FIELD

The present disclosure relates to supercon ducting electronics. In particular, the disclosure re lates to sub-millimeter or even sub-micron scale elec tronics, such as nanoelectronics.

BACKGROUND

Nanoelectronics refers to the use of nano technology in electronic components. The term covers a diverse set of devices and materials, with the common characteristic that they are so small that inter atomic interactions and/or quantum mechanical proper ties affect their performance. Nanoelectronics devices may have one or more critical dimensions with a size range between 1 nm and 100 nm. Nanoelectronics are sometimes considered as disruptive technology because present devices are significantly different from tra ditional transistors. The search for material and structural combinations providing the best performanc es for the required application is continuously ongo ing.

OBJECTIVE

An objective is to provide novel electronic components that may themselves open possibilities for new applications.

SUMMARY

In accordance with the present disclosure, it has been found that a tunnel barrier with a supercon ductor can be utilized for providing a direction- selective structure for electric current transport. This can be achieved when electric current transport across the tunnel barrier is spin-polarized by induc ing spin-splitting to the superconductor in the vicin ity of the tunnel barrier. This can be utilized to provide devices where electric current can be directed to flow primarily in one direction, or direction- selective electric transport devices, such as current limiters.

According to a first aspect, an apparatus comprises a first conductor, a second conductor and a tunnel barrier. The tunnel barrier is coupled between the first conductor and the second conductor to form a tunnel junction. The first conductor or the second conductor is a superconductor (the other conductor may herein be referred as "the other conductor"). The ap paratus is configured for spin-splitting to be induced at the superconductor at the tunnel junction and tun neling across the tunnel barrier to be spin-polarized. The configuration allows electric current transport across the tunnel barrier to become direction- selective. In particular, this applies to the qua siparticle current at the superconductor, so that it can be utilized for direction-selective current transport. The configuration allows electric current across the tunnel barrier to flow primarily in one di rection, making it attractive for various applica tions.

In an embodiment, the tunnel barrier compris es a magnetic insulator, such as a ferromagnetic insu lator, for inducing spin-splitting at the superconduc tor and spin-polarizing tunneling across the tunnel barrier. This allows the tunnel barrier itself to pro vide the effects required for the direction-selective operation. The other conductor may be a magnetic or non-magnetic conductor, in particular a ferromagnetic or a non-ferromagnetic conductor. Furthermore, it al lows the spin-splitting to be provided without an ex ternal magnetic field so that the apparatus may be provided as a passive component. In a further embodi ment, the magnetic insulator is a europium chalco- genide, such as EuS or EuO. This may provide an en hanced spin-polarization for the tunneling in com- partison to a generic magnetic insulator, in particu lar in the case of EuO, and/or simplified manufactur ing, in particular in the case of EuS.

In an embodiment, the apparatus comprises a magnetic insulator, such as a ferromagnetic insulator, coupled to the superconductor in the vicinity of the tunnel barrier for inducing spin-splitting at the su perconductor. The magnetic insulator can thus be sepa rate from the tunnel barrier, for example provided as a separate material layer. This allows the spin splitting to be induced separately from the tunnel barrier. The tunnel barrier may be magnetic or non magnetic, in particular ferromagnetic or non ferromagnetic. The embodiment can also allow the spin filtering to be provided without an external magnetic field so that the apparatus may be provided as a pas sive component.

In an embodiment, the first conductor or the second conductor is a magnetic conductor, such as a ferromagnetic conductor, for spin-polarized tunneling across the tunnel barrier. This allows the tunneling to be spin-polarized irrespective of the tunnel barri er. The tunnel barrier may be magnetic or non magnetic, in particular ferromagnetic or non ferromagnetic. This embodiment may also be used in conjunction with the previous and/or the following em bodiments to provide both the spin-polarization and the spin-splitting. As one of the first and the second conductor is a magnetic conductor, the other would then be the superconductor.

In an embodiment, the apparatus comprises a magnetic field generator for generating a magnetic field for inducing spin-splitting at the superconduc- tor. This allows the spin-splitting to be induced without a separate structure, such as a magnetic structure, at the tunnel junction, and provides a fur ther alternative to be used independently or in con junction with the magnetic tunnel barrier and/or the magnetic insulator for the spin-splitting as described above. It can also be used in conjunction with the magnetic conductor. The magnetic field is an external magnetic field and it may be provided as a temporary, or a transient, magnetic field. This also allows the magnetic field to be utilized as a switch for switch ing the apparatus between a direction-selective state and a non-direction selective-state. The apparatus and the magnetic field generator may be configured ac cordingly. In a further embodiment, the magnetic field generator is configured for generating the magnetic field substantially perpendicular to the flow direc tion of the electric current across the tunnel barri er. This allows the spin-splitting to be optimized for improving the direction-selective transport across the tunnel barrier. This may be used, in particular, when the magnetic material providing the spin-polarization, such as the tunnel barrier and/or the magnetic conduc tor, is polarized in-plane.

