by Alberto Morpurgo, Department of Quantum Matter Physics, UNIGE
based on an article published in Nature Communication
Topological insulators are a new class of materials that are insulating in the bulk but have conducting boundaries (surfaces or edges). Their discovery has been made by analyzing theoretically the influence of spin-orbit interaction on the properties of graphene – a crystal entirely made of carbon, only one atom thick. Despite the conceptual significance of this discovery, in graphene the strength of the spin-orbit interaction naturally present is too weak to allow experiments. Scientists at the University of Geneva have now found a simple way to enhance the strength of spin-orbit interaction in graphene by more than 1000 times, bringing the detection of a topological insulating state in this system much closer to experimental detection.
The energy bands of electrons propagating in a periodic potential can be classified in terms of topological concepts. A band can be topologically trivial or non-trivial depending on how its Bloch states “wind around” as the quantum number k is swept across the Brillouin zone. Theory predicts that in a system with a topologically non-trivial band there must be gapless surface states so that – even when the bulk is a gapped insulator – the surface remains metallic. System possessing these properties are known as topological insulators and exist in the presence of strong spin-orbit interaction (SOI) [1, 2].
Left : magnetoconductance due to weak antilocalization. The empty symbols of different colors represent the data measured at 250 mK at different gate voltages as indicated in the figure and the continuous line the corresponding theoretical fits.
Right : schematics of the dispersion relation close to the charge neutrality point as obtained from the calculated band structure in the presence of spin-orbit interaction. Note the gap that opens between valence and conduction band.
The theoretical discovery of topological insulators is due to Kane and Mele [3, 4] who analyzed the properties of graphene in the presence of SOI. They found that a band gap opens in the “bulk” whose magnitude is determined by the SOI strength, while gapless states persist at the edges. Despite the significance of this result, it soon became clear that the observation of the topological insulating state in graphene was virtually impossible, because the SOI strength is too small (~50 meV). Although, as a result, the search for experimental realizations of topological insulators focused on different material systems, finding a way to induce strong SOI in graphene remained as an important goal.
Different routes have been pursued. Proximity with metals such as lead , decoration with indium atoms , graphene hydrogenation  have been proposed or shown to induce SOI. All these mechanisms, however, either alter drastically the properties of graphene (so that the theory of Kane and Mele does not hold any more) or significantly reduce its quality. Inducing SOI in graphene while preserving all its other electronic properties – and its high quality – has not been possible so far.
Zhe Wang and coworkers now show how the problem can be solved . They use crystalline flakes of layered WS2 as a substrate to realize high-quality graphene devices, similarly to what is normally done with hBN (WS2 can be used as substrate if the Fermi level in graphene falls within its band gap, which is 1.4 eV wide).
The SOI strength in WS2 is huge : ~400 meV in the valence band and 30 meV in the conduction band and – using the language of perturbation theory – the idea is that virtual hopping of electrons from graphene into WS2 and back results in a strong in SOI in graphene as well.
The experiments rely on the measurement of a negative low-field magnetoconductance, a phenomenon known as weak antilocalization (WAL), due to quantum interference of electrons in the presence of SOI (WAL is not seen in graphene on conventional substrates, where SOI is negligible). A quantitative analysis shows that the spin relaxation time in graphene on WS2 is ~100-1000 times shorter than for graphene on SiO2 or hBN, which implies that SOI in graphene on WS2 is larger by approximately the same amount.
The observation of WAL does not enable the form of the induced SOI to be determined. In collaboration with Allan MacDonald group at UTexas (Austin), the authors present ab-initio calculations which confirm that a strong enhancement of SOI should be expected when WS2 is used as substrate, and that the SOI strength is at least several meV (~100 x time stronger than in bare graphene). The functional form differs from the SOI in pristine graphene. It comprises a Rashba term and a second term that couples spin and valley. If this second term is stronger, the system is a topological insulator, with a microscopic Hamiltonian different from the one studied by Kane and Mele, and a gap of few meV, two orders of magnitude larger than in pristine graphene.
These results revive the hopes to find a topological insulating state in graphene, open new possibilities in the field of graphene spintronics, and illustrate how interfacial interactions provide new ways to engineer the electronic properties of 2D materials at the atomic scale.
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 C. L. Kane and E. J. Mele, Z(2) topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95, 146802 (2005).
 F. Calleja et al., Spatial variation of a giant spin-orbit effect induces electron confinement in graphene on Pb islands, Nat. Phys. 11, 43 (2015).
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