Patent Description:
By forming a network of such nanowires and inducing the topological regime in parts of the network, it is possible to create a quantum bit (qubit) which can be manipulated for the purpose of quantum computing. A quantum bit, or qubit, is an element upon which a measurement with two possible outcomes can be performed, but which at any given time (when not being measured) can in fact be in a quantum superposition of the two states corresponding to the different outcomes.

To induce an MZM the device is cooled to a temperature where the superconductor (e.g. Aluminium, Al) exhibits superconducting behaviour. The superconductor causes a proximity effect in the adjacent semiconductor, whereby a region of the semiconductor near the interface with the superconductor also exhibits superconducting properties. a topological phase behaviour is induced in the adjacent semiconductor as well as the superconductor. It is in this region of the semiconductor where the MZMs are formed.

Another condition for inducing the topological phase where MZMs can form is the application of a magnetic field in order to lift the spin degeneracy in the semiconductor. Degeneracy in the context of a quantum system refers to the case where different quantum states have the same energy level. Lifting the degeneracy means causing such states to adopt different energy levels. Spin degeneracy refers to the case where different spin states have the same energy level. Spin degeneracy can be lifted by means of a magnetic field, causing an energy level split between the differently spin-polarized electrons. This is known as the Zeeman effect. The g-factor refers to the coefficient between the applied magnetic field and the spin splitting. Typically, the magnetic field is applied by an external electromagnet. However, <CIT> has also disclosed a heterostructure in which a layer of a ferromagnetic insulator is disposed between the superconductor and semiconductor in order to internally apply the magnetic field for lifting the spin degeneracy, without the need for an external magnet. Examples given for the ferromagnetic insulator included compounds of heavy elements in the form of EuS, GdN, Y<NUM>Fe<NUM>O<NUM>, Bi<NUM>Fe<NUM>O<NUM>, YFeO<NUM>, Fe<NUM>O<NUM>, Fe<NUM>O<NUM>, GdN, Sr<NUM>CrReO<NUM>, CrBr<NUM>/CrI<NUM>, YTiO<NUM> (the heavy elements being Europium, Gadolinium, Yttrium, Iron, Strontium and Rhenium).

Inducing MZMs typically also requires gating the nanowire with an electrostatic potential. However, <CIT> has also disclosed a structure which is capable of exhibiting topological behaviour including MZMs without the need for gating. In this case the nanowires have a full shell of superconductor all the way around the perimeter of the nanowire, which obviates the need for gating.

As illustrated in <FIG>, in order to create good quality devices in which the MZMs are long-lived, it is preferable to have a large topological gap Eg. A material in the topological phase (whether a superconductor or a region of proximity-induced superconductivity in a semiconductor) exhibits distinct energy bands: a lower band <NUM> and an upper band <NUM>. The lower band <NUM> is a band where the quasiparticle energy E falls in a lower range, and the upper band (or "excitation band") <NUM> is a band of higher quasiparticle energy. The topological gap Eg is an energy window between the upper and lower bands <NUM>, <NUM> where no quasiparticles can exist due to the quantized (discrete) nature of the quasiparticle energy levels. The lower band <NUM>, upper band <NUM> and topological gap Eg are analogous to the valence band, conduction band and band gap for electrons in a semiconductor. In the upper, excitation band <NUM> the quasiparticles can propagate freely through the superconductor (or proximity-induced region in a semiconductor), analogous to the electrons in the valence band in a semiconductor.

The Majoranas, whose states form the MZMs, form the lower band <NUM>. The Majoranas are part of the computational space, i.e. the properties of the system being exploited for the quantum computing application in question. In other words, the MZMs are the operating elements of the qubit. On the other hand, the particle-like excitations (quasiparticles) in the upper band <NUM> are not part of the computational space. If these quasiparticles cross the topological energy gap Eg into the lower band <NUM> due to thermal fluctuations, then they will destroy at least some of the MZMs. This is sometimes referred to as "poisoning" the MZMs. The gap Eg provides protection for the MZMs against such poisoning. The probability of a quasiparticle existing in the upper band and crossing the gap Eg from the upper to the lower band is proportional to e-Eg/kT where T is temperature and k is the Boltzmann constant. Hence the larger the topological gap, the more protection is afforded to the MZMs against poisoning from the harmful quasiparticles in the upper band <NUM>.