In an embodiment, the apparatus is configured for responding to a first external magnetic field so that the electric current across the tunnel barrier flows in a first direction and to a second ex ternal magnetic field so that the electric current across the tunnel barrier flows in a second direction, opposite to the first direction. This can be done, when the second external magnetic field changes a po larization of the apparatus with respect to the polar ization of the magnetic body in presence of the first external magnetic field. This allows the directionali ty of the apparatus, i.e. the preferred direction of current flow across the tunnel barrier, to be changed during the operation of the apparatus. The polariza tion may correspond to a polarization of one or more magnetic bodies of the apparatus, such as the tunnel barrier and/or the other conductor, facilitating the spin-splitting and/or the spin-polarization.In an em bodiment, the tunnel junction is formed as a layered structure with the first conductor stacked on the sec ond conductor with the tunnel barrier in between. This allows effective fabrication and configuration of the structure. In a further embodiment, the first conduc tor is the superconductor allowing the superconductor to be formed as a topmost structure.

In an embodiment, the apparatus comprises two or more terminals for facilitating direction-selective conduction of electric current. At least one of the terminals may be provided at the first conductor or the second conductor for providing electric current to the apparatus. Also, a terminal of the two or more terminals may be provided at the first conductor or the second conductor for providing electric current from the apparatus in a direction-selective manner, or primarily in one direction. In a first embodiment, the apparatus comprises a first terminal provided at the first conductor and a second terminal provided at the second conductor for conducting electric current be tween the first terminal and the second terminal. This conducting can thus be in a direction-selective man ner, or primarily in one direction. In a second embod iment, the apparatus comprises a first terminal pro vided at a first contact point of the second conductor and a second terminal provided at a second contact point of the second conductor for providing an elec tric current, which may in particular be an alternat ing current, between the first terminal and the second terminal. The tunnel junction would then be located between the first contact point and the second contact point for rectifying electric current between the first terminal and the second terminal. The third ter minal may be provided at the first conductor for providing a rectified current and/or voltage from the apparatus. According to both of the first and the sec ond alternative, for the superconductor, the electric current can be conducted as quasiparticle current. In a futher embodiment, the first conductor is the super conductor allowing the rectified current and/or volt age to be provided from a quasiparticle current.

A diode can be a non-linear and non reciprocal circuit in which a lack of spatial inver sion symmetry provides a direction-selective electron transport, which may also be called rectification. Di odes can be used as key elements for electronics, op tics, and/or detection. In the long history of diodes, the material search for this symmetry breaking has been mainly focused on semiconducting and metallic junctions. However, owing to their large energy gap, semiconductors cease to work at the sub-Kelvin temper atures relevant for emerging cryogenic electronics and ultrasensitive detection, especially at sub-THz fre quencies.

One example of a low-dimensional structure that could be proposed for solving such a problem can be provided by quantum dots, which may exhibit current rectification. Yet, the electron-hole symmetry in quantum dots can be tuned only within the level of a single quantum channel, which is why the impedance of such systems tends to be high, and the rectified cur rents thereby very low.

The solution, such as the aspects and embodi ments, described herein provides a structure utilizing a superconductor. This has been found to allow the re alization of a diode, such as a cryogenic diode. The use of a superconductor allows utilizing its intrinsic low impedance and the superconducting gap, the energy scales of which are smaller (~ meV) in comparison to those of semiconductors (~ eV). However, the implemen tation of a superconducting diode is not straightfor ward, since it requires breaking of the electron-hole symmetry, whereas the superconducting state is elec tron-hole symmetric by default. For a superconducting diode, in accordance with the present disclosure, the electron-hole symmetry breaking can be achieved by combining spin-polarization (which may also be re ferred to as "spin-filtering") for electric transport across the tunnel barrier and spin-splitting for the superconductor at the tunnel junction. Such a diode can operate even in the absence of an external magnet ic field, support continuous current values, and rec tify quasiparticle currents, rather than supercur rents.

As exemplified above, the spin-splitting may be induced into the superconductor by various ways, for example by an external magnetic field and/or by exchange interaction between the superconductor and a magnetic material in the vicinity of the superconduc tor, for example the tunnel barrier and/or a separate magnetic body such as the separate magnetic insulator exemplified above. The relative magnitude of the ex change interaction and the spin polarization may be used for determining a preferred direction for the electric current transport across the tunnel barrier.

