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Merging Semiconductors and Superconductors

Postdoc-stipendium i Danmark | 01/09/2016

Often the performance of electrical devices is determined by the quality of interfaces between crystalline layers. In particular, the tremendous success of semiconductor technology is closely tied to the development of extraordinarily pure crystals and the invention of epitaxy which enables atomic-scale design of crystal interfaces and tailoring of electronic band structures, doping levels and strain. In 2011 I received a Postdoctoral Fellowship from the Carlsberg Foundation to pursue low-temperature investigations of electrical devices based on hybrids between superconductors and semiconductor nanowires. A key element of the proposal was a new idea of how to merge the superconductor with semiconductors; something which had been a considerable challenge in our earlier studies. This new concept was developed with collaborators from the Niels Bohr Institute, in particular Dr. P. Krogstrup, Dr. M.H. Madsen, Prof. E. Johnson, Prof. J. Nygård, and Prof. C. Marcus with additional support from the Danish Research Council and Microsoft. The approach turned out extremely successful and it enables atomic integration of superconducting and semiconducting crystals leading to greatly enhanced device performance. The present article summarises the results of the initial activities supported by the Carlsberg Foundation as well as the consequences for subsequent and ongoing research activities.

Introduction

Figure 1. Illustrations from the original proposal. (a) Schematic electrical device designed to investigate topologically protected Majorana states. The central, purple wire is the semiconductor nanowire core, coated with superconducting aluminum (grey). The current (I) flows from a normal metallic end-contact (biased at a voltage Vbias) to the wire and out through the shell. A voltage controlled (Vg) constriction can be tuned to provide a spectroscopic tunnel junction in the nanowire. The entire device is less than 3 micrometres in size. (c) Schematic illustration of the idea of coating the nanowire with a grown superconducting aluminum shell in order to avoid processing the semiconductor surface.

Figure 1 shows a schematic of the proposed electrical device from the original proposal. The project was a basic-research, curiosity-motivated attempt to engineer a new topological state of matter in a semiconductor/superconductor hybrid nanostructure [1,2]. Topological states of matter remain one of the most exciting areas of solid state physics both for fundamental reasons as well as from a long-term technology perspective as they may host exotic Majorana quasi-particles which have been proposed as robust building blocks of future quantum information processors. Such processors – which are at the heart of quantum technology – exploit quantum mechanics to perform calculations and hold the potential to revolutionise the world of computation by allowing extremely efficient algorithms and simulations of quantum mechanical systems, such as the functionality of complicated chemical compounds; pharmaceuticals, catalysts etc. of enormous importance to society. Such simulations are impossible on conventional computers that rely on classical physics.

The Soft-Gap” Problem

At temperatures of a few degrees above absolute zero, many metals turn superconducting; loosing electrical resistance, exhibiting perfect diamagnetism, and are characterised by a gap in their energy spectrum. It is a well-known phenomenon known as the proximity effect, that if a superconductor is brought into contact with a (non-superconducting) normal metal or semiconductor, part of the superconducting character – the energy gap - can be transferred for some distance into the other material (see fact box). Oreg and Lutchyn theoretically showed that hybrids of certain semiconductor nanowires with superconducting gaps induced from nearby superconductors can realise a peculiar topologically non-trivial band structure [1,2]. In 2012 the first experimental study was published [3] indeed showing the first evidence of the elusive Majorana particles in the electronic spectrum. Subsequently, a number of experiments were published [4,5,6], and common for all was a poor quality of the induced superconductivity: The induced gap was “soft” – that is, unlike the ideal case, a substantial amount of states were observed inside the gap. This posed a serious problem for the success of the Majorana states in quantum information processors, since their protection/robustness relies on a “hard” gap in the spectrum [7].

Epitaxial Matching of Semiconductors and Superconductors

Disorder at the semiconductor/superconductor interface was proposed as the origin of the soft gap. The fabrication of semiconductor devices with metallic contacts is common in the semiconductor industry and relies on standard techniques where the semiconductor surface is initially cleaned of oxides (Fig. 2). The cleaning is required to facilitate electrical contacts but as a result, a certain degree of disorder is inevitable. This is irrelevant for conventional devices using normal metal contacts. However, in the case of superconductors it turned out to be crucial for the quality of the induced superconductivity. The central idea of the project was to avoid the surface processing by performing crystal growth merging the semiconductor and the superconductor under ultra-high vacuum. With such an approach the entire semiconductor would be covered with superconductor and the challenge reversed, that is, to remove the superconductor where it was not desired (Fig. 3). Figure 4 shows a scanning electron microscope image of a typical device designed to allow a measurements of the induced gap. Fig. 5 shows an atomic-resolution electron microscope image of the semiconductor/superconductor interface in a grown nanowire hybrid. Not only is the interface completely free of disorder and oxides but atomic registry between the superconductor and the semiconductor is clearly seen. This is striking, as the two materials crystallise in different structures. However, in certain orientations – which are automatically realised in the crystal growth process which seeks a minimisation of the free energy – the two crystals are indeed matched at the interfaces, thus realising the ultimate limit of uniformity. Subsequent measurements of the induced gap confirmed that these hybrids indeed exhibited a hard gap induced in the semiconductor as shown in the fact box. The results were reported in two articles [8,9] and subsequent studies published showed that small segments of epitaxial hybrid nanowires exhibit favorable timescales relevant to quantum processing [10]. Finally, results confirming the presence of Majorana bounds states in the hybrids were published in Nature in 2016 [11]. The research is ongoing and continues to build on the semiconductor-superconductor epitaxial hybrids.

