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

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

Instabilities on graphene's honeycomb lattice with electron-phonon interactions

We study the impact of electron-phonon interactions on the many-body instabilities of electrons on the honeycomb lattice and their interplay with repulsive local and non-local Coulomb interactions at charge neutrality. To that end, we consider in-plane optical phonon modes with wavevectors close to the $\Gamma$ point as well as to the $K, -K$ points and calculate the effective phonon-mediated electron-electron interaction by integrating out the phonon modes. Ordering tendencies are studied by means of a momentum-resolved functional renormalization group approach allowing for an unbiased investigation of the appearing instabilities. In the case of an exclusive and supercritical phonon-mediated interaction, we find a Kekul\'e and a nematic bond ordering tendency being favored over the $s$-wave superconducting state. The competition between the different phonon-induced orderings clearly shows a repulsive interaction between phonons at small and large wavevector transfers. We further discuss the influence of phonon-mediated interactions on electronically-driven instabilities induced by onsite, nearest neighbor and next-to-nearest neighbor density-density interactions. We find an extension of the parameter regime of the spin density wave order going along with an increase of the critical scales where ordering occurs, and a suppression of competing orders.Comment: 9 pages, 5 figure

Ga+ beam lithography for suspended lateral beams and nanowires

The authors demonstrate the fabrication of suspended nanowires and doubly clamped beams by using a focused ion beam implanted Ga etch mask followed by an inductively coupled plasma reactive ion etching of silicon. This method will demonstrate how a two-step, completely dry fabrication sequence can be tuned to generate nanomechanical structures on either silicon substrates or silicon on insulator (SOI). This method was used to generate lateral nanowires suspended between 2 µm scaled structures with lengths up to 16 µm and widths down to 40 nm on a silicon substrate. The authors also fabricate 10 µm long doubly clamped beams on SOIs that are 20 nm thick and a minimum of 150 nm wide. In situ electrical measurements of the beams demonstrate a reduction of resistivity from > 37.5 Ω cm down to 0.25 Ω cm. Transmission electron microscopy for quantifying both surface roughness and crystallinity of the suspended nanowires was performed. Finally, a dose array for repeatable fabrication of a desired beam width was also experimentally determined

Multicritical behavior in models with two competing order parameters

We employ the nonperturbative functional Renormalization Group to study models with an O(N_1)+O(N_2) symmetry. Here, different fixed points exist in three dimensions, corresponding to bicritical and tetracritical behavior induced by the competition of two order parameters. We discuss the critical behavior of the symmetry-enhanced isotropic, the decoupled and the biconical fixed point, and analyze their stability in the N_1, N_2 plane. We study the fate of non-trivial fixed points during the transition from three to four dimensions, finding evidence for a triviality problem for coupled two-scalar models in high-energy physics. We also point out the possibility of non-canonical critical exponents at semi-Gaussian fixed points and show the emergence of Goldstone modes from discrete symmetries.Comment: 16 pages, 7 figures, 5 tables, minor changes in updated version, identical to published one in Phys. Rev.