According to a second aspect, a diode is pro vided. The diode comprises a first terminal and a sec ond terminal. It also comprises the apparatus accord ing to the first aspect or any of its embodiments, alone or in any combination. The first terminal is provided at the first conductor and the second termi nal is provided at the second conductor for conducting electric current between the first terminal and the second terminal. This conducting can thus be in a di rection-selective manner, or primarily in one direc tion. For the superconductor, the electric current can be conducted as quasiparticle current. The diode may be used at a lower voltage and thereby at lower dissi pation levels than conventional semiconductor-based diodes.

According to a third aspect, a rectifier is provided. The rectifier comprises a first terminal, a second terminal and a third terminal. It also compris es the apparatus according to the first aspect or any of its embodiments, alone or in any combination. The first terminal is provided at a first contact point of the second conductor and the second terminal is pro vided at a second contact point of the second conduc tor for providing an electric current, which may in particular be an alternating current, between the first terminal and the second terminal. The tunnel junction may be located between the first contact point and the second contact point for rectifying electric current between the first terminal and the second terminal. The third terminal may be provided at the first conductor for providing a rectified current and/or voltage from the apparatus. For the supercon ductor, the rectified current and/or voltage can be provided from a quasiparticle current.

According to a fourth aspect, a method for facilitating direction-selective, or primarily one- directional, conduction of electric current is dis closed. The method comprises facilitating spin splitting at a superconductor and spin-polarization for tunneling across a tunnel barrier. This can be performed so that electric current across the tunnel barrier between a conductor and the superconductor be comes direction-selective, or flows primarily in one direction. Using this method, a diode and/or a recti fier, for example according to the second and the third aspect may be provided, including the apparatus according to the first aspect or any of its embodi ments, alone or in any combination. It is to be understood that the aspects and embodiments described above may be used in any combi nation with each other. Several of the aspects and em bodiments may be combined together to form a further embodiment of the invention.

The present solutions allow providing elec tric current rectification for the quasiparticles of the superconductor, in contrast to rectification of Cooper pairs i.e. the supercurrent. The solution can take advantage of the magnetic proximity effect on a superconductor and a spin-split density of states. The solutions are not restricted to any specific current range only and can be made to function with continuous electric current values. They can also be provided with reduced impedance. The solutions may be provided utilizing low-dimensional structures. Any solutions disclosed herein may be configured for operation at cryogenic temperatures, or for sub-Kelvin temperatures in particular. They may be configured for operation at any temperature below the critical temperature of the superconductor. Thereby, the solutions can also be provided compatible with superconducting electronics and already existing fabrication technologies. The ap paratus according to the first aspect, the diode ac cording to the second aspect and the rectifier accord ing to the third aspect may be provided as a passive electronic component. Any of the aspects and the em bodiments may be provided as or for a nanoelectronics device. They may be provided, for example, as a part of a detector with improved sensitivity, for example at temperatures where conventional electric components such as diodes fail to operate. The present solutions may also allow improved energy efficiency and/or oper ating frequency. They may be utilized at mixers, re verse current regulators, voltage clamping and passive superconductive electronics, for example. BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a further understanding and constitute a part of this specification, illustrate examples and together with the description help to explain the principles of the disclosure. In the drawings:

Fig. la schematically illustrates an appa ratus according to an example,

Fig. lb illustrates a diode according to an example.

Fig. 2 illustrates an apparatus according to an example in a perspective view,

Figs. 3a,b schematically illustrate an appa ratus according to another example,

Fig. 4 illustrates examples of an apparatus, and

Fig. 5 illustrates a method according to an example.

Like references are used to designate equiva lent or at least functionally equivalent parts in the accompanying drawings.

DETAILED DESCRIPTION

The detailed description provided below in connection with the appended drawings is intended as a description of examples and is not intended to repre sent the only forms in which the example may be con structed or utilized. However, the same or equivalent functions and structures may be accomplished by dif ferent examples.

Figure 1 shows an example of an apparatus 100 according to an example. The apparatus comprises a first conductor 110 and a second conductor 120. At least one of the first conductor and the second con ductor is a superconductor, for example an aluminum superconductor. In general, the superconductor may be of any superconducting material, including for exam ple: Al, Ti, V, NbN and Nb. The superconductor is su perconducting at least in the operating temperature of the apparatus but may naturally be superconducting al so at an extended temperature range. The superconduc tor may be a low-temperature superconductor. It may be of material, which becomes superconductive at a cryo genic temperature, for example below 10 Kelvin. The superconductor may be formed as a layer of supercon ducting material. The other conductor of the first and the second conductor may also be a superconductor, in which case any of the above alternatives regarding the properties of the superconductor may apply also to the other conductor. The properties may be the same or different for the two superconductors. For example, they may be of same or different material.

