The SPS Award committee under the lead of Professor Louis Schlapbach selected the winners for 2015 out of numerous submissions. Their work was presented at the annual meeting in Vienna. Please find in the following the laudationes written by Louis Schlapbach and the summaries written by the authors.

The SPS 2015 Prize in General Physics is awarded to **Gregor Jotzu**, for his excellent PhD-work on the "*Experimental realization of the topological Haldane model with ultracold fermions*" (Nature **515**, 237–240; 2014), which is at the intersection between quantum optics and solid-state physics.

He realized a singular advance towards the long-standing goal of exploring topological phases of matter using ultracold atomic gases, by establishing and demonstrating the necessary methodology both to prepare and to probe cold atoms in topological bands. The platform he developed, based on fermionic potassium atoms, opens up the possibility of using ultracold atomic gases to explore novel strongly correlated topological phases. This new approach is of great significance beyond the realm of cold atoms — it is of direct relevance to current research in solid-state physics, for example on topological insulators, and might well lead to surprising insights into topological properties of matter.

**Experimental realisation of the topological Haldane model with ultracold fermions**

Just like surfaces such as a sphere or a torus can be assigned to distinct topological classes, the wave-function of electrons in a solid may also be characterised by its topological properties. In 1988, F.D.M. Haldane proposed the Hamiltonian for a material which could intrinsically feature non-trivial topological properties [1]. Although physical implementation has been considered unlikely, Haldane's model has provided the conceptual basis for theoretical and experimental research exploring topological insulators and superconductors. Using ultracold fermionic atoms in a periodically modulated honeycomb optical lattice, we have experimentally realized Hadane's model as a Floquet Hamiltonian [2]. Such Hamiltonians can be used to describe the behaviour of a periodically modulated system on longer time-scales. They may contain novel features not present in the original system. Using circular modulation of a honeycomb lattice, we hence induce complex next-nearest-neighbour tunnelling terms, which break time-reversal symmetry - a crucial ingredient for Haldane's model. In addition, inversion symmetry is broken by introducing an energy offset between neighbouring sites. Breaking either of these symmetries opens a gap in the band structure, which we probe using momentum-resolved interband transitions. We explore the resulting Berry curvatures, which characterize the topology of the lowest band, by applying a constant force to the atoms and find orthogonal drifts analogous to a Hall current. The competition between the two broken symmetries gives rise to a transition between topologically distinct regimes. By identifying the vanishing gap at a single Dirac point, we map out this transition line experimentally. We verify that our approach is suitable even for interacting fermionic systems, allowing for future studies of the interplay of topological bands and magnetism or superfluidity.

[1] F. D. M. Haldane. Physical Review Letters 61, 2015 (1988)

[2] G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger. Nature 515, 237-240 (2014)

The SPS 2015 Prize in Condensed Matter Physics is shared between **Simon Gerber** and **Bastien Dalla Piazza**.

**Simon Gerber** receives the award for his excellent PhD work that lead to the remarkable identification of a novel exotic quantum phase in CeCoIn_{5}. This novel phase features the direct coupling of unconventional superconductivity of d- and p- wave symmetry to a spin-density wave. This makes this material a truly exceptional example of an exotic quantum phase that is of general importance for physics.

For his experimental work, Simon Gerber used a combination of high-magnetic field neutron diffraction - close to the upper critical field of CeCoIn_{5} - together with a specially designed and constructed attocube piezo goniometer. His findings allow to identify the Q-phase as a novel quantum phase where d-wave and p-wave superconductivity combine into a novel Cooper pair density wave that couples to a spin density wave. The results were published as "*Switching of magnetic domains reveals spatially inhomogeneous superconductivity*" in Nature Physics **10**, 126 (2014).

