Quantum spin Hall materials hold the promise of revolutionary devices with dissipationless spin currents but have required cryogenic temperatures owing to small energy gaps. Here we show theoretically that a room-temperature regime with a large energy gap may be achievable within a paradigm that exploits the atomic spin-orbit coupling. The concept is based on a substrate-supported monolayer of a high-atomic number element and is experimentally realized as a bismuth honeycomb lattice on top of the insulating silicon carbide substrate SiC(0001). Using scanning tunneling spectroscopy, we detect a gap of ~0.8 electron volt and conductive edge states consistent with theory. Our combined theoretical and experimental results demonstrate a concept for a quantum spin Hall wide-gap scenario, where the chemical potential resides in the global system gap, ensuring robust edge conductance.

Antiferromagnetism and superconductivity are both fundamental and common states of matter. In many strongly correlated systems, including the high-T c cuprates, the heavy-fermion compounds, and the organic superconductors, they occur next to each other in the phase diagram and influence each other's physical properties. The SO͑5͒ theory unifies these two basic states of matter by a symmetry principle and describes their rich phenomenology through a single low-energy effective model. In this paper, the authors review the framework of the SO͑5͒ theory and compare it with numerical and experimental results.

The band structure of graphene exhibits van Hove singularities (VHS) at doping x = ±1/8 away from the Dirac point. Near the VHS, interactions effects, enhanced due to the large density of states, can give rise to various many-body phases at experimentally accessible temperatures. We study the competition between different many-body instabilities in graphene using functional renormalization group (FRG). We predict a rich phase diagram, which, depending on long range hopping as well as screening strength and absolute scale of the Coulomb interaction, contains a d + id-wave superconducting (SC) phase, or a spin density wave phase at the VHS. The d + id state is expected to exhibit quantized charge and spin Hall response, as well as Majorana modes bound to vortices. In the vicinity of the VHS, we find singlet d + id-wave as well as triplet f -wave SC phases.

Theories based on the coupling between spin fluctuations and fermionic quasiparticles are among the leading contenders to explain the origin of high-temperature superconductivity, but estimates of the strength of this interaction differ widely 1 . Here, we analyse the charge-and spin-excitation spectra determined by angle-resolved photoemission and inelastic neutron scattering, respectively, on the same crystals of the high-temperature superconductor YBa 2 Cu 3 O 6.6 . We show that a self-consistent description of both spectra can be obtained by adjusting a single parameter, the spin-fermion coupling constant. In particular, we find a quantitative link between two spectral features that have been established as universal for the cuprates, namely high-energy spin excitations [2][3][4][5][6][7] and 'kinks' in the fermionic band dispersions along the nodal direction [8][9][10][11][12] . The superconducting transition temperature computed with this coupling constant exceeds 150 K, demonstrating that spin fluctuations have sufficient strength to mediate high-temperature superconductivity.Looking back at conventional superconductors, the most convincing demonstration of the electron-phonon interaction as the source of electron pairing was based on the quantitative correspondence between features in the electronic tunnelling conductance and the phonon spectrum measured by inelastic neutron scattering (INS; for reviews, see the articles by Scalapino, McMillan and Rowell in ref. 13). The rigorous comparison of fermionic and bosonic spectra was made possible by the Eliashberg theory, which enabled the tunnelling conductance to be derived from the experimentally determined phonon spectrum. Various difficulties have impeded a similar approach to the origin of high-temperature superconductivity. First, the d-wave pairing state found in these materials implies a strongly momentum-dependent pairing interaction. A more elaborate analysis based on data from momentum-resolved experimental techniques such as INS and angle-resolved photoemission spectroscopy (ARPES) is thus required. These methods, in turn, impose conflicting constraints on the materials. (refs 11,12) have overcome problems related to polar surfaces and enabled the observation of superconducting gaps and band renormalization effects ('kinks') akin to those previously reported in La-and Bi-based cuprates 8 . Third, calculations based on the two-dimensional Hubbard model have demonstrated Fermi surfaces, single-particle spectral weights, antiferromagnetic spin correlations and d x 2 −y 2 pairing correlations in qualitative agreement with experimental measurements [15][16][17] . Numerically accurate solutions of this model can thus serve as a valuable guideline for a treatment of the spin-fluctuation interaction in the cuprates. This is the approach we take here.Recent quantum Monte Carlo calculations of the twodimensional Hubbard model within the dynamical cluster approximation 17 for a realistic value of the bare U /t = 8 and different doping levels ranging from un...

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