The other conductor of the first and the sec ond conductor may also be non-superconducting conduc tor, at least in the operating temperature of the ap paratus, for example a copper conductor. In general, the other conductor may be of any electrically con ducting material. It may be magnetic, in particular ferromagnetic, for example of Co, Fe, Ni, or Gd. It may also be non-magnetic, in particular non ferromagnetic, for example of: Cu, AIMn, Au, Ag, Pd or Pt. The other conductor may be formed as a layer of electrically conducting material.

The apparatus 100 comprises a tunnel barrier 130, which is coupled between the first conductor 110 and the second conductor 120 to form a tunnel junc tion. The tunnel barrier allows physically separating the first conductor from the second conductor, thereby preventing direct electric conduction between the two, while still allowing quantum tunneling for electric conduction between them. For the superconducting, this may correspond in particular to quasiparticle tunnel- ing. The tunnel barrier may be of electrically insu lating material. In particular, it may comprise or consist of a magnetic insulator, in particular a fer romagnetic insulator, such as EuS, EuO or GnN. The tunnel barrier may be formed as a layer of electrical ly insulating material. In some embodiments, in par ticular when the other conductor is a magnetic conduc tor, the tunnel barrier may comprise or consist of a non-magnetic insulator, for example AlOx.

The apparatus is configured for spin splitting to be induced at the superconductor at the tunnel junction and tunneling across the tunnel barri er to be spin-polarized so that electric current across the tunnel barrier flows in a direction- selective manner or primarily in one direction. For the superconductor, this electric current may corre spond to quasiparticle current. Correspondingly, the spin-splitting may correspond to a split in the qua siparticle density of states for the superconductor so that the superconducting density of states for one spin state, such as a spin-up state, is different from the quasiparticle density of states for an opposite spin state, such as spin-down state. Since the qua siparticle density of states for a superconductor can comprise large peaks, such spin-splitting may markedly affect the electric transport properties for the su perconductor. It has been found that, since the super conductor comprises an energy gap and since the tun neling across the tunnel barrier is spin-polarized, electric current transport in one direction across the tunnel barrier can be favored with respect to electric current transport in the opposite direction.

The spin-splitting may be provided by one or more permanently magnetic bodies, which may be located in the vicinity of the tunnel barrier, and/or by an external magnetic field, which may be a temporary, or a transient, magnetic field. The spin-polarization for tunneling may be provided by one or more magnetic bod ies, such as the tunnel barrier and/or the other con ductor comprising or consisting of a magnetic materi al. The magnetic material may be ferromagnetic. The spin-splitting and the spin-polarization for tunneling may even be provided by the same magnetic body, such as the tunnel barrier being magnetic or ferromagnetic, such as a ferromagnetic insulator. However, the spin splitting may also be provided by a magnetic body sep arate from the tunnel barrier. It may be separately coupled to the superconductor, for example as an addi tional material layer. In an embodiment, the magnetic body is a magnetic insulator, in particular a ferro magnetic insulator such as a europium chalcogenide, e.g. EuS and/or EuO.

The apparatus 100 may comprise a first termi nal 140 and a second terminal 150. This can be used for facilitating direction-selective conduction of electric current through tunnel barrier 130. The first terminal may be provided at the first conductor 110 and the second terminal may be provided at the second conductor 120 for receiving electric current to the apparatus and providing electric current from the ap paratus in a direction-selective manner, or primarily in one direction. This allows realizing a diode. Cor respondingly, the apparatus may be provided as a diode 200, for example as illustrated in Figure lb. The di ode of Fig. lb is illustrated side-to-side with the apparatus of Fig. la to show how an electric current can be conducted in a direction-selective manner from the first terminal 140 to the second terminal 150 in both cases. The preferred direction is not necessarily that from the first conductor 110 to the second con ductor 120. The apparatus and the diode may well be configured for the preferred direction to be from the second terminal to the first terminal, in which case the sign for the diode 200 in Fig. lb may be flipped upside down. Correspondingly, the apparatus may be configured for the preferred direction to be either from the superconductor or to the superconductor. The configuration, and thereby the preferred direction, may be dependent on the relative strength of the spin- polarization and the spin-splitting.

