Table Of ContentBroadly Tunable Sub-terahertz Emission from Internal Branches of the
Current-voltage Characteristics of Superconducting Bi Sr CaCu O Single Crystals
2 2 2 8+δ
Manabu Tsujimoto,1,∗ Takashi Yamamoto,1,† Kaveh Delfanazari,1 Ryo
Nakayama,1 Takeo Kitamura,1 Masashi Sawamura,1 Takanari Kashiwagi,1 Hidetoshi
Minami,1 Masashi Tachiki,1 Kazuo Kadowaki,1,‡ and Richard A. Klemm2
1Graduate School of Pure & Applied Sciences, University of Tsukuba,
1-1-1, Tennodai, Tsukuba, Ibaraki 305-8573, Japan
2Department of Physics, University of Central Florida, Orlando, Florida 32816, USA
2
(Dated: January 10, 2012)
1
0
Continuous,coherentsub-terahertzradiation ariseswhenadcvoltageisappliedacrossastackof
2
the many intrinsic Josephson junctions in a Bi2Sr2CaCu2O8+δ single crystal. The active junctions
n produceanequalnumberofI-V characteristicbranches. Eachbranchradiatesataslightlytunable
a frequency obeying the ac Josephson relation. The overall output is broadly tunable and nearly
J independent of heating effects and internal cavity frequencies. Amplification by a surrounding
7 externalcavity to allow for the developmentof a useful high-power source is proposed.
] PACSnumbers: 07.57.Hm,74.50.+r,85.25.Cp
n
o
c
Continuous, broadly tunable, and coherent sources of
-
r electromagnetic (EM) radiation are presently unavail-
p
able for frequencies within the “terahertz gap”, the 0.3–
u
s 10 THz range of crucial importance for many applica-
. tions [1, 2]. This gap can be filled by the ac Josephson
t
a effect intrinsic to a atomic-scale layered superconductor.
m
Application of a dc voltage V across a single Joseph-
- son junction between identical superconductors leads to
d
n an ac Josephson current and EM radiation with the
o same frequency f satisfying the ac Josephson relation,
c f = f = (2e/h)V, where e is the electric charge and h
J
[
is Planck’s constant[3–5]. Using two-dimensionalarrays
1 of Josephson junctions between wires of superconduct-
v ing Nb, coherent radiation was observed when the array
8
wasplacedparallelto aNbgroundplane[6], thatampli-
5
fiedthe radiation,butdid notaffect its frequency,which
5
1 obeyed the Josephson relation. However, the technical
. problems involved in mass production were formidable.
1 FIG. 1: (color online) R1 structure, c-axis resistivity,
The layered,hightransitiontemperature T supercon-
0 c outermost-branchIVC,emission output,andfrequencyspec-
2 ductor, Bi2Sr2CaCu2O8+δ (Bi-2212), behaves as a stack tra. (a) SIM image. (b) AFM image along A–B in Fig. 1(a).
1 of intrinsic Josephson junctions (IJJs) [7]. In Bi-2212, (c)Outer-branchIVC.Inset: Rc(T). (d)Plot ofI(Vout)cor-
v: each of the junctions is naturally identical, as they are respondingtoFig.1(c). Opencircles: Ttop =Tonset =84.4K.
i evenly spaced with two junctions per unit cell c-axis (e) Spectral intensities from points A–E in Fig. 1(d).
X
edge length of 1.533 nm. Recently, continuous, coher-
r
ent EM radiation was induced by applying a V across
a
the stack of N IJJs present in small mesas milled out internal cavity mode frequency fc , where m and p
m,p
of single crystalline Bi-2212 [8–18]. The mesas typically are integers appropriate for the geometry. Neglecting
have thicknesses d 1–2 µm and areas that vary from heating effects, for a very thin (d w ℓ) rect-
4 10−9 m2 to ∼4 10−8 m2. The thin mesa shapes angular cavity of length ℓ and width≪w, th≤e relevant
∼ × ∼ ×
were mostly rectangular, but some were square or circu- transverse magnetic TMz(m,p) modes have frequencies
lar[16]. SinceBi-2212isextremelyanisotropic,behaving
for E cˆas an insulator [7], the three-dimensionalmesa fmc,p =(c0/2n)q(m/w)2+(p/ℓ)2,where c0 is the speed
structukre also behaves as an internal EM cavity, which of light in vacuum and n = √ǫ 4.2 is the index of
couplestothenon-linearacJosephsoncurrentsgenerated refraction for E cˆin Bi-2212 [8–2≈4].
