EPS CMD Europhysics Prize Previous Recipients

Previous Recipient of the EPS CMD Europhysics Prize

2010 Europhysics Condensed Matter Prize awarded to Hartmut Buhmann, Charles Kane, Eugene Mele, Laurens W. Molenkamp and
Shoucheng Zhang

Theoretical prediction and the experimental observation of the quantum spin Hall effect and topological insulators..

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Until recently the (single particle) band structure of semiconductors was believed to be a textbook subject, with no more surprises to be discovered. The theoretical analysis,
and the subsequent experiments that revealed the existence of topological insulators, have shown otherwise.

A material with a gap separating occupied and empty states, i.e., a band insulator, is understood as a medium having a localised electronic response to any stimulus. If conducting probes are attached to opposite ends of an insulator and a voltage is applied, no current flows. There is only an electric polarisation, due to a small shift in the electron density. This behaviour is the same as that of a collection of electronically decoupled atoms with electrons tightly bound to them. It was formerly believed that the properties of all band insulators
can be described in this way. But a set of band insulators is now known to exist in which the topology of the band structure implies the existence of edge or surface states that are
insensitive to disorder. These states impart to the material some unusual electromagnetic properties. That such behaviour can arise from features in the band structure of a  seemingly “normal” bulk material had not been recognized before. One bulk insulating state with extremely robust (topologically protected) conducting states at its edges has been known for 30 years. This is the quantum Hall state observed in two-dimensional systems at high magnetic fields. A topological insulator can be considered to be a cousin of a
quantum Hall state, specifically one which does not break time reversal symmetry (i.e., it exists at zero magnetic field) and in which the spin-orbit interaction is the source of a pseudo-magnetic field in the reciprocal space. Research on the quantum spin Hall effect (of which Shoucheng Zhang of Stanford University was a pioneer), and analogies for the topological description of the quantum Hall state, have been crucial to the development of the notion of topological insulators. The key theoretical breakthrough, which brought all the ingredients together, was the 2005 work by Charles Kane and Eugene Mele (University of Pennsylvania). Taking graphene as an example, they realized that every two-dimensional timereversal-
invariant insulator belongs to one of two classes (whence a Z2 name for the classification): either a “usual” class, or a topologically nontrivial one. The nontrivial class is characterised  by the existence of robust gapless edge states (in the form of ‘Dirac cones’ corresponding to a linear dependence of the energy on the k vector), immune to localization and having a surprising spin structure. This distinction is not manifest in the bulk band structure of a material. To see it, it is necessary to consider the topological properties of the manifold which results by mapping the Brillouin zone (a torus in k-space, due to the periodicity of the crystal) to the band structure – or, equivalently, to a space of Bloch Hamiltonians defined at each k-point. The observation of such an insulating phase proved not to be feasible in graphene, but the existence of a topologically nontrivial phase in HgTe-based systems was predicted soon afterwards by B. Andrei Bernevig, Taylor Hughes, and Zhang. Experimental confirmation was provided by the group of Hartmut Buhmann and Laurens Molenkamp at Würzburg University. Through a series of elegant experiments on HgTe/CdTe quantum wells, in which the Fermi level was tuned by a gate voltage to the band gap region, they demonstrated that the conductance s was quantised, taking the value s = 2e2/h predicted for topologically protected edge states in such a microstructure.

Further developments include the generalization of the concept of topological insulating states to three dimensions, and experimental confirmation of the existence of characteristic (Dirac-like) surface states in 3D materials; the development of topological field theory for 2D and 3D materials and the prediction of magnetoelectric effects (by Xiao-Liang Qi, Hughes, and Zhang); and a growing number of predictions of novel effects at the interfaces between topological insulators and other materials (such as superconductors and ferromagnets). More surprises undoubtedly await discovery. But the major change to textbooks that the discovery of topological insulators will bring is that the topological classification of phases of
matter is relevant for seemingly simple systems such as band insulators, not just the quantum Hall problem or more exotic strongly correlated systems. Topological classification of phases could someday become as established as the use of symmetry (and its breaking) to describe distinct states of matter.

Questions remain over the size of the family of topological insulators. Experimental and theoretical developments indicate that bismuth chalcogenides and bismuth-antimony alloys are, like the quantum structures of mercury telluride, topological insulators. Furthermore, Dirac cones were predicted in the 1980s to exist at interfaces involving lead chalcogenides. Topological characteristics of these states were not, however, discussed in this pioneering work,
undertaken by Oleg Pankratov and Vladimir Volkov (then in Moscow), Eduardo Fradkin (University of Illinois at Urbana-Champaign), Elbio Dagotto (then also at UIUC), and Daniel Boyanovsky (then at Stanford).

[1] X.-L. Qi and S.-C. Zhang, Phys. Today, January 2010, p 33.

[2] J. E. Moore, Nature 464, 194 (2010).

[3] M. Z. Hasan and C. L. Kane, http://arxiv.org/abs/1002.3895

The EPS Condensed Matter Division appreciates the long-standing support of Hewlett Packard and of Agilent Technologies, who were sponsors of this prize until 2006.

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