The apparatus 100 may be specifically config ured for changing its directionality on the fly so that it can be direction-selective in favor of both of the opposite directions across the tunnel barrier dur ing its operation, for example in response to an ex ternal magnetic field. The apparatus may be configured for responding to a first external magnetic field so that the electric current across the tunnel barrier flows primarily in a first direction and to a second external magnetic field so that the electric current across the tunnel barrier flows primarily in a second direction. The first external magnetic field may here be opposite to the second external magnetic field. The first direction may be opposite to the second direc tion. The apparatus may comprise one or more magnetic field generator for providing the first and/or the second magnetic field. The generator may be configured for switching between the two directionalities, which may be done automatically. The apparatus, and the mag netic field generator, may be configured for changing the polarization of a magnetic body facilitating the spin-splitting and/or the spin-polarization with re spect to the polarization in presence of the first ex ternal magnetic field. The magnetic body may be one or more of the tunnel barrier, the other conductor and the magnetic body separate from the tunnel barrier, in any combination. As an example, the apparatus may com prise two such magnetic bodies, in which case the ap paratus may be configured for changing the polariza tion of one of these bodies with respect to the other for changing the directionality. The strength of the first and/or the second magnetic field may be selected accordingly. The directionality of the apparatus, i.e. the preferred direction of current flow across the tunnel barrier, to be changed during the operation of the apparatus.

An electric current to be transmitted through the tunnel barrier may be provided by an electric cur rent source, which may be part of the apparatus 100 or separate from it. Similarly, the electric current pro vided in a direction-selective manner from the tunnel barrier may be provided to one or more devices and/or electric circuits utilizing the electric current, and these device(s) and/or electric circuits may be part of the apparatus or separate from it.

Figure 2 illustrates an apparatus 100 accord ing to an example in a perspective view. The tunnel junction may be formed as a layered structure and/or as a thin-film structure. For example, the first con ductor 110 and/or the second conductor 120, in partic ular the topmost of the two, may have thickness as their smallest dimension. The tunnel junction may be formed as a stacked structure. The apparatus 100 may comprise a substrate, on which the tunnel junction may be formed. The first conductor and/or the second con ductor may be deposited on top of the substrate, di rectly or indirectly. The tunnel barrier 130 may be deposited as a layer partially or fully between the first conductor and the second conductor. The first conductor may be deposited partially or fully overlap ping the second conductor or the second conductor may be deposited partially or fully overlapping the first conductor. The tunnel barrier may be formed together with the first conductor or the second conductor as a bilayer. The other conductor of the first conductor and the second conductor may then be deposited par tially or fully on top of the bilayer. In an embodi ment, the superconductor, which may have thickness as its smallest dimension, is deposited partially or ful ly on top of the conductor. The tunnel junction may thereby be formed with the first conductor, such as the superconductor, stacked on the second conductor with the tunnel barrier between the first conductor and the second conductor. In an alternative or an ad ditional embodiment, the first conductor is aligned parallel or perpendicular with respect to the second conductor. Correspondingly, the tunnel junction may be provided as a crossbar stack.

As illustrated, a current may be transported, in a direction-selective manner, between the first conductor 110 and the second conductor 120. Similarly, a voltage can be generated and a voltage drop be meas ured between the first conductor and the second con ductor. The leads for voltage measurement and current transport connected to the second conductor are illus trated on the same side of the second conductor in Fig. 2 with respect to the tunnel junction for clari ty. In an actual measurement, the leads may also be connected to the second conductor at the opposite sides of the tunnel junction, which allows mitigating or removing an additional resistive part from the measurement, when measuring across the tunnel barrier.

Figures 3a and 3b schematically illustrate an apparatus 300 according to another example. The appa ratus may have any or all of the features of the appa ratus 100 described above. However, it may be config ured for rectifying an alternating current. Corre spondingly, the apparatus may be provided as a recti fier.

As above, the apparatus 300 comprises the first conductor 110, the second conductor 120 and the tunnel barrier 130 forming the tunnel junction, in volving the superconductor. Here, the apparatus may additionally comprise a first terminal 310 provided at a first contact point of the second conductor and a second terminal 320 provided at a second contact point of the second conductor for providing an electric cur rent, which may in particular be an alternating cur rent, between the first terminal and the second termi nal. The tunnel junction may now be located between the first contact point and the second contact point for rectifying electric current between the first ter minal 310 and the second terminal 320. The electric current may be provided by one or more electric cur rent sources, such as alternating current sources, which may be part of the apparatus or separate from it. The electric current may be provided as a bias current.

The apparatus 300 may additionally comprise a third terminal 330, which may be provided at the first conductor 110 for providing a rectified current and/or voltage from the apparatus. The rectified current and/or voltage can be provided from a quasiparticle current. The rectified current and/or voltage may be provided to one or more devices and/or electric cir cuits utilizing the rectified current and/or voltage, and these device(s) and/or electric circuits may be part of the apparatus or separate from it. In an em bodiment, the first conductor is the superconductor, for example a layered superconductor, which may be de posited on the tunnel barrier and the second conduc tor.

