Interface Superconductivity: Get It Strained

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INTERFACE SUPERCONDUCTIVITY Get it strained Stretching a sheet of graphene could induce a superconducting state. Similar strain-induced superconductivity may be realized at the interface between a topological crystalline insulator and a trivial band insulator. Fakher F. Assaad

ne of the reasons for the excitement Occupied states are therefore shifted to crystalline insulator and the trivial band surrounding graphene is that it lower energy leading to an energy gain. insulator is expected. Note that graphene Orepresents a solid-state realization In other words, when the system becomes and topological crystalline insulator of the Dirac equation — the cornerstone infinitely large — in the thermodynamic surface states differ from the topological of relativistic quantum theory unifying limit — it is bound to be unstable to a insulator surface state. In the latter case, quantum mechanics and the special correlation-dominated collective state. the Dirac point is pinned at time-reversal- theory of relativity. The equation provides Tang and Fu demonstrated that, assuming invariant momenta, so it cannot meander a mathematical framework for the the electron–phonon coupling is the in momentum space and the proposed relativistic description of the electron, and dominant interaction, one can expect that mechanism of a strained-induced flat automatically accounts for the electron’s the stretching of a sheet of graphene will band fails7. spin and that of its antimatter partner, the induce a superconducting state2. In contrast, Superconductivity stemming from positron. Stretching a sheet of graphene dominant repulsive interactions have the a flat band is interesting in its own corresponds to the inclusion of a magnetic potential to generate magnetic instabilities5,6. right as it is not explained by the field in the equation1, as the strain applied Tang and Fu suggested how one could Bardeen–Cooper–Schrieffer theory of to a two-dimensional honeycomb lattice of take this thought experiment into the superconductivity8. The density of states carbon atoms induces a ‘pseudo-magnetic’ laboratory2. The scheme they proposed is at the Fermi level is infinite and the Fermi field. ow,N Evelyn Tang and Liang Fu a self-organized realization of the strain- energy vanishes. This means that one report in Nature Physics that stretching induced superconductivity effect involving cannot rely blindly on the Migdal theorem9, graphene can, in essence, also produce a the physics of topological crystalline which provides a precise method for superconducting state2. insulators. These materials are insulating in calculating the electron–phonon coupling For low energies, the electronic the bulk, but metallic at the surface. Their and predicting superconducting transition structure of a sheet of graphene features metallic surface state is robust due to crystal temperatures. linear dispersions known as Dirac cones. symmetries and not due to time-reversal Topological crystalline and trivial band The vector potential associated with the symmetry, as is the case for ordinary insulators are semiconductors that, taken strain-induced pseudo-magnetic field topological insulators. This has important on their own, often do not show dominant has opposite signs for graphene’s two consequences and renders the metallic correlation effects. Put together, however, types of Dirac cone, which reflects the surface state of the topological crystalline a piece of correlation-dominated physics fact that elastic deformations, unlike real insulator very similar to that of graphene, emerges at the interface. This mechanism magnetic fields, do not violate time-reversal giving rise to the desired Dirac Hamiltonian. provides an interesting way to understand symmetry. For mathematical reasons, which But what about strain? To produce a the observed superconductivity in IV–VI are collectively known as index theorems, uniform pseudo-magnetic field in the semiconductor interfaces10, and it may lead this effective pseudo-magnetic field leads to thermodynamic limit, one would need to a novel route to generate correlation- the formation of zero-energy modes3. The infinite strain, which would rip apart dominated and exotic states of matter in number of zero-energy modes corresponds any crystalline structure. To get around partially filled flat bands. ❐ to the number of pseudo-magnetic flux this issue, the authors considered an quanta threading the graphene sheet. interface between a topological crystalline Fakher F. Assaad is at the Institut für Theoretische Therefore, one obtains a flat band pinned insulator and a trivial band insulator Physik und Astrophysik, Universität Würzburg, at zero energy that is half-filled with (a semiconductor with no topological Am Hubland, D-97074 Würzburg, Germany. electrons. The resulting large density of properties). The metallic surface state e-mail: [email protected] states at zero energy has been observed resides at the interface of the topological experimentally for so-called molecular crystalline insulator and the trivial band References graphene4 — carbon monoxide molecules insulator because the band insulator can 1. Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. Rev. Mod. Phys. 81, 109–162 (2009). carefully placed on a copper substrate in a essentially be considered a vacuum. By 2. Tang, E. & Fu, L. Nature Phys. 10, 964–969 (2014). hexagonal arrangement. choosing a trivial band insulator with a 3. Aharonov, Y. & Casher, A. Phys. Rev. A 19, 2461–2462 (1979). A partially filled flat band is generically different lattice constant than that of the 4. Gomes, K. K., Mar, W., Ko, W., Guinea, F. & Manoharan, H. C. Nature 483, 306–310 (2012). very susceptible to electronic correlations. topological crystalline insulator, a periodic 5. Herbut, I. F. Phys. Rev. B 78, 205433 (2008). When the system becomes very large, array of dislocations, or a periodic strain, 6. Roy, B., Assaad, F. F. & Herbut, I. F. Phys. Rev. X 4, 021042 (2014). at a constant pseudo-magnetic field the can be induced at the interface. This leads 7. Liu, Y. et al. Nature Phys. 10, 294–299 (2014). 8. Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Phys. Rev. density of states at zero energy grows to the desired flat band. In semiconductors, 106, 162–164 (1957). proportionally to the volume of the system. the dominant correlation effects stem 9. Migdal, A. JETP 34, 996–1001 (1958). In this situation even weak correlations from the electron–phonon coupling 10. Fogel, N. Ya. et al. Phys. Rev. Lett. 86, 512–515 (2001). can play an important role by opening up such that an emergent superconducting a gap in the density of states at zero energy. state at the interface of the topological Published online: 2 November 2014

NATURE PHYSICS | VOL 10 | DECEMBER 2014 | www.nature.com/naturephysics 905