The winners of the SPS Awards 2013

A central theme of condensed matter physics is to classify and understand phases of matter. The Landau theory of symmetry breaking has been the long-standing paradigm for this classification: Two phases are distinct if they have different symmetries. In recent years, the study of topological phases showed that a second paradigm must be considered on equal footing: Two phases are distinct if they have different topological character, even if they share the same symmetries. Topological properties cannot be changed smoothly, thus endowing a topological state with a natural universality and protection against perturbations.
Topological phases are understood and classified in the limit of small electron–electron interactions. The opposite limit, in contrast, is at the frontier of current research. Strong electron–electron interactions can be responsible for the emergence of correlated topological states with excitations that have a fraction of the electron's charge, so-called fractional topological insulators (FTIs). The first example of an FTI that is well studied both experimentally and theoretically is the fractional quantum Hall effect of electrons in partially filled Landau levels. Recently, we discovered another type of FTIs, the fractional Chern insulator [1]. These states arise in lattice models in two spatial dimensions, if a nearly dispersionless band with a nonzero Chern number is partially filled with repulsively interacting electrons. Fractional Chern insulators share many universal and topological properties with the fractional quantum Hall effect in Landau levels, where the role of the strong magnetic field is replaced by time-reversal symmetry breaking electronic hopping integrals on the lattice. Comparing and contrasting the fractional Chern insulators with the fractional quantum Hall effect allows us to better understand what are the core ingredients for a fractional topological state to emerge.
In a combination of numerical and analytical work, we have studied several aspects of FTIs in two spatial dimensions. For example, we found that if a topological insulator, as is realized in HgTe quantum wells, has a sufficiently small bandwidth, repulsive electron–electron interactions can favor a spontaneous breaking of time-reversal symmetry along with the formation of an anomalous quantum Hall effect or a fractional Chern insulator state [2].

_{[1] T. Neupert, L. Santos, C. Chamon, and C. Mudry, Phys. Rev. Lett. 106, 236804 (2011).
[2] T. Neupert, L. Santos, S. Ryu, C. Chamon, and C. Mudry, Phys. Rev. B 84, 165107 (2011).}

In a recent theoretical study, we found a new mechanism for generating Majorana bound states in nanowires with proximity gap that is based on spatially rotating magnetic fields, being present in addition to Rashba spin orbit interaction [1]. The topological phases can be completely characterized by a new method to find explicit solutions for Majorana fermions and other exotic fermion bound states of Jackiw-Rebbi type carrying fractional charge e/2. Due to their non-Abelian statistics such states can be used for braiding and are of potential use in topological quantum computing. More specifically, we analyzed hybrid superconducting-semiconducting nanowires in the presence of Rashba spin-orbit interaction as well as helical magnetic fields and showed that the interplay between them leads to a competition of phases with two topological gaps closing and reopening, resulting in unexpected reentrance behavior. Besides the topological phase with localized Majorana fermions (MFs) there are novel phases characterized by fractionally charged fermion (FF) bound states of Jackiw-Rebbi type. The system can be fully gapped by the magnetic fields alone, giving rise to FFs that transmute into MFs upon turning on superconductivity. Explicit analytical solutions for MF and FF bound states which allowed us to determine the phase diagram numerically by determining the corresponding Wronskian null space. Electron-electron interactions leave the bound states intact and even enhance the required Zeeman gaps opened by the fields.

In a follow up work on graphene, where some of the physics discovered in the first work might be implemented experimentally, we found an unusally large spin orbit effect in graphene nanoribbons (with armchair edges) produced by nanomagnets [2]. As a consequence, helical modes exist in armchair nanoribbons that exhibit nearly perfect spin polarization and are robust against boundary defects. This result paves the way for realizing spin-filter devices in graphene nanoribbons in the temperature regime of a few kelvins. If a nanoribbon in the helical regime is in proximity contact to an s-wave superconductor, the nanoribbon can be tuned into a topological phase that sustains Majorana fermions.

_{[1] Jelena Klinovaja, Peter Stano, and Daniel Loss, "Transition from fractional to Majorana fermions in Rashba nanowires", Phys. Rev. Lett. 109, 236801 (2012).
[2] Jelena Klinovaja and Daniel Loss, "Giant spin orbit interaction due to rotating magnetic fields in graphene nanoribbons", Phys. Rev. X 3, 011008 (2013).}

We explored the complex structure of the Landau levels and cyclotron resonances in graphene epitaxially grown on silicon carbide. Epitaxial graphene is of particular practical importance because of a possibility for scalable growth. However, its properties are rather complicated because of a strong coupling of the carbon layers to the substrate, their unusual stacking and variation of doping across the layers. We were the first to apply the technique of the infrared Hall effect in monolayer and multilayer graphene, where both transmission and the Faraday rotation are measured. This allowed us to distinguish and classify spectroscopically various Landau-level transitions that stem from different graphene layers, including the buried ones, which are not accessible by other techniques. In particular, a multicomponent cyclotron resonance structure was observed in multilayer graphene grown on the C-face of silicon carbide.
In our study of doped monolayer graphene on Si-face of SiC, we discovered a giant Faraday rotation in the terahertz range that originates from the cyclotron resonance of free carriers [1]. The unprecedented value of the rotation angles (about 6 degrees at 7 T) by the thinnest material in condensed matter physics, contradicts common sense, since the Faraday effect is known to be proportional to the thickness. Nevertheless, we explained our observation by the extremely small mass of Dirac fermions and their high mobility, and numerically reproduced the experimental curves. In a follow-up publication [2], we found that due to the presence of substrate terraces, a strong terahertz plasmonic peak appears in epitaxial graphene. Furthermore, we found that the plasmon peak splits in magnetic field into bulk and edge magnetoplasmon branches, similar to the ones observed in some classical experiments on GaAs based 2D electron gases. This was actually the first observation of magnetoplasmons in graphene. Importantly, the plasmonic effects found by us modify dramatically the wavelengths dependence of the Faraday rotation. All these results are of a high practical importance as they suggest that graphene can be used in ultrathin and ultrafast switchable magneto-optical devices.

_{[1] I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, Th. Seyller, D. van der Marel, and A. B. Kuzmenko, Giant Faraday rotation in single- and multilayer graphene, Nature Physics 7, 48–51, 2011.
[2] I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, Th. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, Intrinsic Terahertz Plasmons and Magnetoplasmons in Large Scale Monolayer Graphene, Nano Letters 12, 2470-2474, 2012.}