In Figure 3a, it is illustrated how the rec tification works according to an example. The electric current between the first terminal 310 and the second terminal 320 can give rise to electric currents 340 confined within the second conductor but also to elec tric currents 342 across the tunnel barrier 130. It has now been found that, due to the direction- selective nature of electric current transport across the tunnel barrier, a voltage can thus be generated across the tunnel barrier so that rectified current and/or voltage may be provided from the third terminal 330. As shown, the electric current, such as an alter nating current, within the second conductor can be provided as a bias current transverse to the electric current transported across the tunnel barrier, thereby facilitating transverse rectification of electric cur rent for providing the rectified current and/or volt age.

The apparatus 300 may thus be configured for performing transverse rectification of electric cur rent, or quasiparticle current in particular. This can be done to provide a rectified current and/or voltage from the apparatus. The apparatus may be operated with a current bias i _Bias applied along the second conduc tor, while a voltage drop may be measured across the tunnel barrier between the first and the second con ductor. However, a signal injected to the apparatus 300 for rectification may be a voltage signal and/or a current signal. By the apparatus, the injected signal can be partially or fully decoupled from the rectified signal. At the tunnel junction, I _B ias may partially flow in the first conductor and generate a voltage due to the non-symmetric response of the junction to the flowing current.

A possible implementation of the transverse rectification includes injecting an alternating cur rent signal into the second conductor 120 and measur ing a (DC) rectified voltage present at the third ter minal 330 at the first conductor 110.

Figure 3b further illustrates the apparatus 300 as a circuit diagram according to an example. The electric current, such as an alternating current, is provided to the second conductor from an electric cur rent source 370, such as an alternating current source, which may be separate from the apparatus or a part of the apparatus. The tunnel junction is here represented by the diode signs 350, and the apparatus may alternatively be configured also for them to be upside down in contrast to how they are illustrated in the example. In the illustration, two diode signs are used since the electric current within the second con ductor can flow parallel to the tunnel barrier, there by allowing tunneling across the tunnel barrier to take place at multiple points between the first termi nal and the second terminal. In practice, the tunnel ing can take place continuously along the tunnel bar rier between the first terminal and the second termi nal so that the number of diode signs in the illustra tion could be made infinite. Any electric resistance 360 within the second conductor along the tunnel bar rier also means that tunneling at different points of the second conductor could be illustrated as separate branches in the circuit diagram, which may thus be re peated continuously along the second conductor between the first terminal and the second terminal. The recti fied voltage can be measured between, the first and the second conductor, for example by a voltmeter 380.

Figure 4 illustrates examples of an appa ratus, which may be any of the apparatuses 100, 300 disclosed herein, including the diode and the rectifi er.

In the topmost example, a magnetic field 410 is generated for inducing spin-splitting at the super conductor. This magnetic field is an external magnetic field, so that it can be provided as a temporary, or a transient, magnetic field. It can be provided by a magnetic field generator, for example the one or more magnetic field generators as mentioned above, which may be part of the apparatus or separate from it. The spin-splitting facilitates the transport of electric current across the tunnel barrier 130 becoming direc tion-selective. As an example, the electric current may flow primarily in one direction when the magnetic field is present in contrast to flowing substantially in both directions when the magnetic field is absent. The magnetic field may be utilized as a switch for switching the apparatus between a direction-selective state and a non-direction selective-state. The appa ratus and the magnetic field generator may be config ured accordingly. The magnetic field may be generated substantially perpendicular to the flow direction of the electric current across the tunnel barrier.

In an embodiment of this example, the first conductor 110 or the second conductor 120 may be the superconductor. The other conductor of the first and the second conductor may be a magnetic conductor, such as a ferromagnetic conductor, which may be non superconducting, at least in the operating temperature of the apparatus 100, 300. The tunnel barrier 130 may comprise or consist of an insulator, which may be a non-magnetic insulator, such as a non-ferromagnetic insulator, for example when the magnetic conductor al ready provides the required spin-polarization for the transport across the tunnel barrier.

In the centermost example, the apparatus 100, 300 comprises one or more magnetic bodies 420, in par ticular ferromagnetic bodies, such as ferromagnetic insulators, coupled to the superconductor in the vi cinity of the tunnel barrier for inducing spin splitting at the superconductor. In the illustrated example, the first conductor 110 is the superconductor so the magnetic body may be coupled to the first con ductor. The bodies are separate from the tunnel barri er 130, which may also be magnetic or ferromagnetic, for example a ferromagnetic insulator, but does not necessarily need to be as the spin-splitting required for direction-selective current transport across the tunnel barrier may be induced solely by the magnetic body or bodies, even without an external magnetic field. The other conductor, illustrated as the second conductor 120, may be a magnetic conductor, such as a ferromagnetic conductor, so that tunneling across the tunnel barrier is spin-polarized regardless of whether the tunnel barrier is magnetic or non-magnetic.

