PROCEDIMIENTOS ESPECIALES PARA LA REMOCION DE ASOCIADOS Y DIRECTIVOS

Superconductivity is a low temperature state of matter first observed by Heike Kammerlingh Onnes in 1911 [64]. Through the 20th century the phenomena associated with superconductivity have been studied and increasingly sophisti- cated theoretical descriptions of the macroscopic effects and microscopic physics [65–67] have been adopted.

The sudden onset of zero-resistance is one of the hallmark macroscopic effects observed at small range of temperature below a critical level TC, originally

observed in bulk samples of Hg, Pb and Ti, the effect was observed to be material dependent.

The second hallmark of superconductivity is the complete and active expul- sion of magnetic field from inside a piece of superconducting material, known as the Meissner effect [68]. This effect suggests the existence of a critical magnetic field density HC within a material above which the superconducting state is

unable to form. Below HC the magnetic field expulsion is analogous to the

skin depth effect of the electric field in metals. The magnetic field intensity outside a superconducting material drops off exponentially at the materials edge with a characteristic length, or penetration depth, ⁄L first described by

Fig. 2.6 Photon detection in a superconducting nanowire. A thin strip of super- conducting material (shown in blue) is patterned to sub-micron dimensions (width 100 nm, thickness 7 nm) and current biased at low temperature. Absorption of an optical or infrared photon causes a perturbation of the superconducting charge carriers (shown in red). Being confined by the wire edges this quickly spreads to create a resistive hotspot that covers the width of the nanowire. Current is diverted into a load resistor creating a measureable voltage pulse. The superconductor cools as heat is lost into the substrate causing the nanowire to reset to its initial state.

F. and H. London [69]. The later discovery of superconductivity in another class of materials, known as Type II superconductors, found that magnetic flux was in fact able to penetrate these superconductors but it does so only in quantised amounts. Magnetic field penetrating a Type II superconductor creates a vortex of supercurrent the centre of which contains a single quantum of magnetic flux 0, and with the absence of supercurrent carriers this core

has finite resistance. The presence of a persistent supercurrent generates a Lorentz force on the vortex moving it laterally to the current. Material defects will tend to pin vortices in place until an increase in current generates a large enough force to move them on.

The first full microscopic theory of superconductivity came in 1965 from Bardeen, Cooper, and Schrieffer [65]. They described the effect where at low temperatures sympathetic phonon modes allow the resistance free movement of pairs of charge carriers with opposite momenta through the material lattice. So called Cooper pairs were bosons with charge 2e, condensation energy of

2—, and an effectively infinite mean free path L. Each half of the Cooper pair requires an excitation of — to become an electron-like quasi particle that will travel with finite L obeying Ohmic behaviour. Later Ginzburg and Landau published a more comprehensive theory [66, 70] that describes time-dependent and spatially varying superconducting states in terms of a quantum mechanical wavefunction  with coherence over the length scale ›.

Thin films of superconducting material below TC and HC will support the

flow of superconducting current up to a critical density JC which is determined

by the material and geometry of the film. Although TC is a material dependent

parameter for bulk superconductors a thin film will see a sharp reduction in TC

for films with thickness d close to d ƒ › the coherence length [71]. The lateral magnetic penetration depth is described by ⁄L. For NbN nanowires of width

wƒ 100 nm the length scale of ⁄L∫ w leaving the magnetic field fairly uniform

across the narrow nanowire. Under normal conditions, the Earth’s magnetic field is expelled from NbN nanowires however magnetic penetration effects can be observed in wider strip lines [72], or wires of different superconducting materials.

In 2001 thin films of NbN (2— ƒ 6 meV) were under investigation [60]. When patterned to sub-micron dimensions and current biased slightly below the critical level JC the absorption of optical photons (energy ≥1 eV) were observed

to cause a transient normal resistive spot which diverts the supercurrent causing nearby current density to exceed JC thus making the resistive hotspot

grow in size [61]. With the hotspot being confined to the nano-patterned region it grows in a number of picoseconds to create a resistive barrier with a measurable voltage drop. Although Joule heating causes the superconductor’s temperature to increase and the resistive region to grow the device current can be diverted to a load resistor RL allowing the hot quasi particles to relax back

to the superconducting state dissipating energy into the substrate. This basic description of the detection mechanism is illustrated in Figure 2.6.

The development from basic principles followed a technology driven path with device specifications being ever improved and new avenues for application opened by progress. A firm theoretical understanding of the microscopic physics occurring within a triggered device on the picosecond timescale has tended to follow behind [73–78].

Current biased nanowires of superconducting material have a current dis- tribution dependent on the geometry of the nanowire [79]. Straight sections of wire have slightly higher JC in the centre compared to the edges. This

is inferred from measurements of superconducting detectors using polarised light, which also has a lateral variation in absorption probability for different polarisations [80]. Arguably the greater effect on current distribution comes from bent or curved nanowires. Current crowds around the inside of a curve raising JC locally and ultimately reducing the limit of IC in the connected

straight sections of wire [81]. This can cause increased dark count rates in detectors as well as a reduction in local ÷registering on the outside of the bend,

a particular problem for waveguide integrated nanowires [82].

Naturally the applicability of SNSPDs has been boosted greatly by advances in supporting technology. Primarily the cooling technology required to operate detectors at < 5 K has come a long way in the past 20 years [83]. Refrigeration is no longer limited to low temperature physics labs and innovative designs for practical cooling systems are commercially available [84, 85]. Bench top systems capable of continuous closed-cycle operation at 2 K are now commonly used for SNSPD detector systems [86] and paired with “turn-key” electronics to make systems accessible to non-expert users. Cutting edge cooling technology will continue to allow SNSPDs to be operated in more flexible environments [87].

The SNSPD offers highly desirable performance in terms of most SPD figures of merit (see Section 2.1.2). Since its inception in 2001 the technology has matured and in doing so is finding ever-increasing applications. Several review articles cover the development of the field in considerable detail [88, 89, 41]. The following is a broad selection of noteworthy applications of SNSPDs: remote sensing [90–93], life sciences [94, 95], SPS characterisation [96–100], fundamental physics and metrology [101–108], quantum key distribution [109– 112], arrayed detectors for imaging [113–117], ground-to-space communications [118], and pseudo photon number resolution [119–121]. For a comprehensive review of SNSPDs integrated with quantum photonic circuits see Section 2.3.2.