Applied Physics Letters ARTICLE scitation.

org/journal/apl

Electrically tunable electromagnetically

induced transparency in superconducting
terahertz metamaterials
Cite as: Appl. Phys. Lett. 119, 052602 (2021); doi: 10.1063/5.0056489
Submitted: 11 May 2021 . Accepted: 28 July 2021 .
Published Online: 5 August 2021

Chun Li,1,2 Weili Li,1 Siyu Duan,1 Jingbo Wu,1,a) Benwen Chen,1 Shengxin Yang,1 Runfeng Su,1
1 1
Chengtao Jiang, Caihong Zhang, Biaobing Jin,1 Ling Jiang,2 Lin Kang,1 Weiwei Xu,1 Jian Chen,1
and Peiheng Wu1

AFFILIATIONS
1
Research Institute of Superconductor Electronics (RISE), School of Electronic Science and Engineering, Nanjing University,
Nanjing 210023, China
2
College of Information Science and Technology, Nanjing Forestry University, 159 Longpan Road, Nanjing 210037, China

a)
Author to whom correspondence should be addressed: jbwu@nju.edu.cn

ABSTRACT
We present an electrically tunable superconducting metamaterial capable of modulating terahertz (THz) waves. The device consists of two
concentric ring resonators, which exhibits the electromagnetically induced transparency-like spectral response. A relatively high modulation
depth of 86.8% and a group delay of 25.4 ps were achieved at the transmission window. The experimental and simulated transmission spectra
show good agreement. The hybrid coupling model could well explain the physical mechanism. The tuning of group delay of THz waves is of
great significance to the applications of THz technology.
Published under an exclusive license by AIP Publishing. https://doi.org/10.1063/5.0056489

With the advent of various solid-state sources and sensitive detec- information technologies. By mimicking the quantum transitions in
tors, terahertz (THz) science and technology have experienced rapid atomic systems, the EIT phenomenon can also be realized in classical
development.1 The expansion of THz technology from basic science to systems such as coupled resonators, electric circuits, and plasmonic
“real-world” applications is accelerating. More attention has been paid structures.7–12 These classical analogues have attracted enormous
to the research relevant to our daily lives such as THz wireless commu- interest from the microwave to the visible region due to the sharp dis-
nication, security, sensing, and biomedical imaging.2–5 To realize prac- persion in spectral responses. In the THz regime, an EIT metamaterial
tical and widely available implementation, superior THz tunable is a promising candidate for developing functional devices. Numerous
devices, such as switches and modulators, with high modulation depth designs have been proposed to realize the EIT effect using the coupled
and speed are desirable. Metamaterials, which are composed of subwavelength resonators. A variety of applications have been pro-
artificially designed subwavelength resonators, are widely adopted into posed for THz EIT devices such as biosensors, filters, switches, and
the THz devices to strengthen their interaction with THz waves. modulators.13–17
Metamaterials offer us a powerful avenue to obtain advantageous Toward practical applications, the dynamic control of electro-
electromagnetic properties and to design high high-performance THz magnetic waves is highly expected.18 Many studies have shown that
functional devices. EIT-like effects can be controlled by various stimuli such as thermal,
Electromagnetically induced transparency (EIT) is an exciting optical, electric field, and magnetic field.11,19–21 Among these tuning
quantum interference phenomenon present in a three-level atomic methods, electric tuning is always convenient and cost-effective, espe-
system. The destructive interference results in reducing light absorp- cially for miniaturized and integrated systems. However, few works
tion and slowing down of a light pulse over a narrow spectral region. have demonstrated the electrical manipulation of EIT-like spectral
This effect can promote a light–matter interaction and temporarily response. Kim et al. recently proposed an EIT-like metamaterial by
store light.6 The considerable group delay of light enables the EIT integrating single-layer graphene into the metallic structures. The
effect to impact many fields ranging from nonlinear optics to quantum group delay of THz waves can be effectively controlled by changing