A more detailed treatment of the theory of operation of semiconductor-superconductor hybrid devices is provided by <NPL>)) and <NPL>)). <CIT> describes that, for the purpose of increasing the quantization unit of conductance of a propagation channel which changes discontinuously due to quantization for the continuous change in the gate voltage of a quantization point contact element and to control the quantization unit of conductance, a drain electrode is constituted by a superconductor and the distance between the drain electrode and a split type metal electrode is reduced as compared with the mean free path of a two-dimensional electron gas, and an electrode for applying magnetic field is formed on the drain electrode via an insulation film. <NPL>, describes fabrication of submicron-gate superconducting junctions coupled with an InAs channel inserted in an InAlAs/InGaAs heterostructure. <NPL>, describes that the coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconducting circuits, from setting qubit transition frequencies and interqubit coupling strengths, to the gain of parametric amplifiers for quantum-limited readout. The inductance is either set by tailoring the metal-oxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices (SQUIDs) with local current-biased flux lines. JJs based on superconductor-semiconductor hybrids represent a tantalizing all-electric alternative. The gatemon is a recently developed transmon variant which employs locally gated nanowire (NW) superconductor-semiconductor JJs for qubit control. <NPL> describes that nanowires can serve as flexible substrates for hybrid epitaxial growth on selected facets, allowing for design of heterostructures with complex material combinations and geometries. In this work the authors report on hybrid epitaxy of semiconductor - ferromagnetic insulator - superconductor (InAs/EuS/Al) nanowire heterostructures. The authors study the crystal growth and complex epitaxial matching of wurtzite InAs / rock-salt EuS interfaces as well as rock-salt EuS / face-centered cubic Al interfaces. Because of the magnetic anisotropy originating from the nanowire shape, the magnetic structure of the EuS phase are easily tuned into single magnetic domains. This effect efficiently ejects the stray field lines along the nanowires. With tunnel spectroscopy measurements of the density of states, the authors show the material has a hard induced superconducting gap, and magnetic hysteretic evolution which indicates that the magnetic exchange fields are not negligible. These hybrid nanowires fulfil key material requirements for serving as a platform for spin-based quantum applications, such as scalable topological quantum computing. <CIT> describes that a mixed semiconductor-superconductor platform is fabricated in phases. In a masking phase, a dielectric mask is formed on a substrate, such that the dielectric mask leaves one or more regions of the substrate exposed. In a selective area growth phase, a semiconductor material is selectively grown on the substrate in the one or more exposed regions. In a superconductor growth phase, a layer of superconducting material is formed, at least part of which is in direct contact with the selectively grown semiconductor material. The mixed semiconductor- superconductor platform comprises the selectively grown semiconductor material and the superconducting material in direct contact with the selectively grown semiconductor material.

It would be desirable to provide a semiconductor-superconductor hybrid device with a large topological gap, more particularly a topological gap which is as close as possible to the theoretical limit. It would also be desirable to provide a semiconductor-superconductor hybrid device with improved tolerance to manufacturing variations.

A semiconductor-superconductor hybrid device comprises a semiconductor layer and a superconductor layer. The superconductor layer is arranged over an edge of the semiconductor layer so as to enable energy level hybridisation between the semiconductor layer and the superconductor layer. The semiconductor layer is arranged in a sandwich structure between first and second insulating layers, each insulating layer being in contact with a respective opposed face of the semiconductor layer. This configuration may allow for good control over the geometry of the semiconductor layer and may improve tolerance to manufacturing variations. The device may be useful in a quantum computer. Also provided is a method of manufacturing the device, and a method of inducing topological behaviour in the device.

Nor is the claimed subject matter limited to implementations that solve any or all of the disadvantages noted herein.

To assist understanding of embodiments of the present invention and to show how such embodiments may be put into effect, reference is made, by way of example only, to the accompanying drawings in which:.

<FIG> are schematic, and are not to scale. The relative proportions of components shown in these Figs. may be exaggerated for ease of representation.

As used herein, the verb 'to comprise' is used as shorthand for 'to include or to consist of'. In other words, although the verb 'to comprise' is intended to be an open term, the replacement of this term with the closed term 'to consist of' is explicitly contemplated, particularly where used in connection with chemical compositions.