k
ineachjunction[8–18]. BesidessatisfyingtheacJoseph- Most workers have thought the enhancement of the
sonrelationfor a stack ofN IJJs, f =f =(2e/h)V/N, output radiation by the excitation of an internal cav-
J
it was also consistently reported that f locked onto an ity mode was so strong that the radiation from the ac
2
FIG. 3: (color online) Emission frequencies f and intensities
from R1, and f versusresistive junction numbersNfit for R1
FIG.2: (coloronline)EmissionfromIVCpointsatthecolor- and R2. (a) f(V) plots for 11 R1 IVC branches. Dashed
coded frequencies was observed at the filled diamonds. No lines: Fits to f = fJ = (2e/h)V/Nfit. Inset: f(V/Nfit) plot
radiationwasdetectedattheopendiamonds. Arrowsindicate for all R1 data. Dotted line: f =fJ. (b), (c) f(Nfit) ranges
the numbers Nfit of resistive junctions from fits to the ac forR1andR2,withdottedeyeguides. (d)Peakintensityon
Josephson relation. (a) R1. (b) R2. Insets: Full IVCs. a logarithmic scale versus f for R1. Calculated fc ranges
m,p
are given at the top. Nfit values are color coded.
Josephson current source alone was too weak to ob-
serve [8–14, 20–22]. However, recently the contributions shown in the inset of Fig. 1(c). On the return region of
totheoutputpowerfromtheacJosephsoncurrentsource the I-V loopwhereI 5 mA, we observedseveralsmall
∼
alone and that enhanced by resonance with an internal steps, indicating that some of the IJJs make the transi-
EM cavity source were found to be comparable in mag- tion from the resistive to the superconducting state.
nitude [15, 16, 23, 24]. This created a great deal of con- Figure 1(d) shows the R1 radiation output intensity
troversy. Here we show clear evidence that the mesas Vout generated from I on the same scale as in Fig. 1(c).
can emit radiation at many frequencies, without strong The dashed curve indicates the expected drift due to
interaction with an internal EM cavity mode. More im- thermal radiation from the sample and its holder. Soon
portant, the resulting radiation is tunable over a broad after the largest jump in the I-V loop, intense emission
range of frequencies, allowing for the construction of a of EM waves was clearly observed. Strong spatial vari-
powerful device that could fill the terahertz gap. ation of the temperature Ttop over the top mesa surface
Westudiedtworectangularmesas,R1andR2. R1was was previously observed [11, 13, 14], and was thought
prepared by milling a groove into the Bi-2212 substrate, to stronglyaffect the cavity mode-locking condition. We
but R2 was sandwiched between two Au layers. Further take Ttop to be the spatial average of the temperature
informationon R1, R2, and three other mesas of various on the mesa top. For R1, Tc = 81.1 K with a width
shapes are presented in the Supplemental Material [25]. ∆Tc =6.6K.BelowTtop =Tonset =84.4K,indicatedby
Figure1(a)isascanningionmicroscope(SIM)pictureof theopencirclesinFigs.1(c)and1(d),R1makesthetran-
the top of R1, with w = 99.2–102 µm, ℓ = 137–140 µm, sitiontothesuperconductingstate,asshowninFig.1(d).
and groove depth d 1.3 µm, before the electrode at- Figure 1(e) shows the radiation spectra, offset by 150
∼
tachments. R1is 3%longerandwideratthebottomof countsforclarity,measuredatpointsA–EinFig.1(d),at
∼
thegroovethanatthetop. Figure1(b)isanatomicforce whichallof the Nmax IJJs arein the resistivestate. The
microscope (AFM) scan of the groove profile along the narrowandintense peaksin the emissionspectraofB–E
A–BlineinFig.1(a). Fromthisdvalue,weestimatethe have maxima varying from 0.47 THz to 0.53 THz. The
number of IJJs in the stack to be N 850. The hys- detector resolution-limited widths of the B, C peaks are
max
∼
teresisloopindicatedbythearrowsinFig.1(c)istypical too narrow to arise from synchronization by an internal
oftheoutermostbranchoftheI-V characteristics(IVCs) cavitymodealone,andmightinvolveheatingeffects[13].