Applications in Technology

As mentioned, the research project was driven by curiosity of fundamental physics, however with long-term potential application for quantum information processors. There are a number of possible ways of implementing quantum bits and it is not clear if the Majorana particles in the hybrid semiconductor/superconductor nanowires will in the end turn out to be the most successful. However, while a working quantum computer capable of solving real problems does not lie around the corner, many of the enabling technologies are now being developed. Three patent applications have been filed through the University of Copenhagen to secure the IP of the semiconductor/superconductor technology.  The superconducting ground state provides a natural resource of quantum coherence which may also be used in other areas of quantum technologies, and the development and maturing of the epitaxial approach will be continued towards technology also within the framework of the new national Quantum Innovation Center (Qubiz).

About: The proximity induced gap

In a superconductor an attractive interaction between electrons leads to a condensed state of electron pairs – so called Cooper pairs. The density of states exhibits a gap around the Fermi level which can be experimentally verified by measuring the current between the superconductor and a weakly coupled electrode in the tunneling regime – such as the tip of a scanning tunneling microscope. The electrical conductance at a voltage V is then proportional to the density of states at the corresponding energy: see figure on the right. When the superconductor is brought in good electrical contact to a normal metal such as in the epitaxial InAs/aluminum nanowire hybrids, Cooper pairs can leak for some distance into the semiconductor. The process responsible for this transfer is known as Andreev reflection where an electron impinging from the normal metal on the superconductor is coherently reflected as a hole upon the creation of a Cooper pair in the superconductor. This transfer of Cooper pairs leads to superconductor-like properties in the semiconductor even though the electrons in the semiconductor do not feel an attractive potential. The device used to access the density of states (DOS) in the InAs/aluminum nanowire hybrids is shown in Fig. 4. Local electrical fields are used to tune the resistance of a small segment of InAs where the aluminum has been removed. In this way a contact is realised in the tunnel regime and the conductance reflects the DOS. The figure below shows representative results for an expitaxial hybrid device (epi) compared to the best result obtained using a superconductor deposited by standard evaporation (evap). The epitaxial contact clearly results in a much harder gap (i.e. no stated below the gap), while the evaporated contact leads to the problematic soft gap.

Understanding the details of the proximity effect is a rich problem involving the interplay of many energy and length scales (superconducting gap, Fermi energy, temperature, Thouless energy, coherence length of the superconductor, coherence length of the semiconductor, Fermi wavelength, mean-free path, dimensions of the involved materials etc.). It has been the focus of numerous experimental and theoretical treatments since the 1960s with renewed recent attention spurred by the relevance to the engineering topological phases. 


Thomas Sand Jespersen about the Support from the Carlsberg Foundation

The support from the Carlsberg Foundation provided the freedom to pursue fundamental, curiosity-driven research and is a good example of how such activities can lead to innovation, surprises and unanticipated applications in technology. The support was an important point early in the process of establishing an independent research profile.  

References

[1] Lutchyn, R. M., Sau, J. D. & Das Sarma, S. Phys. Rev. Lett. 105, 077001 (2010).
[2] Oreg, Y., Refael, G. & von Oppen, F. Phys. Rev. Lett. 105, 177002 (2010).
[3] Mourik, V. et al.  Science 336, 1003_1007 (2012).
[4] Das, A. Nature Phys. 8, 887_895 (2012).
[5] Deng, M. T. Nano Lett. 12, 6414_6419 (2012).
[6] Churchill, H. O. H. Phys. Rev. B 87, 241401 (2013).
[7] Stanescu, Lutchyn & Das Sarma, Phys. Rev. B 90, 085302 (2014)
[8] Krogstrup, P. et al., Nat. Mater 14, 400 (2015)
[9] Chang, W. et al.,  Nat. Nanotech. 10, 232 (2015)
[10] Higginbotham, A.P. et al., Nat. Phys. 11, 1017 (2015)
[11] Albrect S. et al., Nature 531, 206–209 (2016).