Normal Metal-insulator-superconductor Junctions Research Articles

Charge dynamics in quantum-circuit refrigeration: Thermalization and microwave gain

Previous studies of photon-assisted tunneling through normal-metal–insulator–superconductor junctions have exhibited potential for providing a convenient tool to control the dissipation of quantum-electric circuits in situ. However, the current literature on such a quantum-circuit refrigerator (QCR) does not present a detailed description for the charge dynamics of the tunneling processes or the phase coherence of the open quantum system. Here, we derive a master equation describing both quantum-electric and charge degrees of freedom, and discover that typical experimental parameters of low temperature and yet lower charging energy yield a separation of time scales for the charge and quantum dynamics. Consequently, the minor effect of the different charge states can be taken into account by averaging over the charge distribution. We also consider applying an ac voltage to the tunnel junction, which enables control of the decay rate of a superconducting qubit over four orders of magnitude by changing the drive amplitude; we find an order-of-magnitude drop in the qubit excitation in 40 ns and a residual reset infidelity below 10−4. Furthermore, for the normal island, we consider the case of charging energy and single-particle level spacing large compared to the superconducting gap, i.e., a quantum dot. Although the decay rates arising from such a dot QCR appear low for use in qubit reset, the device can provide effective negative damping (gain) to the coupled microwave resonator. The Fano factor of such a millikelvin microwave source may be smaller than unity, with the latter value being reached close to the maximum attainable power.

Calibration of cryogenic amplification chains using normal-metal–insulator–superconductor junctions

Various applications of quantum devices call for an accurate calibration of cryogenic amplification chains. To this end, we present an experimentally feasible calibration scheme and use it to accurately measure the total gain and noise temperature of an amplification chain by employing normal-metal–insulator–superconductor (NIS) junctions. Our method is based on the radiation emitted by inelastic electron tunneling across voltage-biased NIS junctions. We derive an analytical expression that relates the generated power to the applied bias voltage which is the only control parameter of the device. After the setup has been characterized using a standard voltage reflection measurement, the total gain and the noise temperature are extracted by fitting the analytical expression to the microwave power measured at the output of the amplification chain. The 1σ uncertainty of the total gain of 51.84 dB appears to be of the order of 0.10 dB.

A Robust Cooling Platform for NIS Junction Refrigeration and sub-Kelvin Cryogenic Systems

Recent advances in Normal metal–insulator-superconductor (NIS) tunnel junctions (Clark et al. Appl Phys Lett 86: 173508, 2005, Appl Phys Lett 84: 4, 2004) have proven these devices to be a viable technology for sub-Kelvin refrigeration. NIS junction coolers, coupled to a separate cold stage, provide a flexible platform for cooling a wide range of user-supplied payloads. Recently, a stage was cooled from 290 to 256 mK (Lowell et al. Appl Phys Lett 102: 082601 2013), but further mechanical and electrical improvements are necessary for the stage to reach its full potential. We have designed and built a new Kevlar suspended cooling platform for NIS junction refrigeration that is both lightweight and well thermally isolated; the calculated parasitic loading is $$<\!\!300$$ pW from 300 to 100 mK. The platform is structurally rigid with a measured deflection of 25 $$\upmu $$ m under a 2.5 kg load and has an integrated mechanical heat switch driven by a superconducting stepper motor with thermal conductivity G $$ = 4.5 \times 10^{-7}$$ W/K at 300 mK. An integrated radiation shield limits thermal loading and a modular platform accommodates enough junctions to provide nanowatts of continuous cooling power. The compact stage size of 7.6 cm $$\times $$ 8.6 cm $$\times $$ 4.8 cm and overall radiation shield size of 8.9 cm $$\times $$ 10.0 cm $$\times $$ 7.0 cm along with minimal electrical power requirements allow easy integration into a range of cryostats. We present the design, construction, and performance of this cooling platform as well as projections for coupling to arrays of NIS junctions and other future applications.

Leakage current of a superconductor–normal metal tunnel junction connected to a high-temperature environment

We consider a voltage-biased Normal metal-Insulator-Superconductor (NIS) tunnel junction, connected to a high-temperature external electromagnetic environment. This model system features the commonly observed subgap leakage current in NIS junctions through photon-assisted tunneling which is detrimental for applications. We first consider a NIS junction directly coupled to the environment and analyze the subgap leakage current both analytically and numerically; we discuss the link with the phenomenological Dynes parameter. Then we focus on a circuit where a low-temperature lossy transmission line is inserted between the NIS junction and the environment. We show that the subgap leakage current is exponentially suppressed as the length, $\ell$, and the resistance per unit length, $R_0$, of the line are increased. We finally discuss our results in view of the performance of NIS junctions in applications.

