Multiple mobile excitons manifested as sidebands in quasi-one-dimensional metallic TaSe3.

Charge neutrality and their expected itinerant nature makes excitons potential transmitters of information. However, exciton mobility remains inaccessible to traditional optical experiments that only create and detect excitons with negligible momentum. Here, using angle-resolved photoemission spectroscopy, we detect dispersing excitons in the quasi-one-dimensional metallic trichalcogenide, TaSe3. The low density of conduction electrons and the low dimensionality in TaSe3 combined with a polaronic renormalization of the conduction band and the poorly screened interaction between these polarons and photo-induced valence holes leads to various excitonic bound states that we interpret as intrachain and interchain excitons, and possibly trions. The thresholds for the formation of a photo-hole together with an exciton appear as side valence bands with dispersions nearly parallel to the main valence band, but shifted to lower excitation energies. The energy separation between side and main valence bands can be controlled by surface doping, enabling the tuning of certain exciton properties.

Testing of asymptomatic individuals for fast feedback-control of COVID-19 pandemic.

We argue that frequent sampling of the fraction of a priori non-symptomatic but infectious humans (either by random or cohort testing) significantly improves the management of the COVID-19 pandemic, when compared to intervention strategies relying on data from symptomatic cases only. This is because such sampling measures the incidence of the disease, the key variable controlled by restrictive measures, and thus anticipates the load on the healthcare system due to progression of the disease. The frequent testing of non-symptomatic infectiousness will (i) significantly improve the predictability of the pandemic, (ii) allow informed and optimized decisions on how to modify restrictive measures, with shorter delay times than the present ones, and (iii) enable the real-time assessment of the efficiency of new means to reduce transmission rates. These advantages are quantified by considering a feedback and control model of mitigation where the feedback is derived from the evolution of the daily measured prevalence. While the basic model we propose aggregates data for the entire population of a country such as Switzerland, we point out generalizations which account for hot spots which are analogous to Anderson-localized regions in the theory of diffusion in random media.

Fractional Chern insulators with strong interactions that far exceed band gaps.

We study two models for spinless fermions featuring topologically nontrivial bands characterized by Chern numbers C=±1 at fractional filling. Using exact diagonalization, we show that, even for infinitely strong nearest-neighbor repulsion, the ground states of these models belong to the recently discovered class of quantum liquids called fractional Chern insulators (FCI). Thus, we establish that FCI states can arise even if interaction strengths are arbitrarily larger than the noninteracting band gap, going beyond the limits in which FCI states have been previously studied. The strong-coupling FCI states, therefore, depart from the usual isolated-band picture that parallels the fractional quantum Hall effect in Landau levels and demonstrate how a topologically ordered state can arise in a truly multiband system.

Topological Hubbard model and its high-temperature quantum Hall effect.

The quintessential two-dimensional lattice model that describes the competition between the kinetic energy of electrons and their short-range repulsive interactions is the repulsive Hubbard model. We study a time-reversal symmetric variant of the repulsive Hubbard model defined on a planar lattice: Whereas the interaction is unchanged, any fully occupied band supports a quantized spin Hall effect. We show that at 1/2 filling of this band, the ground state develops spontaneously and simultaneously Ising ferromagnetic long-range order and a quantized charge Hall effect when the interaction is sufficiently strong. We ponder on the possible practical applications, beyond metrology, that the quantized charge Hall effect might have if it could be realized at high temperatures and without external magnetic fields in strongly correlated materials.

Fractional quantum Hall states at zero magnetic field.

We present a simple prescription to flatten isolated Bloch bands with a nonzero Chern number. We first show that approximate flattening of bands with a nonzero Chern number is possible by tuning ratios of nearest-neighbor and next-nearest-neighbor hoppings in the Haldane model and, similarly, in the chiral-π-flux square lattice model. Then we show that perfect flattening can be attained with further range hoppings that decrease exponentially with distance. Finally, we add interactions to the model and present exact diagonalization results for a small system at 1/3 filling that support (i) the existence of a spectral gap, (ii) that the ground state is a topological state, and (iii) that the Hall conductance is quantized.

Quantum Hall effect of massless dirac fermions in a vanishing magnetic field.

The effect of strong long-range disorder on the quantization of the Hall conductivity sigma{xy} in graphene is studied numerically. It is shown that increasing Landau-level mixing progressively destroys all plateaus in sigma{xy} except the plateaus at sigma{xy}=-/+e{2}/2h (per valley and per spin). The critical state at the Dirac point is robust to strong disorder and belongs to the universality class of the conventional plateau transitions in the integer quantum Hall effect. We propose that the breaking of time-reversal symmetry by ripples in graphene can realize this quantum critical point in a vanishing magnetic field.

Irrational versus rational charge and statistics in two-dimensional quantum systems.

We show that quasiparticle excitations with irrational charge and irrational exchange statistics exist in tight-binding systems described, in the continuum approximation, by the Dirac equation in (2+1)-dimensional space and time. These excitations can be deconfined at zero temperature, but when they are, the charge rerationalizes to the value 1/2 and the exchange statistics to that of "quartons" (half-semions).

Electron fractionalization in two-dimensional graphenelike structures.

Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall fluids, where time-reversal symmetry is broken by a large external magnetic field. Recently, there has been a tremendous effort in the search for examples of fractionalization in two-dimensional systems with time-reversal symmetry. In this Letter, we show that fractionally charged topological excitations exist on graphenelike structures, where quasiparticles are described by two flavors of Dirac fermions and time-reversal symmetry is respected. The topological zero modes are mathematically similar to fractional vortices in p-wave superconductors. They correspond to a twist in the phase in the mass of the Dirac fermions, akin to cosmic strings in particle physics.

Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization.

We discuss, for a two-dimensional Dirac Hamiltonian with a random scalar potential, the presence of a Z2 topological term in the nonlinear sigma model encoding the physics of Anderson localization in the symplectic symmetry class. The Z2 topological term realizes the sign of the Pfaffian of a family of Dirac operators. We compute the corresponding global anomaly, i.e., the change in the sign of the Pfaffian by studying a spectral flow numerically. This Z2 topological effect can be relevant to graphene when the impurity potential is long ranged and, also, to the two-dimensional boundaries of a three-dimensional lattice model of Z2 topological insulators in the symplectic symmetry class.