We demonstrate theoretically the possibility of spinodal de-wetting in heterostructures made of light--atom liquids (hydrogen, helium, and nitrogen) deposited on suspended graphene. Extending our theory of film growth on two-dimensional materials to
include analysis of surface instabilities via the hydrodynamic Cahn--Hilliard-type equation, we characterize in detail the resulting spinodal de-wetting patterns. Both linear stability analysis and advanced computational treatment of the surface hydrodynamics show micron-sized (generally material and atom dependent) patterns of dry regions. The physical reason for the development of such instabilities on graphene can be traced back to the inherently weak van der Waals interactions between atomically thin materials and atoms in the liquid. Similar phenomena occur in doped graphene and other two-dimensional materials, such as monolayer dichalcogenides. Thus two-dimensional materials represent a universal theoretical and technological platform for studies of spinodal de-wetting.
We aim to understand how the spectrum of semi-Dirac fermions is renormalized due to long-range Coulomb electron-electron interactions at a topological Lifshitz transition, where two Dirac cones merge. At the transition, the electronic spectrum is cha
racterized by massive quadratic dispersion in one direction, while it remains linear in the other. We have found that, to lowest order, the unconventional log squared (double logarithmic) correction to the quasiparticle mass in bare perturbation theory leads to resummation into strong mass renormalization in the exact full solution of the perturbative renormalization group equations. This behavior effectively wipes out the curvature of the dispersion and leads to Dirac cone restoration at low energy: the system flows towards Dirac dispersion which is anisotropic but linear in momentum, with interaction-depended logarithmic modulation. The Berry phase associated with the restored critical Dirac spectrum is zero - a property guaranteed by time-reversal symmetry and unchanged by renormalization. Our results are in contrast with the behavior that has been found within the large-$N$ approach.
We study the infrared dynamics of low-energy atoms interacting with a sample of suspended graphene at finite temperature. The dynamics exhibits severe infrared divergences order by order in perturbation theory as a result of the singular nature of lo
w-energy flexural phonon emission. Our model can be viewed as a two-channel generalization of the independent boson model with asymmetric atom-phonon coupling. This allows us to take advantage of the exact non-perturbative solution of the independent boson model in the stronger channel while treating the weaker one perturbatively. In the low-energy limit, the exact solution can be viewed as a resummation (exponentiation) of the most divergent diagrams in the perturbative expansion. As a result of this procedure, we obtain the atoms Green function which we use to calculate the atom damping rate, a quantity equal to the quantum sticking rate. A characteristic feature of our results is that the Greens function retains a weak, infrared cutoff dependence that reflects the reduced dimensionality of the problem. As a consequence, we predict a measurable dependence of the sticking rate on graphene sample size. We provide detailed predictions for the sticking rate of atomic hydrogen as a function of temperature and sample size. The resummation yields an enhanced sticking rate relative to the conventional Fermi golden rule result (equivalent to the one-loop atom self-energy), as higher-order processes increase damping at finite temperature.
We aim to understand how the van der Waals force between neutral adatoms and a graphene layer is modified by uniaxial strain and electron correlation effects. A detailed analysis is presented for three atoms (He, H, and Na) and graphene strain rangin
g from weak to moderately strong. We show that the van der Waals potential can be significantly enhanced by strain, and present applications of our results to the problem of elastic scattering of atoms from graphene. In particular we find that quantum reflection can be significantly suppressed by strain, meaning that dissipative inelastic effects near the surface become of increased importance. Furthermore we introduce a method to independently estimate the Lennard-Jones parameters used in an effective model of He interacting with graphene, and determine how they depend on strain. At short distances, we find that strain tends to reduce the interaction strength by pushing the location of the adsorption potential minima to higher distances above the deformed graphene sheet. This opens up the exciting possibility of mechanically engineering an adsorption potential, with implications for the formation and observation of anisotropic low dimensional superfluid phases.
In this letter, we examine the role of Coulomb interactions in the emergence of macroscopically ordered states in graphene supported on hexagonal boron nitride substrates. Due to incommensuration effects with the substrate, graphene can develop gappe
d low energy modes that spatially conform into a triangular superlattice of quantum rings. In the presence of these modes, we show that Coulomb interactions lead to spontaneous formation of chiral loop currents in bulk and to macroscopic spin-valley order at zero temperature. We show that this exotic state breaks time reversal symmetry and can be detected with interferometry and polar Kerr measurements.
We study the role of long-range electron-electron interactions in a system of two-dimensional anisotropic Dirac fermions, which naturally appear in uniaxially strained graphene, graphene in external potentials, some strongly anisotropic topological i
nsulators, and engineered anisotropic graphene structures. We find that while for small interactions and anisotropy the system restores the conventional isotropic Dirac liquid behavior, strong enough anisotropy can lead to the formation of a quasi-one dimensional electronic phase with dominant charge order (anisotropic excitonic insulator).
We review the problem of electron-electron interactions in graphene. Starting from the screening of long range interactions in these systems, we discuss the existence of an emerging Dirac liquid of Lorentz invariant quasi-particles in the weak coupli
ng regime, and strongly correlated electronic states in the strong coupling regime. We also analyze the analogy and connections between the many-body problem and the Coulomb impurity problem. The problem of the magnetic instability and Kondo effect of impurities and/or adatoms in graphene is also discussed in analogy with classical models of many-body effects in ordinary metals. We show that Lorentz invariance plays a fundamental role and leads to effects that span the whole spectrum, from the ultraviolet to the infrared. The effect of an emerging Lorentz invariance is also discussed in the context of finite size and edge effects as well as mesoscopic physics. We also briefly discuss the effects of strong magnetic fields in single layers and review some of the main aspects of the many-body problem in graphene bilayers. In addition to reviewing the fully understood aspects of the many-body problem in graphene, we show that a plethora of interesting issues remain open, both theoretically and experimentally, and that the field of graphene research is still exciting and vibrant.
We argue that our analysis of the J-Q model, presented in Phys. Rev. B 80, 174403 (2009), and based on a field-theory description of coupled dimers, captures properly the strong quantum fluctuations tendencies, and the objections outlined by L. Isaev
, G. Ortiz, and J. Dukelsky, arXiv:1003.5205, are misplaced.
We study the S=1/2 Heisenberg antiferromagnet on a square lattice with nearest-neighbor and plaquette four-spin exchanges (introduced by A.W. Sandvik, Phys. Rev. Lett. {bf 98}, 227202 (2007).) This model undergoes a quantum phase transition from a
spontaneously dimerized phase to Neel order at a critical coupling. We show that as the critical point is approached from the dimerized side, the system exhibits strong fluctuations in the dimer background, reflected in the presence of a low-energy singlet mode, with a simultaneous rise in the triplet quasiparticle density. We find that both singlet and triplet modes of high density condense at the transition, signaling restoration of lattice symmetry. In our approach, which goes beyond mean-field theory in terms of the triplet excitations, the transition appears sharp; however since our method breaks down near the critical point, we argue that we cannot make a definite conclusion regarding the order of the transition.