Adiabatic quantum pumping in normal-metal–insulator–superconductor junctions in a monolayer of graphene

We investigate adiabatic quantum pumping through a normal-metal--``insulator''--superconductor (NIS) junction in a monolayer of graphene. The pumped current is generated by periodic modulation of two gate voltages, applied to the insulating and superconducting regions, respectively. In the bilinear response regime and in the limit of a thin high insulating barrier, we find that the presence of the superconductor enhances the pumped current per mode by a factor of 4 at resonance. Compared to the pumped current in an analogous semiconductor NIS junction, the resonances have a $\ensuremath{\pi}/2$ phase difference. We also predict experimentally distinguishable differences between the pumped current and the tunneling conductance in graphene NIS junctions.

Laterally proximized aluminum tunnel junctions

This letter presents experiments on junctions fabricated by a technique that enables the use of high-quality aluminum oxide tunnel barriers with normal metal electrodes at low temperatures. Inverse proximity effect is applied to diminish the superconductivity of an aluminum dot through a clean lateral connection to a normal metal electrode. To demonstrate the effectiveness of this method, fully normal-state single electron transistors (SETs) and normal metal-insulator-superconductor (NIS) junctions applying proximized Al junctions were fabricated. The transport characteristics of the junctions were similar to those obtained from standard theoretical models of regular SETs and NIS junctions.

Tunneling conductance in gapped graphene-based normal metal–insulator–superconductor junctions: Case of massive Dirac electrons

We study the quantum transport property in a gapped graphene-based normal metal–insulator–superconductor junctions ( NG/ IG/ SG), in the limit of a thin barrier. The charged fermions in NG/ IG/ SG structure are treated as massive relativistic particles. Based on Andreev and normal reflections in normal-superconductor graphene-based junction and BTK formalism, the tunneling conductance’s in terms of some different electrostatic superconductor, U 0 and barrier, V 0 potential are obtained. Using the experimental based values of the Fermi energy in the NG and SG ( E FN and E FN + U 0, respectively), energy gap in graphene 2 mv F 2 and superconducting order parameter, Δ, it is shown that the conductance spectra of such system represent a new behavior, i.e. if we take | E FN - mv F 2 | → 0 , it becomes as a step function of V 0. This behavior of charge transportation can be considered as a nano switch.

Tunneling conductance in graphene-based normal metal–insulator–superconductor junctions

Based on the transfer-matrix method, we have investigated the coherent quantum transport in a graphene-based normal metal–insulator–superconductor ( NG / IG / SG ) junctions, in the limit of a thin barrier. It is found that the conductance spectra of such system, in contrast to a π periodic oscillatory behavior is shown for aligned Fermi surfaces of the normal and superconducting regions, exhibit a new π / 2 periodic oscillatory behavior as a function of barrier strength ( χ) for a large Fermi surface mismatch.

Tunneling Conductance of Graphene NIS Junctions

We show that, in contrast with conventional normal metal-insulator-superconductor (NIS) junctions, the tunneling conductance of a NIS junction in graphene is an oscillatory function of the effective barrier strength of the insulating region, in the limit of a thin barrier. The amplitude of these oscillations is maximum for aligned Fermi surfaces of the normal and superconducting regions and vanishes for a large Fermi surface mismatch. The zero-bias tunneling conductance, in sharp contrast to its counterpart in conventional NIS junctions, becomes maximum for a finite barrier strength. We also suggest experiments to test these predictions.

Rf-SQUID microcalorimeter

We propose an rf-SQUID microcalorimeter in which the critical current of a Josephson junction can be varied by an electron temperature in the normal metal barrier of the superconductor–normal metal–superconductor or superconductor–normal metal–insulator–superconductor junctions. In this detector, a Josephson junction with a radiation absorber is included in a superconductor loop and the change of its critical current is converted into a change of the terminal voltage of a tank circuit. We estimated the energy resolution of this detector by calculating the noise equivalent power of the detector. The estimated energy resolution is 1.5 eV with an Ag absorber of 500 × 500 × 2 µm3 at 100 mK.

Thermal characterization of a hot-electron micro-bolometer

Abstract We report on a hot-electron micro-bolometer fabricated by electron beam lithography consisting of a small normal-metal absorber capacitively coupled to a planar antenna. Both the thermometer and the coupling capacitors are made by sub-micron normal metal–insulator–superconductor junctions. By adding two extra Andreev contacts to the absorber it is possible to characterize the bolometer by dc measurements.