of an IJJ system. At the largest jump from V =0.25 to Such outermost branch f tunability of up to 40% was
0.85 V, all of the N junctions switch into the resis- found previously by varying both V and the bath T [13,
max
tive state simultaneously. In the high-V bias region, R1 18, 19]. Although the wide f range strongly violates the
is inevitably Joule heated at a rate of 16 mW. This internal cavity resonance condition, f = fc , the ac
m,p
∼
huge power dissipation may cause the negative differen- JosephsonrelationforastackofNmax resistiveIJJs[13],
tialresistancebetweenI =7and25mA,sincethe c-axis f =fJ =(2e/h)V/Nmax, is excellently obeyed.
quasiparticleresistanceR hasastrongT-dependenceas WefoundthatEMemissionalsooccursatmanypoints
c
3
intheinnerregionofthemultiply-branchedIVCs,where 0.255and0.357THz correspondingto the TMz(1,0)and
N =1,2,...,N is fixed butdifferentfor eachbranch. TMz(0,1) modes. Moreover, the spectrum observed in
max
ThesynchronizationoftheN IJJsonasingleI-V branch Fig. 3(d) is almost completely unrelated to any of the
isalsonotcontrolledbyaninternalcavityresonance[26], internal cavity modes. For example, the strongest in-
unlike some predictions [27]. In Figs. 2(a) and 2(b), the tensity observed for f 0.575 THz, corresponding to
≈
radiationfrequencies, f, are plotted as color-scaledsym- V = 0.894 V, I = 9.56 mA, and N = 753, is far
fit
bols on the high-bias regions of the multiply-branched from the two nearest cavity resonance frequencies. Al-
I-V structures for R1 at 35.0 K and R2 at 52.5 K, re- though the indicated cavity frequency ranges could be
spectively. The insets show the full IVCs. All of the R1 shifted to higher frequencies by shorter effective ℓ or d
curves in Fig. 2(a) bend backwards with increasing cur- valuesduetohotspots[13],sinceT =35Kineachmea-
rent,indicativeofJouleheating[11,13,14,28]. However, surement, such shifts could still not explain the broad
R2 is less susceptible to heating effects, and its IVCs in range of observed frequencies. For N = 851, there
max
Fig.2(b)aremonotonic. The f spectrawereobtainedat are 4.3 10130waystohaveN oftheN junctions
fit max
∼ ×
asmany(I,V)biaspointsaspossible. Atthebiaspoints in the resistive state, each of which could in principle
denoted by open diamonds, no emission was detected. lead to a different emission intensity. Hence, multiply
Byrepeatedmeasurementsoftheemissionfromapar- cyclingthroughthe IVCs ledto alargevariationinpeak
ticularI-V branchwithconstantN,weconfirmedthatf intensity at that (I,V) point. The synchronization of
satisfies the ac Josephsonrelationf =fJ =(2e/h)V/N. the Nfit <Nmax resistive junctions thus occurs indepen-
In Figs. 3(a) and 4(a), we replotted the emission data dently ofthe internalcavitymode excitations [26]. More
fromtheIVCsofR1andR2showninFigs.2(a)and2(b) important, the emission spectrum in Fig. 3(d) is contin-
intermsoff(V),representingthedatafromeachbranch uous from 0.44 THz f 0.78 THz, except for a gap
≤ ≤
intermsofuniquesymbolsandcolors. Byfitsofthedata between0.66THzand0.73THz. Thegapmaybedueto
for aparticularbranchto the acJosephsonrelationwith someexperimentaldifficultyinaccessingtheappropriate
N = N , the experimental best-fit value N for each branches. This widely continuous spectrum independent
fit fit
emitting branch was determined. Three examples each of internal cavity resonances implies that f is broadly
for R1 and R2 are respectively indicated by the dashed tunable. Figure 3(b) suggests that the f values from
lines in Figs. 3(a) and 4(a) and the arrows in Figs. 2(a) lowerbranch-numberemissionscouldexceed1THz. Fur-
and 2(b). In the insets to Figs. 3(a) and 4(a), the entire ther tunability might arise from base T variations [13],
emissiondatafromtheinnerIVCbranchesofR1andR2 as discussed in the Supplemental Material [25].
