Flux-flow cavity resonances in intrinsic Josephson junctions (IJJs) with long c-axis periodicity by artificial critical-current (Jc) modulation are studied numerically and theoretically. For an n-1–n-1–n-1–n IJJ system with n-layer high-Jc and one-layer low-Jc alternately stacked, numerical simulation confirms fluxon penetration only in the low-Jc junctions under proper low magnetic fields. The simulation also shows pronounced cavity-resonance steps in the I–V curves of the low-Jc junctions, meaning that fluxon dynamics can be generated under much lower magnetic fields, compared to the fields for usual IJJs with homogeneous Jc. A theoretical method for describing the flux-flow cavity-resonance properties is presented. The general disperse k–ω relationship shows that, at low-k regions, the critical-current-modulated junction system can be regarded as simple homogeneous stacked junctions with a new effective thickness and a new inductive coupling strength. For general-k cases, the cavity-resonant voltage steps on the I–V curves at various magnetic fields can be well indexed by integers, which means excellent agreement between the theoretical analysis and the numerical simulations.
Flux-flow cavity-resonance properties in twofold Josephson junctions with different critical currents are investigated. While the critical current
J21 of one of junctions is fixed, the critical current
J10 of the other junction is parametrically increased up to extremely large values. Numerical simulations for inductively coupled twofold Josephson junctions are performed under several magnetic fields, and we observe resonance voltage steps at various ratios $M\ensuremath{\equiv}{J}_{10}∕{J}_{21}$. Obtained theoretical eigenequations include the parameter
J10 that is different from the equations by the existent conventional theory for the homogeneous system. Almost all data points on a resonance voltage vs
M domain obtained by the numerical simulations exist on the theoretical curves of eigenfrequency in voltage unit vs
M. At $M\ensuremath{\rightarrow}\ensuremath{\infty}$ the twofold Josephson junctions can be regarded as a single junction. The lower critical-current
(J21) junction works as a single junction with a new effective barrier thickness, and cavity resonance occurs in this single junction. At $M\ensuremath{\rightarrow}1$ the theoretical eigenfrequencies in the voltage unit asymptotically approach the resonance voltages of the antiphase and in-phase modes of the conventional system. For the range with intermediate
M values, there are no asymptotic approximate solutions, but the agreement of the results of the present theory with the numerical simulation results is excellent. The theory of the twofold Josephson junctions is able to extend to that of multifold junction with general index number
N. At
N=9, numerical simulations are performed and the agreement of its results with the theoretical results is good. At $M\ensuremath{\rightarrow}\ensuremath{\infty}$, the
N-fold Josephson junction can also be regarded as a single junction with a new effective barrier thickness, ${d}_{N}^{\ensuremath{''}}$.
During last decade, considerable efforts were made to achieve coherent emission from stacks of many Josephson junctions. It is known that strong emission from a junction in the presence of external magnetic field appears at the so-called Fiske steps in the IV-characteristic at voltages which correspond to frequencies of geometrical resonances. However, it is possible to obtain resonant steps in long junctions without external magnetic field. The periodical movement of fluxons is excited due to some disorder in the distribution of critical currents along junctions. The so-called zero-field steps are formed in the IV-curve due to the interaction of fluxons with oscillations of voltage at Josephson frequencies. We investigated numerically IV-characteristics and the dependence of the average square of ac voltage at the end of the stack of two long Josephson junctions on the average voltage. Junctions interacted inductively with each other. We introduced not only the Gaussian distribution of critical currents along junctions but also the Gaussian distribution of coefficients of the interaction between junctions (mutual inductances). Zero-field steps in the IV-characteristic were found at voltages which corresponded to frequencies of in-phase collective modes in the stack as well as to frequencies of uncoupled junctions. Zero-field steps appeared in the hysteretic region of the IV-curve. There appeared also jumps of voltage from the resistive branch to the zero-field step. We showed that there existed distributions of mutual inductances along junctions which provided jumps to voltages at which the average square of ac voltage at the end of the stack (which is proportional to power of emission) was larger than that for the stack with the uniform distribution of mutual inductances.