Directional terms such as "top", "bottom", "left", "right", "above", "below", "horizontal" and "vertical" are used herein for convenience of description and relate to the semiconductor-superconductor hybrid device in the orientation shown in <FIG>. For the avoidance of any doubt, this terminology is not intended to limit the orientation of the device in an external frame of reference.

As used herein, the term "superconductor" refers to a material which becomes superconductive when cooled to a temperature below a critical temperature, Tc, of the material. The use of this term is not intended to limit the temperature of the device.

A "nanowire" as referred to herein is an elongate member having a nano-scale width, and a length-to-width ratio of at least <NUM>, or at least <NUM>, or at least <NUM>. A typical example of a nanowire has a width in the range <NUM> to <NUM>, optionally <NUM> to <NUM> or <NUM> to <NUM>. Lengths are typically of the order of micrometers, e.g. at least <NUM>, or at least <NUM>. In the present context, the nanowires are typically formed of a semiconductor material.

The term "coupling" in the context of the present disclosure refers in particular to the hybridisation of energy levels.

A first example of a semiconductor-superconductor hybrid device <NUM> will now be explained with reference to <FIG>.

The semiconductor-superconductor device <NUM> includes a semiconductor layer <NUM> and a superconductor layer <NUM>. The semiconductor layer has an edge <NUM> and two opposed faces. The edge <NUM> of the semiconductor layer <NUM> is, in this example, in direct contact with the superconductor layer <NUM>. At least when the device is in use, there is energy level hybridisation between the semiconductor layer <NUM> and the superconductor layer <NUM> in a region near the edge <NUM>.

Semiconductor layer <NUM> in the present example is a layer of a material having the general formula:.

where x is in the range <NUM> to <NUM>. In other words, semiconductor layer <NUM> may comprise indium antimonide (x=<NUM>), indium monoarsenide (x=<NUM>), or a ternary mixture comprising <NUM>% indium on a molar basis and variable proportions of arsenic and antimony (<NUM> <x < <NUM>).

Indium monoarsenide, InAs, has been found to have good handling properties during manufacture of the device, and provides devices with good performance. Indium antimonide, InSb, provides further improvements to device performance but may be more difficult to use during manufacturing processes. The ternary mixtures have intermediate properties between those of the binary compounds InAs and InSb. Improvements in device performance compared to InAs may be observed when x is in the range <NUM> to <NUM>, or <NUM> to <NUM>. Values of x in the range <NUM> to <NUM> may provide a particularly good balance of device performance and handling properties. The present example uses indium antimonide as the semiconductor layer <NUM>.

The semiconductor layer <NUM> has a thickness d in the range <NUM> to <NUM>. Increases in topological gap are observed when using semiconductor layers within thicknesses within this range. Without wishing to be bound by theory, the inventors believe that varying the thickness d may vary the number of occupied energy levels ("sub-bands") and the degree of hybridisation between the semiconductor layer <NUM> and the superconductor layer <NUM>.

In the present example, superconductor layer <NUM> is a layer of aluminium. Winkler et al (cited above) report that aluminium couples strongly to InAs and InSb, and that the strength of the coupling may vary depending on the thickness of the superconductor layer. The thickness may be in the range <NUM> to <NUM>, for example.

The semiconductor-superconductor hybrid device <NUM> further includes a first insulating layer 16a and a second insulating layer 16b. The first and second insulating layers 16a, 16b are arranged to sandwich the semiconductor layer <NUM>. First insulating layer 16a extends from a substrate <NUM> on which the device is arranged. In this example, the first insulating layer 16a is formed integrally with the substrate <NUM>. Second insulating layer 16b is arranged as a cap, covering the semiconductor layer <NUM>. The first insulating layer 16a, second insulating layer 16b and semiconductor layer <NUM> are referred to collectively herein as a sandwich structure.

The first insulating layer 16a spaces the semiconductor layer <NUM> away from the substrate 16a, and away from bottom corners 26a, 26b between the device and substrate <NUM>. Second insulating layer 16b spaces the semiconductor layer away from the top surface and corners of the device.