**Switching of magnetic domains reveals spatially inhomogeneous superconductivity**

The cerium 115 heavy-fermions represent a prototypical material family to study the interdependence of quantum phases due to strong electron correlations. In particular, CeCoIn_{5} has been at the focus of intense research activity and serves a model material for studies of unconventional superconductivity in the proximity of magnetism. Using high-field neutron scattering we have shown that a long-range ordered, incommensurate spin-density wave (SDW) emerges in a continuous quantum phase transition inside the, so-called, superconducting Q-phase [1]. Both the superconducting and the SDW order parameters then break down simultaneously at the upper critical field, suggesting a direct coupling between magnetism and superconductivity. Furthermore, we find that always only one of two possible SDW domains is populated in the Q-phase, which however cannot be explained by magnetic spin anisotropies. Carefully rotating the magnetic field direction allows for direct control and hypersensitive switching of the domain population. This sharp and binary switching behavior provides strong evidence that the Q-phase in CeCoIn_{5} is governed by a tri-linear coupling term of singlet d-wave superconductivity, incommensurate SDW order and a spatially inhomogeneous triplet p-wave Cooper pair-density wave, forming a complex quantum state that can be sensitively manipulated via the control parameter of the respective quantum phase transition.

[1] S. Gerber, M. Bartkowiak, J. L. Gavilano, E. Ressouche, N. Egetenmeyer, C. Niedermayer, A. D. Bianchi, R. Movshovich, E. D. Bauer, J. D. Thompson, and M. Kenzelmann, Nature Physics 10, 126 (2014).

**Bastien Dalla Piazza** receives the award for his outstanding PhD work on the fundamental understanding of the excitation spectrum in the two-dimensional quantum antiferromagnet - which is among the most fundamental models in quantum many body theory.

Bastien Dalla Piazza created a theoretical approach based on variational wave-function Monte-Carlo, providing the best description to date of the dynamics in the model. He was able to demonstrate that the high-energy excitations are fractional "spinons" – a phenomenon normally associated with one-dimensional systems. The results were published as "*Fractional excitations in the square lattice quantum antiferromagnet*" in Nature Physics **11**, 62-68 (2015).

**Fractional excitations in the square lattice quantum antiferromagnet.**

While quantum mechanics underlies all the macroscopic physics that forms our reality, it rarely manifests itself explicitly at that scale. From that observation follows the traditional view that quantum mechanics becomes most relevant for infinitesimally small systems. However strong quantum effects at macroscopic scales do exist and the keys for this are dimensionality and many- body interactions. In the quantum magnetism field, these key elements are best studied in the corner stone model: the Heisenberg model. It describes quantum magnetic moments interacting together on a lattice and its parameters are the lattice topology and the form of the interaction. In a three- dimensional cubic lattice for instance, the physics is dominantly classical with long range magnetic order only slightly renormalized by quantum effects. In contrast in a one-dimensional spin-chain, the quantum effects dominate causing the magnetic system to lie in a disordered quantum spin- liquid state. A salient property of such systems is the emergence of quasi-particles excitations -- spinons in this particular case -- that are only fractions of those found in vacuum or, equivalently, those found in the non-interacting limit. Between these two cases lies the two-dimensional square lattice studied here. The system has long-range order strongly renormalized by quantum effects and low-energy/long wavelength excitations are fluctuations of the magnetic order called spin waves, similar to phonons in solids. However recent experimental work [1] evidenced strong deviations from the spin-wave predictions in the high-energy/short wavelength regime. In recent work, we showed that these deviations are compatible with a model where spin-waves fractionalize into pairs of spin-1/2 quasi-particles [2] not unlike those found in one-dimensional systems.

[1] Quantum dynamics and entanglement of spins on a square lattice, N. B. Christensen, et al., Proceedings of the National Academy of Sciences 104 15264–15269 (2007)

[2] Fractional excitations in the square lattice quantum antiferromagnet, B. Dalla Piazza et al., Nature Physics 11, 62-68 (2015)

**Branimir Radisavljevic** is awarded with the SPS 2015 Prize in Applied Physics for his exploring PhD studies of the electronic properties of monolayered transition-metal dichalcogenide - single-layer MoS_{2} - published as "*Mobility engineering and metal-insulator transition in monolayer MoS _{2}*" (Nature Materials

**Single-layer MoS _{2}: Electronics in two dimensions**

On this project we were confident that by proper substrate and dielectric engineering and by better electrostatic control of the single-layer MoS_{2} channel, carrier mobility, current on/off ratio and subtreshold swing in field-effect transistors can be improved enough to become at least close to state-of-the-art semiconductor technology. In fact, any potential replacement of silicon in CMOS-like digital logic devices is desired to have a current on/off ratio Ion/Ioff between 10^{4} and 10^{7} and a band gap exceeding 400 meV. For the first time high current on/off ratio ~10^{8}, subtreshold swing as low as 74 mV/dec and moderately high electron mobility ~50 cm^{2}/Vs are demonstrated in any two-dimensional semiconducting material [1].