Appl. Phys. Lett. 119, 052602 (2021); doi: 10.1063/5.0056489 119, 052602-1
Published under an exclusive license by AIP Publishing
 Applied Physics Letters ARTICLE scitation.org/journal/apl

the gate voltage.22 In addition, Pitchappa et al. reported a tunable EIT structures of SC resonators. The gold electrodes with a thickness of
analogue with the microelectromechanical systems (MEMSs).23 By 200 nm were fabricated using the magnetron sputtering and the liftoff
applying different voltages, the cantilevers as a part of bright resona- procedure. In the measurement, the device was mounted into a helium
tors can be reconfigured so that the EIT effect can be switched between continuous flow cryostat with quartz windows. The low-temperature
two states. However, for the graphene metamaterials and MEMS devi- THz time-domain spectroscopy (TDS) measurement was done to
ces, the fabrication processes are relatively complicated. obtain the THz transmission spectra. The transmission
 coefficient was
In recent years, superconducting (SC) metamaterials have drawn obtained based on ~t ðxÞ ¼ E ~ R ðxÞ2 , where the E
~ S ðxÞ2 =E ~ S ðxÞ and
significant attention because of their remarkably low Ohmic loss24–28 ~ R ðxÞ are Fourier transforms of the transmitted electric field signals
E
and sensitivity to external stimuli such as current, light, magnetic through the sample and the substrate, respectively.
fields, and temperature.21,29–32 Compared with the traditional meta- We simulated the transmission spectra of the periodic structures
materials made from a metallic film, the SC devices are more suitable of IRR, ORR, and DRR using the full-wave electromagnetic simulation
for developing THz switchable devices with a large tuning range and software. In the simulation, the complex conductivity of the NbN film
low loss. By applying a sinusoidal voltage signal, we have proved that at 4.5 K was calculated from the impurity scattering model in the Born
the SC metamaterials’ modulator could achieve a modulation speed of limit based on the BCS theory.34 In the simulated THz transmission
around 1 MHz in the previous works.33 The SC metamaterials offer a spectra of Fig. 2, the resonance dips of ORR and IRR were observed at
promising approach for designing dynamic slow-light devices with 0.303 and 0.445 THz, respectively. They can both be excited by the
high modulation speed. incident THz wave directly. Therefore, the interaction between two
In this work, we demonstrate an electrical tuning of EIT-like resonators is bright–bright mode coupling.35 For the transmission
spectral response in SC niobium nitride (NbN) metamaterials. The spectra of DRR, the coupling between the two resonators results in a
unit cell of the metamaterial consists of two coupled concentric ring sharp transmission peak at 0.320 THz. Two resonance modes appear
resonators. The EIT-like spectral response was observed, and a modu- at x ¼ 0.269 and xþ ¼ 0.450 THz. Their resonance modes are
lation depth of 86.8% was achieved. A hybrid coupling model using a shifted from the resonance modes of IRR and ORR, which means a
coupled-mode theory is introduced to illustrate the physical mecha- splitting of energy levels based on the hybridization theory.35–37
nism. A significant slow-light effect could be observed at the transmis- At 4.5 K, we measured the switching performances of the device
sion window, and the maximum group delay is 25.4 ps. Our work with different voltages (currents) using the low-temperature THz-TDS
offers a pathway for electrically tunable slow light devices. system. The inset of Fig. 3 shows the obtained temporal pulses after
The designed device consists of a periodic array of double-ring transmission through the sample. After the main transmitted pulse,
resonators (DRRs). The geometry of the unit cell is shown in Fig. 1(a). the oscillations are apparent and gradually fall with bias voltage. The
The unit cell consists of an outer-ring resonator (ORR) and an inner- oscillation frequency falls exactly on the transparency window fre-
ring resonator (IRR). Each row of ORRs is connected to the gold elec- quencies, indicating that the THz wave at the window indeed slows
trodes on the two opposite sides of the chip via a continuous NbN down. Without an electric bias, the maximum transmission amplitude
wire, as shown in Fig. 1(b). The plane wave is normally incident is 0.98 at 0.340 THz. With the variation of the bias voltage, the trans-
(z-direction) onto the metamaterials, and the polarization is in the mission amplitude gradually decreases. It demonstrates that the elec-
x-direction. trical tuning of the EIT-like spectral response was achieved using this
The 200 nm-thick NbN film was deposited on a 1 mm-thick device.
magnesium oxide (MgO) substrate using the conventional radio fre- To give insight into the physical mechanism, we used a hybrid
quency magnetron sputtering. The SC critical temperature (Tc ) of the coupling model to investigate the measured transmission spectra.38 In
NbN film is 14.6 K. In the following, photolithography and reactive this model, the dynamic equations for two individual resonance modes
ion etching (with a mixture of SF6 and CHF3) were used to form the (~a 1 ¼ a1 eixt and ~a 2 ¼ a2 eixt ) are written as follows:

FIG. 1. (a) Geometry of a unit cell of the THz metamaterial. r1 ¼ 46 lm,

r2 ¼ 59 lm, w ¼ 5 lm, and with a lattice periodicity of P ¼ 128 lm. (b) Schematic
of the SC THz device. The gold electrodes are located at the opposite ends of the
device. An electric bias is applied to control the conductivity of the SC NbN film. FIG. 2. Simulated THz transmission spectra of ORR, DRR, and IRR metamaterials.