In the present example, first and second insulating layers are formed of indium phosphide. Indium phosphide is a semiconductor material, but its semiconducting properties are not used in the context of the present device. Rather, the indium phosphide serves as an insulator. Indium phosphide has a high band gap. There is a large difference in energy between the conduction band of semiconductor layer <NUM> and the conduction band of indium phosphide. When the device is in use, electrons are trapped in semiconductor layer <NUM> and do not escape into the insulating layers 16a, 16b.

Other illustrative materials useful for forming the first and second insulating layers are those of the formula InAlxAs<NUM>-x where x is at least <NUM>, for example where x is in the range <NUM> to <NUM>. A still further class of illustrative materials are those of the formula InGaxAs<NUM>-x where x is at least <NUM>, for example where x is in the range <NUM> to <NUM>.

In the present example, the substrate <NUM> is formed of indium phosphide.

The semiconductor layer <NUM> and the superconductor layer <NUM> are the active, working portions of the device at which useful excitations (such as Majorana zero modes) are induced during operation. The tops and comers of semiconductor devices in general are difficult to manufacture reproducibly. Small variations in device structure may be present in these areas. Likewise, the substrate surface may have small variations. Spacing the active semiconductor layer away from the areas which are difficult to reproduce may make it easier to manufacture devices consistently. Provided that the thickness d and the edge <NUM> of the device are well-controlled, larger manufacturing variations in other parts of the semiconductor structure may be well tolerated.

The first and second insulating layers 16a, 16b may also serve to trap electrons in the semiconductor layer. This may improve the lifetime of the useful excitations when the device is in use.

The device <NUM> further comprises a protective layer <NUM> arranged over the top and a side of the sandwich structure. This layer may protect the device from oxidation, particularly during manufacturing processes. The protective layer <NUM> may serve as an electrical insulator for preventing flow of current from gate electrode <NUM> into the device. The material which forms the protective layer <NUM> is not particularly limited, and may be any of the various protective materials known in the field of semiconductor manufacture. Protective layer <NUM> is typically of an oxide, such as hafnium oxide.

In the illustrated example, protective layer <NUM> covers only part of the device. In variants, a protective layer may cover the entirety of the device.

A gate electrode <NUM> is provided over a side of the sandwich structure, including a second edge of the semiconductor layer <NUM>. The gate electrode <NUM> is spaced from the semiconductor layer <NUM> by protective layer <NUM>. In this way, the protective layer <NUM> prevents or reduces current leakage from the gate electrode <NUM> into the semiconductor layer <NUM>.

The gate electrode <NUM> may be formed of any suitable material. The gate electrode is typically not superconductive. The gate electrode may be of gold, or a gold-titanium alloy, for example.

Arranging the gate electrode <NUM> over the side and/or top of the sandwich structure, referred to herein as a "side-gated semiconductor-superconductor hybrid device" or a "top-gated semiconductor-superconductor hybrid device", respectively, may make the device easier to manufacture in comparison with the case where the gate electrode is arranged below the substrate <NUM> (a "bottom-gated semiconductor-superconductor hybrid device").

In the example illustrated in <FIG>, gate electrode <NUM> is depicted as being over the sandwich structure. However, the gate electrode <NUM> may be spaced from the sandwich structure by an air gap. The air gap, if present, may help to prevent flow of current from the gate electrode to the semiconductor and superconductor components.

Gate electrode <NUM> is for applying an electrostatic field to the semiconductor layer <NUM>. Providing such gating allows for control over the degree of energy level hybridization between the semiconductor and superconductor. This may be useful for inducing excitations in the device. The configuration of the gate electrode is not particularly limited provided that the gate electrode is capable of gating the device.

<FIG> further shows a mask layer <NUM> arranged on the substrate <NUM>. The present device may be manufactured using selective area growth. Such methods may involve the use of a mask during manufacture of a device. The mask may remain present in the finished device.

An embodiment of a semiconductor-superconductor hybrid device <NUM> according to the present invention will now be described in terms of its differences to the first example and with reference to <FIG>.

The embodiment differs from the first example in that it is a bottom-gated semiconductor-superconductor hybrid device. In this arrangement, a gate electrode <NUM> is arranged below the substrate <NUM> and first insulating layer 16a. The substrate <NUM> and first insulating layer 16a provide electrical insulation between the gate electrode <NUM> and the semiconductor layer <NUM>. In the embodiment, the protective layer <NUM> which was present in the first example is omitted although in variants a protective layer may be provided over all or part of the top surface of the device.