Subsequently, based on this platform we fabricated and demonstrated operations of the first logic gates, integrated circuits [2] and small-signal analog amplifiers which paved the way for two-dimensional semiconducting materials based flexible electronics, and resulted in MoS_{2} being included in the semiconductor industry ITRS roadmap.

The encapsulation of monolayer MoS_{2} in a high-κ dielectric environment was shown to result in an increase of the room-temperature mobility as we have demonstrated in our previous publications. In a follow-up work [3] we showed by cryogenic and Hall-effect measurements that the main reason for this increase was reduced Coulomb scattering due to the high-κ dielectric environment and possible modification of phonon dispersion in MoS_{2} monolayers. An increase of mobility with the dielectric deposition, similar to that in monolayers was also observed in multilayer samples and monolayer samples with polymer gating. Additionally, for the first time, we observed metal-insulator transition in one two-dimensional semiconducting material, which is explained by strong electron-electron interactions. This transition point is in very good agreement with theory and shows that monolayer MoS_{2} could be an interesting new material system for investigating low-dimensional correlated electron behavior.

[1] B. Radisavljevic, et al., "Single-layer MoS_{2} transistors," Nature Nanotechnology, 2011.

[2] B. Radisavljevic, et al., "Integrated Circuits and Logic Operations Based on Single-Layer MoS_{2}," ACS Nano, 2011.

[3] B. Radisavljevic and A. Kis, "Mobility engineering and a metal–insulator transition in monolayer MoS_{2}," Nature Materials, 2013.

The SPS 2015 Prize related to Metrology is awarded to **Peter Rickhaus** for his excellent PhD-work on unique steps on the way to graphene based ballistic electron optics and electronic devices, published as "*Ballistic interferences in suspended graphene*" (Nature Communications **4**, 2342 (2013)) and "*Snake Trajectories in Ultraclean Graphene p-n Junctions*" (Nature Communications **6**, 6470 (2015)).

Peter Rickhaus successfully demonstrated how to increase charge transport mobilities in graphene by three orders auf magnitude to 1’000’000 cm^{2}/Vs - yielding a mean free path in the µm range - using in?situ current annealing techniques of suspended graphene. With these clean materials he realized ballistic p-n junctions demonstrating Fabry-Perot interference oscillations known from optical cavities. Guiding of the electrons was achieved when a p-n junction was combined with a small perpendicular magnetic field. The semi metallic nature and bipolarity of monolayer graphene has made it possible to generate guiding with the aid of a constant magnetic field for the first time.

**Electron-Optics in suspended Graphene**

In ballistic graphene, electrons behave in many ways similar to photons. By changing the electrostatic potential locally, we realized elements in graphene that are known from optics. But in contrast to conventional optics, gapless p-n interfaces can be formed in graphene showing a negative index of refraction and the effect of Klein tunneling. The electron-optics devices that we studied were fabricated using high-mobility suspended monolayer graphene on organic lift-off resists. Recently we demonstrated that with this technique a ballistic p-n junction can be formed representing a Fabry-Pérot etalon. We further studied the transition from the Fabry-Pérot to the Quantum Hall regime of such a p-n interface under perpendicular magnetic field. Striking features appear that can be traced to the formation of “snake states” along the p-n interface [2]. By this electrons can be guided already at very small magnetic fields of 100 mT. Beyond that we demonstrated that electrons in ballistic graphene can be guided by gate potentials the same way as photons in an optical fiber, and that the formation of a p-n interface increases the guiding efficiency due to Klein filtering. We showed that we can fill the electrostatic guiding channel mode by mode.

[1] P. Rickhaus, R. Maurand, Ming-Hao Liu et al., Nature Comm. 4, 2342 (2013)

[2] P. Rickhaus, P. Makk, Ming-Hao Liu et al., Nature Comm. 6, 6470 (2015)