Topological insulators

Oscillations in the ribbons

The observation of Aharonov–Bohm oscillations in nanoribbons of Bi2Se3 opens the way for electronic transport experiments in nanoscale three-dimensional topological insulators.

Topological insulators1 have risen to the attention of the scientific community only in the past few years. They are different from both insulators and metals because, whereas the bulk exhibits a finite electronic bandgap, and is therefore insulating, the surface states are gapless and metallic. Two- and three-dimensional variants of this class of materials have been studied experimentally and theoretically. The gapless metallic states at the surfaces are predicted to lead to unusual transport properties. However, transport experiments have so far been hampered by insufficient control over the bulk. In particular, unintentional and uncontrolled doping leads to residual conductance that masks that of the surfaces. As reported now in Nature Materials, Hailin Peng, Keji Lai and co-workers have succeeded in accessing the surface conductance of the topological insulator Bi2Se3 by fabricating nanoribbons, thus increasing the surface-to-volume ratio2. This approach allowed the observation of Aharonov–Bohm oscillations, which represents the first demonstration of quantum interference in the transport properties of this new class of materials.

The Aharonov–Bohm effect3 is related to the interference of two coherent electron beams. It has been known4 at least since the 1940s that a magnetic flux enclosed by the two interfering partial waves (Fig. 1a) changes their relative phase and can thereby turn constructive interference into destructive, and vice versa. According to the theoretical prediction, the interference pattern is periodic in integer units of the magnetic flux quantum h/e, where h is Planck's constant and e is the elementary charge. A higher-order variant of the effect can occur if a single path takes one full turn around the flux tube (see one of the paths in Fig. 1b). A pair of paths differing only in the direction in which it is taken (that is, clockwise or anticlockwise, see Fig. 1b) is related by time reversal, because the velocities would be inverted if the time ran backwards. Interference of pairs of time-reversed paths is periodic in units of half the magnetic flux quantum h/2e.

Figure 1: Aharonov–Bohm oscillations.
figure1

a, If the two interfering partial waves represented by the blue arrowed lines enclose the magnetic flux once, the intensity of the beam transmitted to the right will be modulated with period h/e. The magnetic flux (ϕ) may be seen as a homogeneous magnetic field B within the area A of the flux tube. b, If the two interfering partial waves are a pair related by time-reversal, each encircling the magnetic flux once, the reflected intensity will always be a maximum at zero flux, and it will be modulated with period h/2e.

In the 1980s the Aharonov–Bohm effect became well known in the field of mesoscopic electron transport, in which conductance is regarded to be proportional to electron transmission5,6. Sharvin and Sharvin7 measured the conductance of a long and thin magnesium cylinder evaporated around a micrometre-thin quartz filament (Fig. 2a). With the magnetic field oriented along the axis of the cylinder they found periodic oscillations in the magnetoconductance with a period given by h/2e, normalized to the cross-sectional area of the cylinder. In the same year, oscillations with this period had been predicted theoretically8. Similar results were later obtained in carbon nanotubes (Fig. 2b)9. The reason why in these experiments the h/e-periodicity was not observed was explained by various studies on metals10 and semiconductors6, for example on ring-shaped planar geometries and arrays of rings. Briefly, pairs of paths contributing to the fundamental h/e period have a specific relative phase at zero magnetic field. If many such pairs with uncorrelated zero-field phases contribute to transport, the h/e oscillations average out. In contrast, the h/2e-periodic oscillations contain a significant contribution of time-reversed paths, which all have the same relative phase of zero at the interference point, and are therefore robust against averaging.

Figure 2: The similarity between different experiments on tube-like geometries.
figure2

a, Geometry of the Sharvin and Sharvin experiment7, in which a magnesium film was evaporated onto a quartz filament. b, Experiment on a carbon nanotube9, where electron motion is confined to the cylindrical surface of the tube. c, The new experiment reported by Peng, Lai and co-workers2, whereby a significant contribution to transport stems from the gapless surface states of the Bi2Se3 nanoribbon.

The experimental specimen of Hailin Peng, Keji Lai and co-workers2 resembles that of the Sharvin and Sharvin experiment7, as shown schematically in Fig. 2c. In the topological insulator however, there is no need for an insulating core and a conducting surface, because the material itself has these characteristics. The interpretation of the new experiment is that the thin nanoribbon geometry reduces the bulk conductivity caused by crystal defects to an extent that allows the signature of the Aharonov–Bohm-type oscillations of surface states to be observed, if a magnetic field is applied along the ribbon axis. The observation of the fundamental h/e period surprisingly indicates the absence of strong self-averaging in these experiments. Peng, Lai and colleagues argue that in the Bi2Se3 nanoribbons the topological protection helps to bring about the fundamental period of the Aharonov–Bohm interference at small magnetic fields, rather than the more robust h/2e period seen in the magnesium cylinders, and in carbon nanotubes.

Present research on topological insulators is still at an early stage, but has the potential to have a bright future. Perhaps nature will provide us with even more materials belonging to this class. Improving the quality of the available materials represents a significant challenge. Nanoribbons made of three-dimensional topological insulators could be natural competitors of today's core–shell nanowires grown epitaxially with great precision and high quality. But two-dimensional topological insulators will also contribute to future research: edge-channel transport in the two-dimensional heterostructure HgTe/HgCdTe, which is a zero magnetic-field topological insulator, has been demonstrated recently11, and Aharonov–Bohm-type oscillations have been seen in this material. Two-dimensional topological insulators have also been proposed in single- and double-layer graphene. Visionary proposals see applications in spintronics, valleytronics or even topological quantum computation, for example with the exotic fractional quantum Hall state at filling factor 5/2 (ref. 12). Although the realization of these goals will be highly challenging, it will no doubt spark a great variety of new basic research on nanoscale structures at the interface between physics, materials science and electronic engineering.

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Ihn, T. Oscillations in the ribbons. Nature Mater 9, 187–188 (2010). https://doi.org/10.1038/nmat2705

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