Hot spots and waves in Bi2Sr2CaCu2O8 intrinsic Josephson junction stacks: a study by low temperature scanning laser microscopy

A distributed active patch antenna model of a Josephson oscillator

Optimization of Josephson oscillators requires a quantitative understanding of their microwave properties. A Josephson junction has a geometry similar to a microstrip patch antenna. However, it is biased by a dc current distributed over the whole area of the junction. The oscillating electric field is generated internally via the ac-Josephson effect. In this work, I present a distributed, active patch antenna model of a Josephson oscillator. It takes into account the internal Josephson electrodynamics and allows for the determination of the effective input resistance, which couples the Josephson current to cavity modes in the transmission line formed by the junction. The model provides full characterization of Josephson oscillators and explains the origin of the low radiative power efficiency. Finally, I discuss the design of an optimized Josephson patch oscillator capable of reaching high efficiency and radiation power for emission into free space.

Space-time crystalline order of a high-critical-temperature superconductor with intrinsic Josephson junctions

We theoretically demonstrate that the high-critical-temperature (high-T_c) superconductor Bi₂Sr₂CaCu₂O_8+x (BSCCO) is a natural candidate for the recently envisioned classical space-time crystal. BSCCO intrinsically forms a stack of Josephson junctions. Under a periodic parametric modulation of the Josephson critical current density, the Josephson currents develop coupled space-time crystalline order, breaking the continuous translational symmetry in both space and time. The modulation frequency and amplitude span a (nonequilibrium) phase diagram for a so-defined spatiotemporal order parameter, which displays rigid pattern formation within a particular region of the phase diagram. Based on our calculations using representative material properties, we propose a laser-modulation experiment to realize the predicted space-time crystalline behavior. Our findings bring new insight into the nature of space-time crystals and, more generally, into nonequilibrium driven condensed matter systems.

Design and characterization of microstrip patch antennas for high-Tc superconducting terahertz emitters

We designed and characterized a microstrip pattern of planar patch antennas compatible with a cuprate high-T_c superconducting terahertz emitter. Antenna parameters were optimized using an electromagnetic simulator. We observed repeatable sub-terahertz emissions from each mesa fabricated on identical Bi₂Sr₂CaCu₂O_8+δ base crystals in a continuous frequency range of 0.35-0.85 THz. Although there was no significant output power enhancement, a plateau behavior at a fixed frequency was observed below 40 K, indicating moderate impedance matching attributable to the ambient microstrip pattern. A remarkably anisotropic polarization at an axial ratio of up to 16.9 indicates a mode-locking effect. Our results enable constructing compactly assembled, monolithic, and broadly tunable superconducting terahertz sources.

Study of Radiation Characteristics of Intrinsic Josephson Junction Terahertz Emitters with Different Thickness of Bi2Sr2CaCu2O8+δ Crystals

The radiation intensity from the intrinsic Josephson junction high-Tc superconductor Bi2Sr2CaCu2O8+δ terahertz emitters (Bi2212-THz emitters) is one of the most important characteristics for application uses of the device. In principle, it would be expected to be improved with increasing the number of intrinsic Josephson junctions N in the emitters. In order to further improve the device characteristics, we have developed a stand alone type of mesa structures (SAMs) of Bi2212 crystals. Here, we understood the radiation characteristics of our SAMs more deeply, after we studied the radiation characteristics from three SAMs (S1, S2, and S3) with different thicknesses. Comparing radiation characteristics of the SAMs in which the number of intrinsic Josephson junctions are N∼ 1300 (S1), 2300 (S2), and 3100 (S3), respectively, the radiation intensity, frequency as well as the characteristics of the device working bath temperature are well understood. The strongest radiation of the order of few tens of microwatt was observed from the thickest SAM of S3. We discussed this feature through the N2-relationship and the radiation efficiency of a patch antenna. The thinner SAM of S1 can generate higher radiation frequencies than the thicker one of S3 due to the difference of the applied voltage per junctions limited by the heat-removal performance of the device structures. The observed features in this study are worthwhile designing Bi2212-THz emitters with better emission characteristics for many applications.