The <FIG> device further includes a ferromagnetic insulator layer <NUM> arranged between the semiconductor layer. The ferromagnetic insulator layer may be as described in <CIT>. The ferromagnetic insulator layer may be a layer of a material selected from EuS, GdN, Y<NUM>Fe<NUM>O<NUM>, Bi<NUM>Fe<NUM>O<NUM>, YFeO<NUM>, Fe<NUM>O<NUM>, Fe<NUM>O<NUM>, GdN, Sr<NUM>CrReO<NUM>, CrBr<NUM>/CrI<NUM>, and YTiO<NUM>. The ferromagnetic insulator layer is configured to apply a magnetic field to the semiconductor and the superconductor.

<FIG> illustrate the effects of varying the thickness d of the semiconductor component of the devices provided herein.

<FIG> is a plot showing the calculated topological gap in µeV as a function of semiconductor layer thickness for a conceptual example device having a band offset between the conductance band of the semiconductor and that of the insulating layers is <NUM> meV and the alpha value (a measure of spin-orbit coupling strength, see Stanescu et al and Winkler et al) is <NUM> eV nm. In this example, the greatest topological gap is achieved for a semiconductor layer thickness of <NUM>. Thus, the topological gap may be optimized by selecting the semiconductor layer thickness.

Illustrative examples of materials for forming an insulating layer which may provide a band offset of at least <NUM> meV to an InAs semiconductor include materials selected from: (i) indium phosphide; (ii) a material of formula InAlxAs<NUM>-x where x is at least <NUM>, e.g. in the range <NUM> to <NUM>; and (iii) InGaxAs<NUM>-x where x is at least <NUM>, e.g. in the range <NUM> to <NUM>.

<FIG> is a plot of the number of occupied states against applied gate voltage for devices having varying semiconductor layer thicknesses. This plot shows that the applied gate voltage controls the degree of hybridization between the semiconductor and the superconductor. It is further illustrated that the number of occupied energy states in the device varies depending on the thickness of the semiconductor layer. For example, at a gate voltage V_gate of <NUM> V, more energy states are occupied in a device having a <NUM> semiconductor layer (dashed-and-dotted line) compared to a device having a <NUM> semiconductor layer (dashed line) or a device having a <NUM> semiconductor layer (solid line).

<FIG> is a set of heat maps illustrating the topological gap as a function of the band offset and alpha value for devices having semiconductor layer thicknesses of <NUM>, <NUM>, and <NUM>, respectively. These Figs. show that the semiconductor layer thickness for obtaining the maximum topological gap varies depending on the properties of the materials selected. For a given value of alpha, when the band offset is large (e.g., greater than <NUM> meV), a thinner semiconductor layer may be preferred (see <FIG>), whereas thicker semiconductor layers may be preferable for smaller band offsets (see <FIG>).

<FIG> is a flowchart outlining steps of an illustrative method for manufacturing a semiconductor-superconductor hybrid device as described herein.

The method generally comprises manufacturing the sandwich structure, and then forming the superconductive components. At block <NUM>, a first insulating layer is formed. At block <NUM>, a semiconductor layer is formed on the first insulating layer. At block <NUM>, a second insulating layer is formed on the semiconductor layer. At block <NUM>, a superconductor is formed over an edge of the semiconductor layer so as to enable energy level hybridisation between the semiconductor layer and the superconductor layer. Additional components may be formed between any of steps <NUM> to <NUM>, or in subsequent steps.

The specific techniques used to form the various components are not particularly limited, and may be selected as appropriate. Various suitable techniques will be known to the person skilled in the art. Examples include selective area growth; chemical vapour deposition; lithography; and the like. Techniques which result in epitaxial growth of components may allow for good contact between those components, and may be preferred.

<FIG> is a flowchart outlining an illustrative method of using a semiconductor-superconductor hybrid device as provided herein.