Appl. Phys. Lett. 119, 052602 (2021); doi: 10.1063/5.0056489 119, 052602-2
Published under an exclusive license by AIP Publishing
 Applied Physics Letters ARTICLE scitation.org/journal/apl

FIG. 4. Extracted fitting parameters of !1 , !2 , C1 , C2 , j from the measured trans-

FIG. 3. Transmission spectra of the SC device with different applied bias voltages mission spectra as a function of bias voltages at 4.5 K.
at 4.5 K. The solid line curves are experimental data, and the symbol curves are
the fitted curves. Inset: the transmitted temporal pulses of the SC switch with differ-
ent bias voltages. Due to the relatively larger geometric size, the radiative loss of ORR is
higher compared with the IRR.41,42 With the increase in Ohmic loss,
d~a 1 pffiffiffiffiffiffi pffiffiffiffiffiffi  more and more energy is dissipated in Ohmic loss rather than radia-
¼ ðix1  !1  C1 Þ~a 1 þ ij~a 2 þ i !1 ~s þ þ i !2 ~a 2 ; (1) tive loss. Therefore, !1 keeps constant at first and dramatically
dt
d~a 2 pffiffiffiffiffiffi pffiffiffiffiffiffi  decreases, when the bias voltage is above 1.5 V. !2 has a similar trend
¼ ðix2  !2  C2 Þ~a 2 þ ij~a 1 þ i !2 ~s þ þ i !1 ~a 1 ; (2) as !1 . The relatively strong jjj between the ORR and IRR leads to a
dt significant energy level splitting.37,43 The value of j mainly depends
where ~a 1 and a~ 2 correspond to the resonance amplitudes of the ORR on the structure. Since the structure is not altered with the variation of
and IRR, respectively. The xj , !j , and Cj are the resonance frequency, the bias voltage, j remains almost the same.
radiative loss, and dissipative loss (j ¼ 1, 2) of each resonator, respec- To further verify the above discussion, we measured the I–V
tively, and j is the near-field coupling coefficient between them. A curve, as shown in Fig. 5(a). The I–V curve of the device was measured
light wave (~s þ ¼ sþ ejxt ) is normally incident to the plane of DRR using a source measure unit (Keithley 2400) with the two-terminal
structures. Though the coupling between neighboring unit cells does method. By changing the voltage bias across the device, we recorded
exist and affect the resonance locations and linewidths,39,40 the cou- the current flowing through it at the same time. At 1.5 V, the current
pling across the two-unit cells is much weaker than the near field inter- goes up to the maximum (160 mA). Correspondingly, the calculated
action. Therefore, the interaction between the neighboring unit cells critical current density is 4:1  105 A=cm2 , which is close to the
was ignored in this model. In the calculation, as two sub-resonators reported values.44 When the applied current exceeds the critical value,
are on the same plane, the phase difference produced by the far-field the current no longer increases linearly with voltage and drops down.
coupling could be ignored as well. The transmission coefficient of the With the increase in Ohmic loss, the resonance dips become less
metamaterials is
pffiffiffiffiffiffi pffiffiffiffiffiffi  TABLE I. Summary of the extracted parameters (in units of THz) obtained by fitting
t ¼1þi !1 a1 þ !2 a2 =Sþ : (3) experimental data of Fig. 3 in the hybrid coupling model.
The experimental transmission spectra under various bias voltages
were fitted using the above model. As shown in Fig. 3, the fitted curves Bias voltage
agree well with the experimental results. We plotted the obtained (V) x1 c1 C1 j x2 c2 C2
parameters as a function of voltage in Fig. 4. Meanwhile, the obtained 0 0.32 0.14 0.0003 0.064 0.41 0.03 0.0002
parameters are listed in Table I. The Ohmic loss in the device is 1.0 0.32 0.14 0.002 0.064 0.4 0.03 0.0018
remarkably low due to the adoption of the SC film. When the bias
1.2 0.313 0.14 0.0045 0.064 0.39 0.03 0.0035
voltage is low, C1 and C2 change slightly with an increase in the bias
voltage. The NbN film remains at the SC state, so the dissipative loss 1.4 0.307 0.14 0.0075 0.064 0.38 0.03 0.0055
of two resonators almost does not change. As the voltage increases fur- 1.8 0.305 0.115 0.0125 0.064 0.36 0.025 0.011
ther, the current flowing through the device increases. When the cur- 2.0 0.284 0.11 0.022 0.064 0.349 0.025 0.0188
rent exceeds the critical value, C1 experiences a significant increase. 2.2 0.276 0.105 0.026 0.061 0.346 0.025 0.022
More and more portions of the NbN film in the ORR structure go into 2.4 0.27 0.102 0.035 0.063 0.338 0.02 0.03
the normal state. Correspondingly, there is a considerable increase in 2.8 0.27 0.095 0.043 0.064 0.305 0.017 0.036
the Ohmic loss. Meanwhile, the heat generated from the ORR could 3.6 0.27 0.09 0.058 0.064 0.29 0.011 0.05
diffuse into the IRR through the substrate, leading to the rise in C2 .