On-Chip Sensing of Hotspots in Superconducting Terahertz Emitters

Intrinsic Josephson junctions in high-temperature superconductor Bi₂Sr₂CaCu₂O_8+δ (BSCCO) are known for their capability to emit high-power terahertz photons with widely tunable frequencies. Hotspots, as inhomogeneous temperature distributions across the junctions, are believed to play a critical role in synchronizing the gauge-invariant phase difference among the junctions, so as to achieve coherent strong emission. In this paper, we demonstrate an on-chip in situ sensing technique that can characterize hotspot distributions on BSCCO. This is achieved by fabricating a series of micro-nanosized "sensor" junctions on top of an "emitter" junction and measuring the critical current on the sensors versus the bias current applied to the emitter. This fully electronic on-chip design can enable efficient close-loop control of hotspots in BSCCO junctions and significantly enhance the functionality of superconducting terahertz emitters.

A high-resolution combined scanning laser and widefield polarizing microscope for imaging at temperatures from 4 K to 300 K

Polarized light microscopy, as a contrast-enhancing technique for optically anisotropic materials, is a method well suited for the investigation of a wide variety of effects in solid-state physics, as, for example, birefringence in crystals or the magneto-optical Kerr effect (MOKE). We present a microscopy setup that combines a widefield microscope and a confocal scanning laser microscope with polarization-sensitive detectors. By using a high numerical aperture objective, a spatial resolution of about 240 nm at a wavelength of 405 nm is achieved. The sample is mounted on a ⁴He continuous flow cryostat providing a temperature range between 4 K and 300 K, and electromagnets are used to apply magnetic fields of up to 800 mT with variable in-plane orientation and 20 mT with out-of-plane orientation. Typical applications of the polarizing microscope are the imaging of the in-plane and out-of-plane magnetization via the longitudinal and polar MOKE, imaging of magnetic flux structures in superconductors covered with a magneto-optical indicator film via the Faraday effect, or imaging of structural features, such as twin-walls in tetragonal SrTiO₃. The scanning laser microscope furthermore offers the possibility to gain local information on electric transport properties of a sample by detecting the beam-induced voltage change across a current-biased sample. This combination of magnetic, structural, and electric imaging capabilities makes the microscope a viable tool for research in the fields of oxide electronics, spintronics, magnetism, and superconductivity.

Josephson emission with frequency span 1-11 THz from small Bi2Sr2CaCu2O8+δ mesa structures

Mesa structures made of Bi₂Sr₂CaCu₂O_8+δ high-temperature superconductor represent stacks of atomic scale intrinsic Josephson junctions. They can be used for generation of high-frequency electromagnetic waves. Here we analyze Josephson emission from small-but-high mesas (with a small area, but containing many stacked junctions). We have found strong evidence for tunable terahertz emission with a good efficacy in a record high-frequency span 1-11 THz, approaching the theoretical upper limit for this superconductor. Emission maxima correspond to in-phase cavity modes in the mesas, indicating coherent superradiant nature of the emission. We conclude that terahertz emission requires a threshold number of junctions N ~ 100. The threshold behavior is not present in the classical description of stacked Josephson junctions and suggests importance of laser-like cascade amplification of the photon number in the cavity.

High-resolution Thermal Micro-imaging Using Europium Chelate Luminescent Coatings

Micro-electronic devices often undergo significant self-heating when biased to their typical operating conditions. This paper describes a convenient optical micro-imaging technique which can be used to map and quantify such behavior. Europium thenoyltrifluoroacetonate (EuTFC) has a 612 nm luminescence line whose activation efficiency drops strongly with increasing temperature, due to T-dependent interactions between the Eu³⁺ ion and the organic chelating compound. This material may be readily coated on to a sample surface by thermal sublimation in vacuum. When the coating is excited with ultraviolet light (337 nm) an optical micro-image of the 612 nm luminescent response can be converted directly into a map of the sample surface temperature. This technique offers spatial resolution limited only by the microscope optics (about 1 micron) and time resolution limited by the speed of the camera employed. It offers the additional advantages of only requiring comparatively simple and non-specialized equipment, and giving a quantitative probe of sample temperature.