Use of the device typically involves inducing topological behaviour, i.e., a particular type of electron excitation, into the device. This is made possible by energy level hybridisation between the semiconductor and the superconductor, creating bands which have a mixture of semiconducting and superconducting character. Hybridisation may also be referred to as "coupling" in the context of the present disclosure. Such excitations may be useful in quantum computing. For example, they may be used to encode a quantum bit (also referred to as a qubit). Without wishing to be bound by theory, it is believed that the semiconductor-superconductor hybrid devices provided herein generate Majorana zero modes.

At block <NUM>, the semiconductor-superconductor hybrid device is cooled to a temperature at which the superconductor layer is superconductive. Put differently, the device is cooled to a temperature below the critical temperature Tc of the superconductor layer such that the layer displays superconductive behaviour (e.g., behaves as if it has zero resistance). Such temperatures are generally of the order of tens of Kelvin or less. Tc depends on the material used, and may in certain cases be influenced by the thickness of the material. The temperature may be selected as appropriate.

At block <NUM>, a magnetic field is applied to the semiconductor layer. The magnetic field lifts spin degeneracy in the device, thereby changing the energy band structure at the interface between the semiconductor and the superconductor. The magnetic field may be applied externally, for example using an electromagnet. Alternatively, in embodiments of the invention where the semiconductor-superconductor hybrid device includes a ferromagnetic insulator layer as described above, the magnetic field is the magnetic field of the ferromagnetic insulator layer.

At block <NUM>, an electrostatic field is applied to the semiconductor layer. Typically, the semiconductor-superconductor hybrid device includes a gate electrode, and the gate electrode is used to apply the electrostatic field. In alternatives, the electrostatic field may be externally applied. The electrostatic field may vary the degree of energy level hybridisation between the semiconductor and the superconductor. For example, hybridisation may be decreased when electrons are drawn away from the superconductor by the electrostatic field. This may make the low-energy states - i.e., the states of interest - more susceptible to the magnetic field. This may in turn allow a topological phase at smaller magnetic fields, leading to enhanced properties for quantum computation.

It will be appreciated that the above examples and embodiments have been described by way of example only.

More generally, according to one aspect disclosed herein, there is provided a semiconductor-superconductor hybrid device comprising: a semiconductor layer; and a superconductor layer; wherein the superconductor layer is arranged over an edge of the semiconductor layer so as to enable energy level hybridisation between the semiconductor layer and the superconductor layer; wherein the semiconductor layer is arranged in a sandwich structure between first and second insulating layers, each insulating layer being in contact with a respective opposed face of the semiconductor layer. The first and second insulating layers space the semiconductor layer away from corners of the device, and from the surface of any underlying substrate. This may improve the tolerance of the device to manufacturing variations, because the working semiconductor part of the device is remote from portions of the device which are more difficult to manufacture reliably. It may be possible to control precisely the thickness of the semiconductor layer. This may allow control over the number of sub-bands in the device.

The semiconductor-superconductor hybrid device may further comprise a gate electrode for applying an electrostatic field to the semiconductor layer. The structure of the gate electrode is not particularly limited. Examples of materials for forming a gate electrode include those selected from gold, and alloys of gold e.g. gold titanium.

The device may be a side-gated superconductor-semiconductor device. For example, the gate electrode may be arranged over a second edge of the semiconductor layer, and the gate electrode may be spaced from the semiconductor layer by a gate insulating layer for preventing a flow of current from the gate electrode to the semiconductor layer. Side-gated devices may be easier to manufacture than bottom-gated devices. The nature of the insulating layer is not particularly limited provided that it restricts current leakage from the gate electrode to the semiconductor layer. Usefully, the insulating layer may also be configured to protect the device from oxygen and/or water vapour. The insulating layer may comprise an oxide, e.g. hafnium oxide. A top-gated arrangement, in which the gate electrode is arranged over the second insulating layer, is also possible.

Alternatively, the semiconductor-superconductor hybrid device may be bottom-gated. In other words, the gate electrode may be arranged below the first insulating layer. In such an arrangement, a separate gate insulating layer is not necessarily required.

Any of the devices provide herein may include a protective oxide layer, e.g. of hafnium oxide, for protecting one or more parts of the device from water vapour and/or oxygen.

The first insulating layer may extend from a surface of a substrate. For example, the first insulating layer may be formed integrally with the surface of the substrate. In such configurations the first insulating layer spaces the semiconductor layer away from the surface of the substrate and away from corners wherein the substrate meets the first insulating layer. This may allow for improved reproducibility of the semiconductor layer during manufacturing, because corners and/or substrate surfaces may be difficult to reproduce precisely.

