Correlated spinless fermions on the honeycomb lattice revisited

We investigate the quantum many-body instabilities of the extended Hubbard model for spinless fermions on the honeycomb lattice with repulsive nearest-neighbor and 2nd nearest-neighbor density-density interactions. Recent exact diagonalization and infinite density matrix renormalization group results suggest that a putative topological Mott insulator phase driven by the 2nd nearest-neighbor repulsion is suppressed, while other numerically exact approaches support the topological Mott insulator scenario. In the present work, we employ the functional renormalization group (fRG) for correlated fermionic systems. Our fRG results hint at a strong suppression of the scattering processes stabilizing the topological Mott insulator. From analyzing the effects of fermionic fluctuations, we obtain a phase diagram which is the result of the competition of various charge ordering instabilities.Comment: 9 pages, 8 figure

International trade and competition policy

With the completion of the Uruguay Round of international trade negotiations, attention turns to plausible next steps. One question on the agenda of possibilities is the adoption of competition policies that complement or substitute for the remedies traditionally used to deal with international trade distortions. This paper examines three cases --industrial diamonds, potash from Saskatchewan, and cement from Greece

International competition policy and economic development

During the past half century many nations have adopted policies whose function is to discourage cartels and other restrictive practices. Industrialized nations led the movement toward pro-competition policies, but more recently, developing nations have begun to join the parade. Initial steps have also been taken toward the implementation of competition policies spanning national borders, and proposals for their extension have been made. This paper analyzes the consequences national and international competition policies would have for developing nations. Topics covered include the dependence of LDCs on cartelized commodity exports, the terms on which intermediate goods and technology are imported by LDCs, access to the markets of industrialized nations, the consequences of substituting predatory pricing standards for the criteria traditionally used to combat dumping in international trade, and the links between domestic and international market structure and the absorption of advanced technology. --

The size distribution of profits from innovation

The research reported in this paper seeks to determine how skewed the distribution of profits from technological innovation is --i.e., whether it conforms most closely to the Paretian, log normal, or some other distribution. The question is important, because high skewness makes it difficult to pursue risk-hedging portfolio strategies. This paper examines data from several sources

Bond-ordered states and ff-wave pairing of spinless fermions on the honeycomb lattice

Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behaviour in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the van-Hove filling, the free Fermi surface is hole-like and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the van-Hove filling the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling the free Fermi surface becomes electron-like and a superconducting instability with $f$-wave symmetry is found to emerge from the interplay of intra-unitcell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.Comment: 11 pages, 11 figure

Unconventional pairing and electronic dimerization instabilities in the doped Kitaev-Heisenberg model

We study the quantum many-body instabilities of the $t -J_{\mathrm{K}} - J_{\mathrm{H}}$ Kitaev-Heisenberg Hamiltonian on the honeycomb lattice as a minimal model for a doped spin-orbit Mott insulator. This spin-$1/2$ model is believed to describe the magnetic properties of the layered transition-metal oxide Na$_2$IrO$_3$. We determine the ground-state of the system with finite charge-carrier density from the functional renormalization group (fRG) for correlated fermionic systems. To this end, we derive fRG flow-equations adapted to the lack of full spin-rotational invariance in the fermionic interactions, here represented by the highly frustrated and anisotropic Kitaev exchange term. Additionally employing a set of Ward identities for the Kitaev-Heisenberg model, the numerical solution of the flow equations suggests a rich phase diagram emerging upon doping charge carriers into the ground-state manifold ($\mathbb{Z}_2$ quantum spin liquids and magnetically ordered phases). We corroborate superconducting triplet $p$-wave instabilities driven by ferromagnetic exchange and various singlet pairing phases. For filling $\delta > 1/4$, the $p$-wave pairing gives rise to a topological state with protected Majorana edge-modes. For antiferromagnetic Kitaev and ferromagnetic Heisenberg exchange we obtain bond-order instabilities at van Hove filling supported by nesting and density-of-states enhancement, yielding dimerization patterns of the electronic degrees of freedom on the honeycomb lattice. Further, our flow equations are applicable to a wider class of model Hamiltonians.Comment: 24 pages, 18 figures, corresponds to journal versio

Instabilities of interacting electrons on the honeycomb bilayer

We investigate the instabilities of interacting electrons on the honeycomb bilayer by means of the functional renormalization group for a range of interactions up to the third-nearest neighbor. Besides a novel instability toward a gapless charge-density wave we find that using interaction parameters as determined by ab-initio calculations for graphene and graphite puts the system close to the boundary between antiferromagnetic and quantum spin Hall instabilities. Importantly, the energy scales for these instabilities are large such that imperfections and deviations from the basic model are expected to play a major role in real bilayer graphene, where interaction effects seem to be seen only at smaller scales. We therefore analyze how reducing the critical scale and small doping of the layers affect the instabilities.Comment: 5 pages, 4 figure

All-Optical Modulation in a Silicon Waveguide Based on a Single-Photon Process

All-optical, low-power modulation is a major goal in photonics. Because of their high mode-field concentration and ease of manufacturing, nanoscale silicon waveguides offer an intriguing platform for photonics. So far, all-optical modulators built with silicon photonic circuits have relied on either two-photon absorption or the Kerr effect. Both effects are weak in silicon, and require extremely high (~5 W) peak optical power levels to achieve modulation. Here, we describe an all-optical Mach-Zehnder modulator based on a single-photon absorption (SPA) process, fabricated entirely in silicon. Our SPA modulator is based on a process by which a single photon at 1.55 mum is absorbed and an apparently free-carrier-mediated process causes an index shift in silicon, even though the photon energy does not exceed that of silicon's bandgap. We demonstrate all-optical modulation with a gate response of 1deg/mW at 0.5 Gb/s. This is over an order of magnitude more responsive than typical previously demonstrated devices. Even without resonant enhancement, further engineering may enable all optical modulation with less than 10 mW of gate power required for complete extinction, and speeds of 5 Gb/s or higher