LS= 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-
ductingYBCOfilms. Weobservedtemperatureinducedmeta-
material resonance switching and frequency tuning, which
canbereproducedbyfinite-elementnumericalsimulationsus-
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
0.20.30.40.50.60.7
0.0
0.2
0.4
0.6
0.8
1.0
82K
80K
78K
75K
70K
60K
50K
40K
20K
Transmission
Frequency (THz)
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-
calsimulations, andfurtherpredictedmoreefficientresonance
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.
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.
This work was performed,
∗Electronic address: chenht@lanl.gov
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