In an embodiment of this example, the super conductor is arranged between the tunnel barrier 130 and the magnetic body or bodies 420. In an alternative or additional embodiment, the tunnel junction is ar ranged on top of the magnetic body or bodies. The mag netic body or bodies may also be arranged on top of the superconductor, in the vicinity of the tunnel bar rier for inducing the spin-splitting for the direc tion-selective transport of electric current across the tunnel barrier.

In the lowermost example, the tunnel barrier 130 comprises or consists of a magnetic insulator, such as a ferromagnetic insulator, for inducing spin splitting at the superconductor and spin-polarized tunneling across the tunnel barrier. The tunnel barri er can thus provide both the spin-splitting and spin- polarization necessary for the direction-selective transport of electric current across the tunnel barri er. In particular, the magnetic insulator may comprise or consist of EuS and/or EuO allowing simplified manu facturing and/or improved spin-polarization.

As a specific example of a material combina tion, where no external magnetic field is necessarily required, the first conductor 110 may be an A1 super conductor, the second conductor 120 a non ferromagnetic, non-superconducting Cu conductor and the tunnel barrier 130 a ferromagnetic EuS insulator. As another such example, the first conductor may be an A1 superconductor, the second conductor a ferromagnet ic, non-superconducting Co conductor and the tunnel barrier a non-ferromagnetic A10 _x insulator.

35 The physics yielding the direction-selective transport may be described as follows. They are here described in terms of being induced by the tunnel bar- rier being a (ferro)magnetic insulator, but may be correspondingly applied for any other ways of inducing the spin-splitting and spin-polarization as disclosed herein. The tunnel barrier, such as a layer of a fer- romagnetic insulator, can induce a spin-splitting en ergy (h) in the superconductor through interface ex change interaction. The material can simultaneously cause a spin-polarization, or spin-filtering, (P) across the junction. The former can yield an opposite energy shift for the density of states at the super conductor, which may be described by Bardeen-Cooper- Schrieffer density of states, of the two spin species (e.g. up and down), while the latter allows forming a tunneling barrier with different heights for the two spin species. This twofold effect can be probed exper imentally by measuring the differential conductance of the tunnel junction and leads to qualitative changes in the system's transport characteristics.

The spin-polarization (P) of the tunnel junc- tion, for example one having a (ferro)magnetic insula tor as the tunnel barrier and non-magnetic conductor as the other conductor, may be described, for example, by using a simple analytical model, which neglects spin-dependent scattering and orbital de-pairing. Within these approximations the electric current (I) tunneling across the junction may be simplified as a function of voltage (V) at temperature (T) in accord ance with the following expression, where ke repre sents the Boltzmann constant and e the elementary charge:

This equation is composed of two elements. The first one represents the Shockley ideal diode equation and dominates when P is close to unity. It describes the asymmetric I(V) curves characteristic of diodes. The second contribution is the first correction to an ide al diode due to the non-ideal spin polarization. This yields the simple result for the rectification, R=P tanh[eV/ (2ksT)]. The maximum rectification at |eV| > 2keT may hence be dictated by the spin-filtering effi ciency P.

The presence of the superconducting gap can be clearly recognized in a typical I(V) characteristic between the first terminal 140 and the second terminal 150 for the apparatus 100, as illustrated for example in Fig. la, with the absence of current flow at low bias, and an Ohmic behavior for relatively large volt age (eV~A and larger). In an intermediate voltage range, non-linearities and non-reciprocity may appear, which can become observable in the symmetric and anti symmetric parts of the I(V) characteristic. They may be defined as Is _y m= (I(V)+1(-V))/2 and iAnti- sym= (I(V)-I(-V))/2. The symmetric component Is _ym (V) can become sizable, suggesting an efficient charge recti fication, which may be equated with the capability to convert an AC input into a DC output signal. Rectifi cation (R) of a circuit can be defined as the ratio between the difference of the forward and backward current divided by the sum of the two,

