Commonly materials are classified as either electrical conductors or insulators. The theoretical discovery of topological insulators (TIs) in 2005 has fundamentally challenged this dichotomy 1 . In a TI, spin-orbit interaction generates a non-trivial topology of the electronic band-structure dictating that its bulk is perfectly insulating, while its surface is fully conducting. The first TI candidate material put forward 2 -graphene -is of limited practical use since its weak spin-orbit interactions produce a band-gap 3 of ∼0.01K. Recent reinvestigation of Bi 2 Se 3 and Bi 2 Te 3 , however, have firmly categorized these materials as strong three-dimensional TI's. [4][5][6][7][8] We have synthesized the first bulk material belonging to an entirely different, weak, topological class, built from stacks of two-dimensional TI's: Bi 14 Rh 3 I 9 .Its Bi-Rh sheets are graphene analogs, but with a honeycomb net composed of RhBi 8 -cubes rather than carbon atoms. The strong bismuth-related spin-orbit interaction renders each graphene-like layer a TI with a 2400K band-gap. 1 arXiv:1303.2193v1 [cond-mat.mtrl-sci]

The lack of structural symmetry which usually characterizes semiconductor quantum dots lifts the energetic degeneracy of the bright excitonic states and hampers severely their use as high-fidelity sources of entangled photons. We demonstrate experimentally and theoretically that it is always possible to restore the excitonic degeneracy by the simultaneous application of large strain and electric fields. This is achieved by using one external perturbation to align the polarization of the exciton emission along the axis of the second perturbation, which then erases completely the energy splitting of the states. This result, which holds for any quantum dot structure, highlights the potential of combining complementary external fields to create artificial atoms meeting the stringent requirements posed by scalable semiconductor-based quantum technology.

Using the unrestricted Hartree-Fock approximation and Landau theory we identify possible phases competing with superconductivity in FeAs layers. We find that close to half-filling the transition from the paramagnet to the magnetically ordered phase is first order, making anharmonicities relevant and leading to a rich phase diagram. Between the already known one-dimensionally modulated magnetic stripe phase and the paramagnet we find a new phase which has the same structure factor as the former but in which magnetic moments at nearest-neighbor sites are at right angles making electrons acquire a nontrivial phase when circulating a plaquette at strong coupling. Another competing phase has magnetic and charge order and may be stabilized by charged impurities.

We provide the bulk topological invariant for chiral higher-order topological insulators in: i) fourfold rotoinversion invariant bulk crystals, and ii) inversion-symmetric systems with or without an additional three-fold rotation symmetry. These states of matter are characterized by a non-trivial Z2 index, which we define in terms of symmetric hybrid Wannier functions of the filled bands, and can be readily calculated from the knowledge of the crystalline symmetry labels of the bulk band structure. The topological invariant determines the generic presence or absence of protected chiral gapless one-dimensional modes localized at the hinges between conventional gapped surfaces. arXiv:1806.04023v3 [cond-mat.mes-hall]

The adhesion of graphene on slightly lattice-mismatched surfaces, for instance of hexagonal boron nitride (hBN) or Ir(111), gives rise to a complex landscape of sublattice symmetry-breaking potentials for the Dirac fermions. Whereas a gap at the Dirac point opens for perfectly lattice-matched graphene on hBN, we show that the small lattice incommensurability prevents the opening of this gap and rather leads to a renormalized Dirac dispersion with a trigonal warping. This warping breaks the effective time reversal symmetry in a single valley. On top of this a new set of massless Dirac fermions is generated, which are characterized by a group velocity that is half the one of pristine graphene. Introduction -One of the main experimental challenges towards the realization of next-generation graphene electronics technology is the possibility to access the low energy Dirac point physics. Silicon oxide (SiO 2 ) substrates, for instance, are not ideal for graphene because of the trapped charges in the oxide. These impurityinduced charge traps limit the device performances and make the low energy physics inaccessible [1]. It has been recently shown that placing graphene on hexagonal boron nitride (hBN) yields improved device performances [2] -graphene on hBN can have mobilities and charge inhomogeneities almost an order of magnitude better than graphene devices on SiO 2 . hBN is interesting because it has the same honeycomb lattice structure of graphene, but only with two atoms in the unit cell, B and N, that are chemically inequivalent. Precisely this causes hBN to be a wide bandgap insulator. When graphene is placed on top of a hBN surface, the lowest energy stacking configuration has one set of C atoms on top of B and the other C sublattice in the middle of the BN hexagons [3, 4] -assuming perfect lattice matching between graphene and hBN. Consequently the substrate-induced potential breaks the graphene sublattice symmetry. This leads to a gap at the Dirac point and hence a robust mass for the Dirac fermions. First principles band structure calculations [3] put this gap at ∼ 50 meV -an energy roughly twice as large as k B T at room temperature. However, recent scanning tunneling microscopy experiments [5,6] do not detect a sizable bandgap.Within an effective continuum approach, here we show that this discrepancy originates from the 1.8 % lattice mismatch [7] between graphene and hBN which leads to a Moiré superstructure with periodicity much larger than the graphene lattice constant. In this Moiré lattice, carbon atoms are embedded in a local environment of boron and nitrogen atoms that is varying continuously and periodically. This leads to a complex landscape of local sublattice symmetry-breaking terms which prevent the

We propose a new method of generating triggered entangled photon pairs with wavelength on demand. The method uses a microstructured semiconductor-piezoelectric device capable of dynamically reshaping the electronic properties of self-assembled quantum dots (QDs) via anisotropic strain engineering. Theoretical models based on k·p theory in combination with finite-element calculations show that the energy of the polarization-entangled photons emitted by QDs can be tuned in a range larger than 100 meV without affecting the degree of entanglement of the quantum source. These results pave the way towards the deterministic implementation of QD entanglement resources in all-electrically-controlled solid-state-based quantum relays.

In several materials, unconventional superconductivity appears nearby a quantum phase transition where long-range magnetic order vanishes as a function of a control parameter like charge doping, pressure or magnetic field. The nature of the quantum phase transition is of key relevance, because continuous transitions are expected to favour superconductivity, due to strong fluctuations. Discontinuous transitions, on the other hand, are not expected to have a similar role. Here we determine the nature of the magnetic quantum phase transition, which occurs as a function of doping, in the iron-based superconductor LaFeAsO1–xFx. We use constrained density functional calculations that provide ab initio coefficients for a Landau order parameter analysis. The outcome is intriguing, as this material turns out to be remarkably close to a quantum tricritical point, where the transition changes from continuous to discontinuous, and several susceptibilities diverge simultaneously. We discuss the consequences for superconductivity and the phase diagram.

We demonstrate the existence of topological insulators in one dimension protected by mirror and time-reversal symmetries. They are characterized by a nontrivial Z2 topological invariant defined in terms of the "partial" polarizations, which we show to be quantized in presence of a 1D mirror point. The topological invariant determines the generic presence or absence of integer boundary charges at the mirror-symmetric boundaries of the system. We check our findings against spin-orbit coupled Aubry-André-Harper models that can be realized, e.g. in cold-atomic Fermi gases loaded in one-dimensional optical lattices or in density-and Rashba spin-orbit-modulated semiconductor nanowires. In this setup, in-gap end-mode Kramers doublets appearing in the topologically nontrivial state effectively constitute a double-quantum-dot with spin-orbit coupling.