An odd number of gapless Dirac fermions is guaranteed to exist at a surface of a strong topological insulator. We show that in a thin-film geometry and under external bias, electron-hole pairs that reside in these surface states can condense to form a novel exotic quantum state which we propose to call "topological exciton condensate" (TEC). This TEC is similar in general terms to the exciton condensate recently argued to exist in a biased graphene bilayer, but with different topological properties. It exhibits a host of unusual properties including a stable zero mode and a fractional charge +/-e/2 carried by a singly quantized vortex in the TEC order parameter.

Floquet Majorana fermions are steady states of equal superposition of electrons and holes in a periodically driven superconductor. We study the experimental signatures of Floquet Majorana fermions in transport measurements and show, both analytically and numerically, that their presence is signaled by a quantized conductance sum rule over discrete values of lead bias differing by multiple absorption or emission energies at drive frequency. We also study the effects of static disorder and find that the quantized sum rule is robust against weak disorder. Thus, we offer a unique way to identify the topological signatures of Floquet Majorana fermions.

We develop a theory of topological transitions in a Floquet topological insulator, using graphene irradiated by circularly polarized light as a concrete realization. We demonstrate that a hallmark signature of such transitions in a static system, i.e., metallic bulk transport with conductivity of order e^{2}/h, is substantially suppressed at some Floquet topological transitions in the clean system. We determine the conditions for this suppression analytically and confirm our results in numerical simulations. Remarkably, introducing disorder dramatically enhances this transport by several orders of magnitude.

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We argue that the compact three dimensional electrodynamics with massless relativistic fermions is always in the confined phase, in spite of the bare interaction between the magnetic monopoles being rendered logarithmic by fermions. The effect is caused by screening by other dipoles, which transforms the logarithmic back into the Coulomb interaction at large distances. Possible implications for the chiral symmetry breaking for fermions are discussed, and the global phase diagram of the theory is proposed.

A real-space formulation is given for the recently discussed exciton condensate in a symmetrically biased graphene bilayer. We show that in the continuum limit an oddly-quantized vortex in this condensate binds exactly one zero mode per valley index of the bilayer. In the full lattice model the zero modes are split slightly due to intervalley mixing. We support these results by an exact numerical diagonalization of the lattice Hamiltonian. We also discuss the effect of the zero modes on the charge content of these vortices and deduce some of their interesting properties.

We propose a two-dimensional time-reversal invariant system of essentially non-interacting electrons on a square lattice that exhibits configurations with fractional charges ±e/2. These are vortex-like topological defects in the dimerization order parameter describing spatial modulation in the electron hopping amplitudes. Charge fractionalization is established by a simple counting argument, analytical calculation within the effective lowenergy theory, and by an exact numerical diagonalization of the lattice Hamiltonian. We comment on the exchange statistics of fractional charges and possible realizations of the system.Introduction.-It is now well-known that fractional quantum numbers can arise as the collective excitations of a manybody system. The canonical example of such fractionalization is a 2D electron gas (2DEG) placed in a transverse magnetic field in the fractional quantum Hall regime. At odd inverse filling factors, ν −1 > 1, the many-body ground state is described by a strongly-correlated Laughlin wave function and the time-reversal symmetry is broken. The excitations carry the fractional charge νe (Ref. 1) and exhibit fractional (Abelian) statistics.2 The search for other systems that exhibit fractionalization is ongoing. Two important questions in this search are whether strong correlations or a broken timereversal symmetry is necessary for fractionalization to happen.

Pyrochlore iridates have recently attracted growing interest in condensed matter physics because of their potential for realizing new topological states. In order to achieve such quantum states, it is essential to understand the magnetic properties of these compounds, as their electronic structures are strongly coupled with their magnetic ground states. In this work, we report a systematic study of the magnetic properties of pyrochlore Y 2 Ir 2 O 7 and its hole-doped compounds by performing magnetic, electron spin resonance (ESR), electrical transport and x-ray photoelectron spectroscopy (XPS) measurements. We demonstrate the existence of weak ferromagnetism on top of a large antiferromagnetic background in the undoped compound. Hole-doping by calcium was found to enhance both the ferromagnetism and the electrical conductivity. The XPS characterization shows the coexistence of Ir 4+ and Ir 5+ in the undoped compound, and the amount of Ir 5+ increases with Ca-doping, which highlights the possible origins of the weak ferromagnetism associated with the formation of Ir 5+ . We also observe a vertical shift in the M -H curves after field cooling, which may arise from a strong coupling between the ferromagnetic phase and the antiferromagnetic background.