The thicknesses of the first and second insulating layer may be independently selected as appropriate. The thickness of each insulating layer may be at least <NUM>, for example, from <NUM> to <NUM>, or <NUM> to <NUM>.

The semiconductor layer may have a thickness in the range <NUM> to <NUM>, optionally <NUM> to <NUM>, further optionally <NUM> to <NUM>. Varying the thickness of the semiconductor layer may vary the number of occupied energy levels (sub-bands) at the interface between the semiconductor and the superconductor. This is useful for tuning the quantum mechanical behaviour of the device.

The thickness of semiconductor layer may be optimised based on the properties of the materials selected to maximize the topological gap. In one particular example where the band offset between the conductance band of the semiconductor and that of the insulating layers is about <NUM> meV and the alpha value for the device is <NUM> eV nm, a semiconductor layer thickness in the range <NUM> to <NUM>, optionally in the range <NUM> to <NUM>, or of about <NUM>, are particularly preferred. Simulation is one useful method for determining an optimum semiconductor layer thickness for a given device. For example, these ranges may be particularly applicable to arrangements where the semiconductor layer comprises a material of Formula <NUM> (below), more particularly when the semiconductor layer comprises InAs; and where the first and second insulating layers are of a material selected from: (i) indium phosphide; (ii) a material of formula InAlxAs<NUM>-x where x is at least <NUM>, e.g. in the range <NUM> to <NUM>; and (iii) a material of formula InGaxAs<NUM>-x where x is at least <NUM>, e.g. in the range <NUM> to <NUM>.

The semiconductor layer may comprise a material of Formula <NUM>:.

where x is in the range <NUM> to <NUM>, for example in the range <NUM> to <NUM>, more particularly <NUM> to <NUM>. The material may be InAs, InSb, or a ternary mixture of In, As and Sb. InAs has good handling properties during manufacture. InSb has excellent electronic properties, e.g. couples particularly well to certain semiconductors, such as Al, but may be more difficult to use in manufacture. Alloys of InAs and InSb have properties in between those of InAs and InSb.

More generally, the principles of the disclosed technology may be applied to any semiconductor, in particular III-V semiconductors.

The first and second insulating layers may be a semiconductor material, the semiconductor material of the first and second insulating layers having a conductance band with an energy level that is at least <NUM> meV higher, preferably <NUM> meV higher, more preferably at least <NUM> meV higher, than a conductance band of a semiconductor material of the semiconductor layer. It may be convenient to use a high band gap semiconductor as the first and second insulating layers. If the conductance band of the material of the insulating layers is at least <NUM> meV higher than that of the semiconductor layer, flow of electrons from the semiconductor layer to the insulating layer may be prevented.

The first and second insulating layers may be each of a material selected from: indium phosphide, gallium antimonide, indium gallium arsenide, and indium aluminium arsenide. In particular examples, indium phosphide, InP, is used as the insulating material.

Certain examples of materials useful as first and second insulating layers include those of Formula II:.

where x is at least <NUM>, for example when x is in the range <NUM> to <NUM>.

Additional examples of indium gallium arsenide materials useful as first and second insulating layers are those of Formula III:.

where x is at least <NUM>, e.g. in the range <NUM> to <NUM>.

The nature of the superconductor is not particularly limited, and may be selected as appropriate. The superconductor is typically an s-wave superconductor. Any of the various s-wave superconductors known the art may be used. Examples include aluminium and lead, with aluminium being preferred.

The thickness of the superconductor may likewise be selected as appropriate. An illustrative thickness range is <NUM> to <NUM>.

In an example, the semiconductor layer is of a material of Formula <NUM>, preferably InSb, and the first and second insulating layers are of a material selected from indium phosphide, indium gallium arsenide (e.g., an indium gallium arsenide of Formula III), and indium aluminium arsenide (e.g. an indium aluminium arsenide of Formula II), preferably indium phosphide. In this example, the superconductor is preferably aluminium.