The first object of this work is to theoretically study the effects of tunnel junction parameters on flux-flow Josephson oscillators (FFOs) by numerical simulation and to experimentally study the rf properties of FFOs by integrating them together with an SIS (superconductor-insulator-superconductor) mixer/detector on a chip. By using a CAD modeled integrated sub-mm wave receiver, the composite linewidth of two FFOs was measured to be less than 2.1 MHz in the band 280-330 GHz. The receiver consists of two identical FFOs and an SIS mixer. The linewidth was determined by mixing the two signals in the SIS mixer and analyzing the intermediate frequency. The output power coupled to a 10 .OMEGA. microstripline was about 0.5 µW, and could be adjusted by changing the current bias of the oscillator. The FFOs are connected to the SIS mixer via interdigital capacitors. The FFOs and the SIS element are made of Nb/NbOx/PbBi junctions by the "reactive ion beam oxidation" technique with the critical current density jc controlled by the oxidation time. Lift-off stencils for defining the junction sizes and the top-electrodes were made by using electron-beam writing on PMMA/Copolymer double layer resist. The jc of a long Josephson junction (LJJ) determines the fluxon motion. For LJJs which had jc > 1 kA/cm2, velocity-matching (VM, where the phase velocity of propagating fluxons equals that of the electromagnetic wave in the LJJ) steps could be tuned linearly from about 0.2 to 1.4 mV by an applied magnetic field. Coupled radiation at around 100 GHz (about 3 nW), 261 GHz (4.6 nW), and 330 GHz (0.43 µW), from flux-flow oscillations, was observed. From the step's steepness, the junction quality factor QJ is determined. QJ is between 4 to 7 in the voltage range of 0.4 to 1 mV. Coupled radiation (> 3 nW) at around 100 GHz corresponding to resonant soliton oscillation in low jc samples (250 to 1000 A/cm2) was detected. Simulations show that, for a uniform bias feed, the height of the VM step .gammam increases almost linearly with the external magnetic field .beta.e and the quasiparticle loss .alpha., but is less dependent on the surface loss .beta.. An approximate expression .gammam = a + .alpha(1+b).beta.e agrees with simulations. The maximum ac output voltage decreases with increasing dampings .alpha. and .beta.. It is important to include the .beta.-term in the mathematical model. The second part of this work is devoted to rf properties of long YBa2Cu3O7-.delta. (YBCO) grain boundary junctions made on 0- 32 °. [001]-tilt YSZ bicrystals. Josephson flux-flow resonances and Fiske resonances were observed. The first resonances could be tuned from about 0.5 to 2.0 mV in a 30 µm long junction at 16 K, and we determined the ratio between barrier thickness and relative dielectric constant td/.epsilon.r=2.9 Å and the loss .alpha.= 1.3 at 16 K. Simulations support the experimental observation that Josephson vortices can propagate unidirectionally in an overdamped, homogeneous junction up to .alpha.Ã? 2. From the Fiske resonances at 256-638 GHz, their Q-values, and the Steward-McCumber parameter, we find td/.epsilon.r=4 Å, the London penetration depth .gamma.L=145±5 nm and the surface resistance RS ~20 m.OMEGA. at 280 GHz. We conclude that the boundary is dielectric and the YBCO grains are well superconducting within 5-20 nm from the boundary. The dielectric between the grains could be part of a tunnel barrier and/or a matrix for filamentary conduction. Josephson flux-flow transitors based on long bicrystal junctions were made with an Au loop used as the control line. The line modulated the critical current Ic. Current gain larger than unity was obtained below 70 K. The gain increased with the junction length and varied roughly like the square root Ic when adjusting the temperature. A transresistance larger than 5 .OMEGA. was obtained at 15 K. Better performance is expected from junctions with high current densities.
A system of two vertically stacked Nb/Al-AlOx/Nb long Josephson junctions is studied experimentally. The magnetic coupling between the junctions is provided by their common electrode of the thickness d∼λL. The current-voltage characteristics of the stack displays resonant steps which are understood to be the phase-locked flux-flow resonances of the two junctions. These modes can be tuned by the magnetic field in a broad voltage range which corresponds to the Josephson frequencies between 150 and 600 GHz. Our observations suggest a possibility of application of the stacked long Josephson junctions as local oscillators for millimeter and submillimeter wave circuits.
Two-stacked intrinsic Josephson junctions (IJJs) on a Bi2Sr2CaCu2O8+δ(Bi-2212) whisker with a submicron hole are micromachined by a 3D focused ion beam (FIB) etching method. The junction area, the number of elementary junctions, and the loop area of the SQUIDs are 3, 20, and 0.42 μm2, respectively. The SQUIDs show typical I–V characteristics of IJJs with a critical current IC of 12 μA at 4.2 K. The modulation parameter βL(=2ICL/Φ0) is 6.4, and the inductance L of the SQUID is 1120 pH. That includes the inductances of the elementary junction around a SQUID loop. In a strong magnetic field, the Fraunhofer pattern is obtained and well fitted to the calculated value from the junction size, ΔB=Φ0/tW; t is the interlayer distance, and W is the junction width. In a low magnetic field, approximately 10% of the IC modulation corresponding to the value of βL is observed. Eighty G of the modulation period approximately agrees with the value calculated from the SQUID.
Vertical stacks of two Nb/Al-AlO/sub x//Nb long Josephson junctions with nearly identical parameters have been studied experimentally. The magnetic coupling between the junctions was provided by their common electrode of thickness d/spl sime//spl lambda//sub L/. The I-V characteristics displayed flux-flow resonances of the two junctions. Two different mutually phase-locked regimes were found: the lower velocity anti-phase mode, and the high velocity in-phase mode. These modes, while staying locked, could be tuned by the magnetic field in a broad voltage range which corresponds to the Josephson frequencies of 150-600 GHz for the lower mode and 280-400 GHz for the upper mode. Our observations suggest applications of the stacked long Josephson junctions as local oscillators for millimeter and sub-millimeter wave circuits.>