Cavity mode enhancement of terahertz emission from equilateral triangular microstrip antennas of the high-T c superconductor Bi2Sr2CaCu2O8 + δ

We study the transverse magnetic (TM) electromagnetic cavity mode wave functions for an ideal equilateral triangular microstrip antenna (MSA) exhibiting C _3v point group symmetry. When the C _3v operations are imposed upon the antenna, the TM(m,n) modes with wave vectors [Formula: see text] are much less dense than commonly thought. The R ₃ operations restrict the integral n and m to satisfy [Formula: see text], where [Formula: see text] and [Formula: see text] for the modes even and odd under reflections about the three mirror planes, respectively. We calculate the forms of representative wave functions and the angular dependence of the output power when these modes are excited by the uniform and non-uniform ac Josephson current sources in thin, ideally equilateral triangular MSAs employing the intrinsic Josephson junctions in the high transition temperature T _c superconductor Bi₂Sr₂CaCu₂ [Formula: see text], and fit the emissions data from an earlier sample for which the C _3v symmetry was apparently broken.

Applications using high-Tc superconducting terahertz emitters

Using recently-developed THz emitters constructed from single crystals of the high-T_c superconductor Bi₂Sr₂CaCu₂O_8+δ, we performed three prototype tests of the devices to demonstrate their unique characteristic properties for various practical applications. The first is a compact and simple transmission type of THz imaging system using a Stirling cryocooler. The second is a high-resolution Michelson interferometer used as a phase-sensitive reflection-type imaging system. The third is a system with precise temperature control to measure the liquid absorption coefficient. The detailed characteristics of these systems are discussed.

Sequence of Quantum Phase Transitions in Bi2Sr2CaCu2O(8+δ) Cuprates Revealed by In Situ Electrical Doping of One and the Same Sample

Our recently discovered electrical doping technique allows a broad-range variation of carrier concentration without changing the chemical composition. We show that it is possible to induce superconductivity in a nondoped insulating sample and to tune it reversibly all the way to an overdoped metallic state. This way, we can investigate the whole doping diagram of one and the same sample. Our study reveals two distinct critical points. The one at the overdoped side is associated with the onset of the pseudogap and with the metal-to-insulator transition in the c-axis transport. The other at optimal doping is associated with the appearance of a "dressed" electron energy. Our study confirms the existence of multiple phase transitions under the superconducting dome in cuprates.

0.43 THz emission from high-T(c) superconducting emitters optimized at 77 K

A liquid helium-free, compact and continuous sub-terahertz radiation system operating at 77 K has been developed using a rectangular mesa device made from a high T(c)-superconducting Bi2Sr2CaCu2O(8+δ) single crystal, based on a different design of a stand-alone mesa sandwich structure to reduce the dc-current Joule heating effects. The mesa was thermally connected to sapphire plates through thin thermal grease embedded with diamond nano-crystals. When immersed in liquid N 2, the device emits intense radiation at 0.437 THz, the highest frequency ever achieved at 77 K, due to excitation of the TM(1, 0) rectangular cavity mode. By varying the dc current-voltage bias and the bath temperature in a He-flow cryostat, the device's emission frequency is broadly tunable from 0.31 THz at 79 K to 1.31 THz at 30 K.

Spectral investigation of hot spot and cavity resonance effects on the terahertz radiation from high-T(c) superconducting Bi2Sr2CaCu2O(8+δ) mesas

Terahertz (THz) electromagnetic radiation emitted from single and series-connected rectangular mesa devices of high-Tc superconducting Bi2Sr2CaCu2O8+δ is investigated spectroscopically during simultaneous temperature distribution observations using a microcrystalline SiC photoluminescence technique. In single mesas, a hot-spot region with its temperature T locally exceeding Tc was observed to jump suddenly in position under small current I-bias changes. Although these hot-spot position jumps cause large changes in the output power with small changes in I, as long as the voltage V per junction number N is kept constant, they do not affect the output frequency f, which is given by the ac Josephson frequency fJ. f can lock onto that of a particular mesa cavity resonance frequency fc, which enhances the emission power and serves as the primary mechanism for the synchronization of the emissions from each of the intrinsic Josephson junctions in the mesa.