are respectively plotted as f(V/N ). For both R1 and ThepeakintensityspectrumofR2measuredat52.5K
fit
R2, the ac Josephson relation f = fJ = (2e/h)V/Nfit, showninFig.4(b)is alsobroadlytunable, withemission
represented by each dotted line, is well obeyed. for 0.43 THz f 0.76 THz, and a small gap between
≤ ≤
Since Figs. 3(a) and 4(a) clearly demonstrate that f 0.67 and 0.75 THz. For R2, the f range from 0.43 THz
is slightly tunable on each branch (indicated by a fixed to 0.55 THz is below the range of the lowest cavity
∼
symbol and color), in Figs. 3(b) and 3(c), we respec- resonance frequency fc values. Unlike the peak inten-
1,0
tively replotted the data from each R1 and R2 branch sity spectrum of R1, the largest intensity at 0.565 THz
as f(N ). Although for both samples f is tunable as is close to this fc range. In this case, the synchroniza-
fit 1,0
indicatedbythe verticalbarsforeachfixedbranchnum- tion of the N resistive junctions could be aided by the
ber N , R1 and R2 display rather different aspects of excitation of this internal cavity mode [26, 27].
fit
tunability. The overall tunability of R1 and R2, which Wemeasuredthefullangulardependenceoftheradia-
are respectively tunable from 0.44 THz f 0.78 THz tionfromR2ontheoutermostbranchatf =0.639THz,
≤ ≤
and from 0.43 THz f 0.76 THz, is nearly the same. and the results are shown and discussed in the Supple-
≤ ≤
However, for R1, this range is primarily due to the f- mental Material [25]. Although the observed angular
dependence on I-V branch number, whereas for R2, the dependence is similar to that expected from the low-Q
tunability is greatest on a single branch. tail of the TMz(1,0) cavity mode excitation, the fre-
We measured the spectrum for each emitting point in quency is far from fc , but could be amplified by ex-
1,0
the inner IVC branches of R1 and R2, and determined citation of a higher frequency mode, as indicated. We
its peak intensity as for points B–E on the outer branch thus determined [15, 16, 23, 24] that the angularly in-
of R1 shown in Fig. 1(e). In Figs. 3(d) and 4(b), we tegrated output power at this frequency is 0.2 µW,
∼
plotted the peak intensity of the emissions on a loga- somewhat smaller than previously reported [8–19]. In
rithmic scale versus f for R1 and R2, respectively, and addition, a much larger emission peak intensity, with an
N is approximately coded with color. The ranges due estimatedoverallemissionpowerof4.8µW,wasfoundat
fit
to mesa profile variations of the respective internal cav- 0.557 THz, which is much closer to fc . Besides the ex-
1,0
ity mode frequencies fc are indicated at the figure citation of the TMz(1,0) mode, this strong inner branch
m,p
tops. For R1, no emission was found for f < 0.40 THz, emission could have been enhanced by R2 being sand-
excluding the expected cavity resonance frequencies of wichedbetween two Au layers[23]. More important, the
4
Hence, it is now relatively straightforward to produce
broadly tunable, continuous,coherent radiation over the
range of the terahertz gap.
TheauthorsthankX.Hu,S.Lin,A.Koshelev,M.Mat-
sumoto, T. Koyama, M. Machida, H. Asai, S. Fukuya,
and K. Ivanovic for valuable discussions and Y. Ootuka,
T. Hattori, A. Kanda, I. Kakeya, B. Markovic, K. Ya-
maki, and H. Yamaguchi for technical assistance. This
work was supported in part by CREST-JST (Japan Sci-
ence and Technology Agency), WPI (World Premier In-
ternational Research Center Initiative)-MANA (Mate-
rials Nanoarchitectonics) project (NIMS) and Strategic
Initiative category (A) at the University of Tsukuba.
FIG. 4: (color online) Emission frequencies and intensities
from R2. (a) Plots of f(V) for 8 branches in the R2 IVCs. ∗ Research Fellow of the Japan Society for the Promotion
Dashed lines: Fits to f = fJ = (2e/h)V/Nfit. Inset: Plot of of Science, 8 Ichiban-cho, Chiyoda-ku, Tokyo 102-8472,
f(V/Nfit) for all R2 data. Dotted line: f = fJ. (b) Peak Japan
intensity on a logarithmic scale versus f for R2. Calculated † Present address: Quantum Beam Science Directorate,
fmc,p ranges are given at thetop. Nfit values are color coded. Japan AtomicEnergy Agency
‡ Electronic address: [email protected]
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