In another example, the semiconductor material is InAs and the first and second insulating layers are of a material selected from indium phosphide, indium gallium arsenide (e.g., an indium gallium arsenide of Formula III), and indium aluminium arsenide (e.g., an indium aluminium arsenide of Formula II), preferably indium phosphide. In this example, the superconductor is preferably aluminium.

In another example, the semiconductor layer is of a material of Formula <NUM>, and the insulating layers are of gallium antimonide, GaSb.

The semiconductor-superconductor hybrid device may further comprise a layer of a ferromagnetic insulator arranged between the superconductor and the semiconductor. Examples of suitable ferromagnetic insulators include materials selected from EuS, GdN, Y<NUM>Fe<NUM>O<NUM>, Bi<NUM>Fe<NUM>O<NUM>, YFeO<NUM>, Fe<NUM>O<NUM>, Fe<NUM>O<NUM>, GdN, Sr<NUM>CrReO<NUM>, CrBr<NUM>/CrI<NUM>, and YTiO<NUM>. Uses of the device typically include applying a magnetic field to the semiconductor layer. The inclusion of a ferromagnetic insulator may avoid the need to apply the magnetic field using an external apparatus.

The semiconductor-superconductor hybrid devices provided herein may be configured as nanowires. The semiconductor-superconductor hybrid devices provided herein may be incorporated into a quantum computer device.

It is to be understood that the above-described features may be used in any combination.

Also provided herein is a method of manufacturing a semiconductor-superconductor hybrid device, which method comprises: forming a first insulating layer; forming a semiconductor layer on the first insulation layer; forming a second insulating layer on the semiconductor layer; and forming a superconductor layer over an edge of the semiconductor layer so as to enable energy level hybridisation between the semiconductor layer and the superconductor layer. Since the semiconductor layer is spaced away from corners and the top and bottom of the device, better control over the geometry of the semiconductor layer may be achieved. This may improve the reliability of the method.

The specific techniques used to form the various components may be selected as appropriate. For example, at least one of the first insulating layer, the second insulating layer, and the semiconductor layer may be formed by selective area growth. Selective area growth, and other techniques involving epitaxial crystal growth, allow very close contact between components. In the case of the semiconductor and superconductor, epitaxial growth may allow for improved energy level hybridisation.

The method may further comprise forming any of the various additional components described above with reference to the device. For example, the method may further comprise forming a gate electrode for applying an electrostatic field to the semiconductor layer.

The semiconductor layer may have a thickness in the range <NUM> to <NUM>. As described above, thicknesses in this range allow for control over the number of occupied bands when the device is in use.

The semiconductor layer may comprise a material of general formula:.

where x is in the range of <NUM> to <NUM>. The first and second insulating layers may each be of a material selected from: indium phosphide, indium gallium arsenide, and indium aluminium arsenide. More generally, it is to be understood that the method may be practiced using any of the various materials (or combinations of materials) described above with reference to the device.

Further provided is a method of inducing topological behaviour in a semiconductor-superconductor hybrid device as provided herein, which method comprises: cooling the semiconductor-superconductor hybrid device to a temperature at which the superconductor layer is superconductive; applying a magnetic field to the semiconductor layer and the superconductor layer; and applying an electrostatic field to the semiconductor layer. The method may comprise inducing an anyon, especially a Majorana zero mode, in the semiconductor-superconductor hybrid device. Without wishing to be bound by theory, a device as provided herein may be capable of generating a Majorana zero mode. The device may be useful in a quantum computer, more particularly a topological quantum computer.

Claim 1:
A semiconductor-superconductor hybrid device (<NUM>) comprising:
a semiconductor layer (<NUM>); and
a superconductor layer (<NUM>);
wherein the superconductor layer (<NUM>) is arranged over an edge (<NUM>) of the semiconductor layer (<NUM>) so as to enable energy level hybridisation between the semiconductor layer (<NUM>) and the superconductor layer (<NUM>);
wherein the semiconductor layer (<NUM>) is arranged in a sandwich structure between first and second insulating layers (16a, 16b), each insulating layer (16a, 16b) being in contact with a respective opposed face of the semiconductor layer (<NUM>),
characterised in that the semiconductor-superconductor hybrid device (<NUM>) further comprises a layer of a ferromagnetic insulator (<NUM>) arranged between the superconductor layer (<NUM>) and the semiconductor layer (<NUM>).