Tunable terahertz emission from the intrinsic Josephson junctions in acute isosceles triangular Bi₂Sr₂CaCu₂O₈+δ mesas

In order to determine if the mesa geometry might affect the properties of the coherent terahertz (THz) radiation emitted from the intrinsic Josephson junctions in mesas constructed from single crystals of the high-temperature superconductor, Bi₂Sr₂CaCu₂O₈+δ, we studied triangular mesas. For equilateral triangular mesas, the observed emission was found to be limited to the single mesa TM(1,0) mode. However, tunable radiation over the range from 0.495 to 0.934 THz was found to arise from an acute isosceles triangular mesa. This 47% tunability is the widest yet observed from the outer current-voltage characteristic branch of such mesas of any geometry. Although the radiation at a few of the frequencies in the tunable range appear to have been enhanced by cavity resonances, most frequencies are far from such resonance frequencies, and can only be attributed to the ac-Josephson effect.

Broadly tunable subterahertz emission from internal branches of the current-voltage characteristics of superconducting Bi2Sr2CaCu2O(8+δ) single crystals

Continuous, coherent subterahertz radiation arises when a dc voltage is applied across a stack of the many intrinsic Josephson junctions in a Bi2Sr2CaCu2O(8+δ) single crystal. The active junctions produce an equal number of I-V characteristic branches. Each branch radiates at a slightly tunable frequency obeying the Josephson relation. The overall output is broadly tunable and nearly independent of heating effects and internal cavity frequencies. Amplification by a surrounding external cavity to allow for the development of a useful high-power source is proposed.

High-power terahertz electromagnetic wave emission from high-T(c) superconducting Bi2Sr2CaCu2O(8+δ) mesa structures

In this paper, we report intense electromagnetic wave emissions generated by the rectangular mesa structure of intrinsic Josephson junctions with high-T(c) superconducting Bi2Sr2CaCu2O(8+δ). The radiated power is an order of magnitude stronger than that of the previously observed power of a few μW. Two emission regions, reversible (R-type) and irreversible (IR-type), with comparable intensities can be observed at different I-V curve locations in the same mesa. We find peculiar temperature dependences of the emission power in both the R- and IR-type radiations, suggesting that a non-equilibrium thermodynamic state may be realized through the dc input current. The R-type emission is quite stable, whereas the IR-type emission is rather unstable. Although the emitted frequency for both cases obey the cavity resonance conditions, this sharp contrast in emission stability is indicative of two different states in a multi-stacked intrinsic Josephson junction system.

Cavity mode waves during terahertz radiation from rectangular Bi(2)Sr(2)CaCu(2)O(8 + δ) mesas

We re-examined the angular dependence of the radiation from the intrinsic Josephson junctions in rectangular mesas of Bi(2)Sr(2)CaCu(2)O(8 + δ), in order to determine if the cavity mode part of the radiation arises from waves across the width w or along the length l of the mesas, associated with 'hot spots' (Wang et al 2010 Phys. Rev. Lett. 105 057002). We derived analytical forms for the angular dependence expected in both cases for a general cavity mode in which the width of the mesa corresponds to an integer multiple of one-half the wavelength of the radiation. Assuming the coherent radiation from the ac Josephson current source and the cavity magnetic surface current density source combine incoherently, fits to the data of Kadowaki et al (2010 J. Phys. Soc. Japan 79 023703) on a mesa with mean l/ω = 5.17 for both wave directions using two models for the incoherent combination were made, which correspond to standing and traveling waves, respectively. The results suggest that the combined output from the uniform ac Josephson current source plus a cavity wave forming along the rectangle length is equally probable as that of the combined output from the uniform ac Josephson current plus a cavity wave across the width. However, for mesas in which nl/2ω is integral, where n is the index of the rectangular TM(z)(n, 0) mode, it is shown that standing cavity mode waves along the length of the mesa do not radiate in the xz plane perpendicular to the length of the mesa, suggesting experiments on such mesas could help to resolve the question.