Appl. Phys. Lett. 119, 052602 (2021); doi: 10.1063/5.0056489 119, 052602-3
Published under an exclusive license by AIP Publishing
 Applied Physics Letters ARTICLE scitation.org/journal/apl

FIG. 5. Switching performance of the active SC metamaterial device at 4.5 K. (a) Current–voltage curve and the modulation depth at 0.34 THz as a function of voltage.
(b)Amplitudes and frequencies of the transmission peak as a function of bias voltages.

pronounced, and the transmission window finally disappears in the coefficient at 0.34 THz decreases to 0.13. Thus, the maximum modula-
transmission spectra. tion depth is 86.8% at 0.34 THz. As shown in Fig. 5(b), both the trans-
When the NbN transits from SC to the normal state, the reso- mission peak and window frequency at 4.5 K showed dependence with
nance frequency decreases significantly due to the surge in kinetic bias voltages. The peak frequency experiences a nearly 110 GHz red-
inductance (Lk ) with the reduction of SC carriers. The Lk of SC films shift from 0.34 to 0.23 THz, and the peak value varies from 0.98 to
can be calculated as Lk  l0 kðTÞcothðkðTÞd
Þ, where l0 is the vacuum 0.35. Thus, the SC device can function as a frequency selective device.
permeability, d is the thickness of the film, and kðTÞ is the London This SC switch has the ability to control “slow light” effects
penetration depth at different temperatures.45,46 Based on the super- dynamically. As shown in the measured phase (u) spectra at 4.5 K
conductivity theory, kðTÞ increases due to the reduction in the SC car- [Fig. 6(a)], a steep dispersion appears around the transparency win-
dow, meaning there exists a significant group delay. The dispersion
rier concentration. Correspondingly, the kinetic inductance increases,
experienced substantial changes with the increase in the applied volt-
resulting in the redshift of two resonance dips as shown in Fig. 5. As a
age and disappeared at 3.4 V. Using the measured phase spectra, we
result, a relatively high modulation depth can be obtained. The modu-
calculated the group delay (tg ), which is defined as tg ¼ duðxÞ=dx.
lation depth is defined as
As shown in Fig. 6(b), the maximum group delay obtained at the
TðV¼0Þ  TðV¼2:4Þ transparency frequencies is 25.4 ps. When the bias voltage is applied,
g¼ ; (4) the group delays and bandwidth of the transparency window decrease
TðV¼0Þ
monotonously. Due to the increase in Ohmic loss and the decrease in
where TðV¼0Þ ¼ 0:98 and TðV¼2:4Þ ¼ 0:13 are the transmission coeffi- coupling, the slow light effect finally disappears in the normal state.
cients at 0.34 THz for the bias voltages of 0 and 2.4 V, respectively. At In conclusion, we have demonstrated electrical tunable EIT-like
4.5 K, we plotted g as a function of the applied voltage in Fig. 5(a). At metamaterials made from the SC film. This SC device exhibits good
zero bias, the transmission peak appears at 0.34 THz, and the peak tuning of spectral response and the slow light effect. The coupled-
value is 0.98. When the bias voltage reaches 2.4 V, the transmission mode theory well explained the experimental results. At 4.5 K, the

FIG. 6. Slow light effect of the active SC metamaterial device. The phase shift spectra (a) and the group delay spectra (b) with different applied voltages at fixed temperature
4.5 K.

Appl. Phys. Lett. 119, 052602 (2021); doi: 10.1063/5.0056489 119, 052602-4
Published under an exclusive license by AIP Publishing
 Applied Physics Letters ARTICLE scitation.org/journal/apl

17
maximum modulation depth is 86.8%, and a group delay of 25.4 ps is X. Yan, M. Yang, Z. Zhang, L. Liang, D. Wei, M. Wang, M. Zhang, T. Wang, L.
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21
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Appl. Phys. Lett. 119, 052602 (2021); doi: 10.1063/5.0056489 119, 052602-5
Published under an exclusive license by AIP Publishing