NIS chip refrigeration

A normal-metal/insulator/superconductor (NIS) tunnel junction can be applied to cool electrons by biasing the junction suitably with external voltage. Two NIS junctions in series can form an efficient microrefrigerator because of the symmetry with bias voltage. Our SINIS microrefrigerator has been capable of reaching electronic temperatures of about 100 mK starting from 300 mK. To achieve appreciable refrigeration of the underlying lattice, the microrefrigerator must be thermally decoupled from the bulk substrate. We have demonstrated experimentally the reduction of lattice temperature by 23 mK at 180 mK by extending the normal electrode on a thin dielectric membrane with four suspended bridges. Methods to improve the efficiency of refrigeration, e.g., by using a superconductor with a large energy gap and/or by increasing the number of tunnel junctions, are discussed.

Electronic refrigerators: optimization studies

Electric current flowing through a normal metal-insulator-superconductor (NIS) junction accompanied by the heat transfer from normal metal to superconductor is able to cool electrons in the normal metal electrode below the lattice temperature under certain conditions. The tunneling electric current dependence on biasing voltage at different normal metal electrode electron temperatures is calculated. Refrigerators with one and with two NIS junctions are investigated. Further, the cooling power of SNIS and SINIS refrigerators, its dependence on biasing voltage and on the temperature of normal metal electrode electrons are investigated. With reduced insulator layer thickness the resistivity of a NIS junction decreases. Thus, the cooling power of a refrigerator increases. But simultaneously the probability for Andreev reflections which diminish the efficiency of the refrigerator increases. Therefore, the optimal thickness of the insulator layer needs to be found. A method for calculating an optimal insulator layer thickness based on the introduction of a new function that needs to be minimized is described. Geometrical limits on the influence of Andreev reflection are determined.

Microrefrigeration by normal-metal/insulator/superconductor tunnel junctions

A normal-metal/insulator/superconductor (NIS) tunnel junction can be applied to cool electrons by biasing the junction suitably with external voltage. Because of the symmetry with bias voltage, two NIS junctions in series can form an efficient microrefrigerator. So far our SINIS microrefrigerator has been capable of reaching electronic temperatures of about 100 mK starting from 300 mK. To achieve appreciable refrigeration of the underlying lattice, microrefrigerator must be thermally decoupled from the bulk substrate. We have demonstrated experimentally the reduction of lattice temperature of a few mK at 200 mK by extending the normal electrode on a thin dielectric membrane. Methods to improve the efficiency of lattice refrigeration are discussed.

Superconducting Ba1−xKxBiO3 thin films and junctions

Superconducting Ba1−xKxBiO3 (BKBO) thin films and heteroepitaxial multilayers were deposited by in situ off-axis sputtering on various substrate at 400 °C. A typical superconducting BKBO thin film on the SrTiO3 and MgO substrates had a very sharp zero resistance transition at a temperature of 22–24 K as measured by transport four point and mutual inductance probes. The normal state resistivity exhibited metallic to semiconductive characteristics depending on film composition with the lowest room temperature resistivity of about 0.25 mΩ cm. The film orientation was highly epitaxial to both SrTiO3 and MgO substrates. Normal metal-insulator-superconductor (NIS) type tunnel functions with native insulator layer and deposited MgO layer were reproducibly fabricated. The superconducting energy gap of about 3.6 meV was obtained from those NIS junctions. Heteroepitaxial superconductor- insulator-superconductor (SIS) trilayer junctions were also fabricated using MgO insulator layers. For a 5 nm thick insulator layer, quasiparticle SIS tunnel junctions with nonhysteric I-V characteristics were obtained. By reducing MgO insulator layer thickness down to 3 nm, SIS tunnel junctions with Josephson supercurrent were obtained with hysteric I-V characteristics.

Tunnel junctions using oxide superconducting thin films epitaxially grown on SrTiO3

Normal-metal/insulator/superconductor (NIS) junctions were fabricated using thin films of YBa2Cu3O7−x (YBCO) or ErBa2Cu3O7−x. These were epitaxially grown on single-crystal SrTiO3 by the activated reactive evaporation method. For some NIS junctions prepared on SrTiO3 (110) substrates, we observed multipeaks in the differential conductance versus voltage curve. NIS junctions using single-crystal YBCO films on SrTiO3 (100) showed a set of peaks, from which we obtained a gap parameter of 11.5±1.5 meV at 4.4 K and a coupling constant of 3.2±0.4.