Output from a Josephson stimulated terahertz amplified radiation emitter

The angular dependence of the radiation-zone output power and electric polarization of stimulated terahertz amplified radiation (STAR) emitted from a dc voltage applied across cylindrical and rectangular stacks of intrinsic Josephson junctions is calculated. The boundary conditions are obtained from Love's equivalence principles. During coherent emission, a spatially uniform ac Josephson current density in the stack acts as a surface electric current density antenna source, leading to a harmonic radiation frequency spectrum, as in experiment, but absent in all cavity models of cylindrical mesas. Spatial fluctuations of the ac Josephson current allow its fundamental mode to lock onto the lowest finite energy cylindrical cavity mode, causing it to resonate, leading to a non-uniform magnetic surface current density radiation source, and a non-trivial combined fundamental frequency output power with linear polarization for general radiation directions, which may be fully or partially coherent. The higher ac Josephson harmonics do not excite other cylindrical cavity modes. For rectangular mesas, the lowest energy modes are empirically not excited, but the non-uniform ac Josephson current can excite the harmonic sequence of modes with spatial variation across the rectangular widths, leading to combined radiation outputs both for the fundamental and the higher harmonics, which combinations also may be either fully or partially coherent. The superconducting substrate is modeled as a perfect magnetic conductor, greatly reducing the STAR emitter power and modifying its angular dependence, especially parallel to the substrate. Based upon this substrate model, existing Bi(2)Sr(2)CaCu(2)O(8 + δ) crystals atop perfect electric conductors could have STAR emitter power in excess of 5 mW, acceptable for many device applications.

Coherent terahertz emission of intrinsic Josephson junction stacks in the hot spot regime [corrected]

We report on THz emission measurements and low temperature scanning laser imaging of Bi2Sr2CaCu2O8 intrinsic Josephson junction stacks. Coherent emission is observed at large dc input power, where a hot spot and a standing wave, formed in the "cold" part of the stack, coexist. By changing bias current and bath temperature, the emission frequency can be varied by more than 40%; the variation matches the Josephson-frequency variation with voltage. The linewidth of radiation is much smaller than expected from a purely cavity-induced synchronization. Thus, an additional mechanism seems to play a role. Some scenarios, related to the presence of the hot spot, are discussed.

Geometrical resonance conditions for THz radiation from the intrinsic Josephson junctions in Bi(2)Sr(2)CaCu(2)O(8+δ)

Subterahertz radiation emitted from a variety of short rectangular-, square-, and disk-shaped mesas of intrinsic Josephson junctions fabricated from a Bi(2)Sr(2)CaCu(2)O(8+δ) single crystal was studied from the observed I-V characteristics, far-infrared spectra, and spatial radiation patterns. In all cases, the radiation frequency satisfies the conditions both for the ac Josephson effect and for a mesa cavity resonance mode. The integer higher harmonics observed in all spectra imply that the ac Josephson effect plays the dominant role in the novel dual-source radiation mechanism.

Nonlinear nonequilibrium quasiparticle relaxation in Josephson junctions

I solve numerically a full set of nonlinear kinetic balance equations for stacked Josephson junctions, which allows analysis of strongly nonequilibrium phenomena. It is shown that nonlinearity becomes significant already at very small disequilibrium. The following new, nonlinear effects are obtained: (i) At even-gap voltages V = 2nDelta/e (n = 2, 3, ...) nonequilibrium bosonic bands overlap. This leads to enhanced emission of Omega = 2Delta bosons and to the appearance of dips in tunnel conductance. (ii) A new type of radiative solution is found at strong disequilibrium. It is characterized by the fast stimulated relaxation of quasiparticles. A stack in this state behaves as a light emitting diode and directly converts electric power to boson emission, without utilization of the ac-Josephson effect. The phenomenon can be used for realization of a new type of superconducting cascade laser in the THz frequency range.