Advances in epitaxial growth of high-quality low-dimensional strained germanium semiconductor structures in recent years have opened up options for studies of these systems that previously were not possible. Maksym Myronov, who led these fabrication advances at Warwick University, Michael Pepper, and colleagues in the UK have seized the opportunity to study the transport behaviour of holes when loosely confined to one dimension (1D). To their great surprise they observed fractional quantized conductance for the first time ever in the absence of strong magnetic fields.
“We’d been looking at electrons for a long time so we thought let’s see if there’s any difference between holes and electrons,” says Pepper, a researcher at University College London (UCL) who pioneered the study of low-dimensional electron gas systems and associated quantum effects. He had been studying electron transport in two-dimensional (2D) systems as they were gradually confined to 1D for several years with Sanjeev Kumar, also at UCL, before turning his attention to the transport of holes – corresponding positive charges where an electron is absent.
At the same time their colleague Maksym Myronov at Warwick University had been perfecting one of the epitaxial growth techniques to create high-quality epitaxial semiconductor materials, including germanium, which had previously been out of reach. Myronov was working with Stuart Holmes at Toshiba Research Europe at Cambridge Research Laboratory to examine the potential of holes in germanium for developing new spintronics systems.
As their interests aligned, Pepper, Kumar, Myronov and Holmes joined forces alongside Yilmaz Gul, who was studying for his PhD with Holmes and Pepper. “We thought we’d see the regular quantization, but we hadn’t expected to see any fractions, because they had not been seen before in any system, unless of course you apply a very strong magnetic field,” explains Pepper.
The researchers studied epitaxial germanium grown on silicon, which makes it strained. They used split gates to confine the hole transport to 1D and gradually relaxed this confinement to allow some lateral drift so that a zig zag developed as opposed to a straight line of transport. With high confinement from the split gates, they measured hole conductance values in regular integers of the quantum unit 2e2/h – where e is the charge of an electron or hole, and h is Planck’s constant. This matched with the behaviour they had observed in studies of 1D electron conductance in other semiconductors such as GaAs. However, to their great surprise, as the confinement was weakened they found conductance values at 1/2, 1/4 and 1/32 of 2e2/h.
Quantized conductance – fractionalized
The first observations of fractional quantum conductance date back to 1982 with the fractional quantum Hall effect. However, this only occurs in the presence of a very high magnetic field, and there have been no observations of fractional quantum conductance besides this effect. In the experiments by Pepper and colleagues’ there is no large applied magnetic field, and the cause of the fractional quantization remains a mystery. The researchers are liaising with theorists to find an explanation.
“It is interesting to note, that so far, the fractional quantum Hall effect has been observed only in 2D systems made of semiconductor and oxide materials,” says Myronov. He adds, referring to work reported in one of his recent papers, “Just recently, in 2015, I and some colleagues observed this effect in superior quality strained germanium that I had grown epitaxially, which outlined the pathway to our latest discovery.”
As for explanations of the effect, Pepper describes some of the approaches to explore. “One is to look at extensions to the theory of the fractional quantum Hall effect, but without the magnetic field; others start from the formation of the zig zag and then seeing what happens when you add various interactions into that – but so far no explanation has emerged.”
Gul, for whom the observations formed the basis of his PhD thesis laughs at how in some ways it was an easy thesis to defend. “I didn’t have to learn any theories because there weren’t any.”
Applications and further work
The effect may find applications in quantum computing where the silicon substrate for the germanium hole wire may have advantages for integrating with silicon electronics processes and systems. Although to see the quantized conductance it is important that the germanium is high purity, as Holmes points out “The states that we observe are naturally protected from the environment, so things like disorder and impurity scattering may not be important. That would mean that you could have slightly impure materials that you might find more in industry – companies like Toshiba would be interested in developing that kind of technology.”
Myronov adds that although in the fractional quantum Hall effect there is no direct observation of a quarter charge, there is indirect evidence that it exists, and theory suggests that it can be very strongly coherent and difficult to decohere. This means that if it were carrying quantum information it would be much more difficult to corrupt than in other types of qubit. “There is of course a very long way to go but if this effect can be exploited in quantum information, then because it is a semiconductor it can be miniaturized with a very high density and germanium can be grown on silicon so the control circuitry can be integrated with the qubits,” says Myronov.
In addition, manipulating quibits with an applied electric field is more manageable than the large magnetic fields required for the fractional quantum Hall effect, although as Holmes emphasizes, it may be a little premature to talk of qubits before the state itself is properly understood.
Alongside discussions with theorists to try and explain the effects, the researchers’ next steps include looking to see if there are any more fractions of the conductance in germanium, studying the system at lower temperatures, and experiments to measure the actual charge itself. “It’s a completely new system,” says Pepper. “So we expect more surprises.”
Full details are reported in Journal of Condensed Matter Physics.