R(V) V)) ⁼ ISym/IAntisym·

For an ideal rectifier R=l, while for R=0 no rectifi cation is present. In accordance with the present dis closure, a sizable rectification can be achieved in the intermediate voltage range (eV~A). In a specific example, where a strong asymmetry is induced by the spin filtering, R can be maximized at a voltage below IV, for example around 225 - 280pV. Correspondingly, the apparatus 100 as described herein may be specifi cally configured for operation at a specified voltage range, for example below IV. This range may be depend ent on the magnitude of the energy gap of the super conductor. For the apparatus 300 comprising the three terminals, as illustrated for example in Fig. 3a, the voltage generated across the tunnel barrier can be measured and represented by a symmetrized voltage V _sym , where the trivial Ohmic component originating in the first conductor may be discarded to emphasize the ef fect provided by the apparatus. A monotonic increase of Vsym(I _Bias ) is visible and more pronounced at large fields due to the larger h and P of the junction. No tably, a sizable transverse rectification can be made present also at zero magnetic field, for example by the (ferro)magnetic tunnel barrier. This characteris tic can be especially relevant for applications since no additional magnetic feed lines need to be integrat ed into the device. On the other hand, the spintronic nature of this effect can be confirmed for example by utilizing at an EuS tunnel barrier a coercive field (e.g. ~14 mT at base temperature) so that the recti fied signal is not visible.

In general, the other conductor, i.e. the conductor not the superconductor, may be a magnetic conductor, in particular a ferromagnetic conductor, for spin-polarizing tunneling across the tunnel barri er. In an embodiment, the solution may be configured for operation at a temperature range below the criti cal temperature of the superconductor, for example at a temperature below half the critical temperature (T _c /2). It has been found that the apparatus can thus be robustly used with no crucial degradation of recti fication.

Figure 5 shows an example of a method 500, which may be used for facilitating direction- selective, or primarily one-directional, conduction of electric current. The method comprises several parts which may be performed independently from each other and/or in any order. In particular, the method 500 comprises fa cilitating spin-splitting 510 at a superconductor and facilitating spin-polarization 520 for tunneling across a tunnel barrier. This can be done to facili tate 530 so that electric current across the tunnel barrier between a conductor and the superconductor flows in a direction-selective manner, or primarily in one direction. Any of the steps and/or apparatuses disclosed herein may be used in conjunction with the method.

The apparatuses disclosed herein may be con figured as nanoelectronics devices. They may be con figured for cryogenic operation. Similarly, the meth ods disclosed herein may be performed for nanoelec tronics circuits. They may be performed at a cryogenic temperature.

Advantageous effects may be obtained from the superconducting nature of the solutions. The solutions allow high energy efficiency in terms of heat dissi pated and absorbed energy, high operating frequency (for example up to one or more THz, e.g. 1-10 THz), compatibility with technologies based on superconduct ing materials and/or high integration potential. The solutions can be operated at cryogenic temperatures and they are therefore suitable for emerging cryogenic electronics and/or ultrasensitive detection. Moreover, operating temperature can be increased by using as the superconductor a superconductor with high critical temperature. The solutions may be operated without the use of an externally applied magnetic field. The solu tions may be utilized with detector or the apparatuses may be or comprise a detector having detector capabil ities such as sensitivities up to~2xl0 ³ A/W or better, for example, and/or noise equivalent power down to ~1x10 ¹⁹ W/ Hz or better, for example. The different functions discussed herein may be performed in a different order and/or concurrently with each other.

Any references to a current may be understood as references to an electric current.

Any range or device value given herein may be extended or altered without losing the effect sought, unless indicated otherwise. Also any example may be combined with another example unless explicitly disal lowed.

Although the subject matter has been de scribed in language specific to structural features and/or acts, it is to be understood that the subject matter defined in the appended claims is not neces sarily limited to the specific features or acts de scribed above. Rather, the specific features and acts described above are disclosed as examples of imple menting the claims and other equivalent features and acts are intended to be within the scope of the claims.

It will be understood that the benefits and advantages described above may relate to one embodi ment or may relate to several embodiments. The embod iments are not limited to those that solve any or all of the stated problems or those that have any or all of the stated benefits and advantages. It will fur ther be understood that reference to 'an' item may re fer to one or more of those items.

The term 'comprising' is used herein to mean including the method, blocks or elements identified, but that such blocks or elements do not comprise an exclusive list and a method or apparatus may contain additional blocks or elements.

Numerical descriptors such as 'first', 'sec ond', and the like are used in this text simply as a way of differentiating between parts that otherwise have similar names. The numerical descriptors are not to be construed as indicating any particular order, such as an order of preference, manufacture, or occur rence in any particular structure.

Although the invention has been described in conjunction with a certain type of apparatus and/or method, it should be understood that the invention is not limited to any certain type of apparatus and/or method. While the present inventions have been de scribed in connection with a number of examples, em- bodiments and implementations, the present inventions are not so limited, but rather cover various modifica tions, and equivalent arrangements, which fall within the purview of the claims. Although various examples have been described above with a certain degree of particularity, or with reference to one or more indi vidual embodiments, those skilled in the art could make numerous alterations to the disclosed examples without departing from the scope of this specifica tion.