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Register a new userDisorder-induced rippled phases and multicriticality in free-standing graphene
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One of the most exciting phenomena observed in crystalline disordered membranes, including a suspended graphene, is rippling, i.e. a formation of static flexural deformations. Despite an active research, it still remains unclear whether the rippled phase exists in the thermodynamic limit, or it is destroyed by thermal fluctuations. We demonstrate that a sufficiently strong short-range disorder stabilizes ripples, whereas in the case of a weak disorder the thermal flexural fluctuations dominate in the thermodynamic limit. The phase diagram of the disordered suspended graphene contains two separatrices: the crumpling transition line dividing the flat and crumpled phases and the rippling transition line demarking the rippled and clean phases. At the intersection of the separatrices there is the unstable, multicritical point which splits up all four phases. Most remarkably, rippled and clean flat phases are described by a single stable fixed point which belongs to the rippling transition line. Coexistence of two flat phases in the single point is possible due to non-analiticity in corresponding renormalization group equations and reflects non-commutativity of limits of vanishing thermal and rippling fluctuations.
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An acoustic plasmon is predicted to occur, in addition to the conventional two-dimensional (2D) plasmon, as the collective motion of a system of two types of electronic carriers coexisting in the very same 2D band of extrinsic (doped or gated) graphene. The origin of this novel mode resides in the strong anisotropy that is present in the graphene band structure near the Dirac point. This anisotropy allows for the coexistence of carriers moving with two distinct Fermi velocities along the Gamma-K direction, which leads to two modes of collective oscillation: one mode in which the two types of electrons oscillate in phase with one another [this is the conventional 2D graphene plasmon, which at long wavelengths (q->0) has the same dispersion, q^1/2, as the conventional 2D plasmon of a 2D free electron gas], and the other mode found here corresponding to a low-frequency acoustic oscillation [whose energy exhibits at long wavelengths a linear dependence on the 2D wavenumber q] in which the two types of electrons oscillate out of phase. If this prediction is confirmed experimentally, it will represent the first realization of acoustic plasmons originated in the collective motion of a system of two types of carriers coexisting within the very same band.
We study the effects that ripples induce on the electrical and magnetic properties of graphene. The variation of the interatomic distance created by the ripples translates in a modulation of the hopping parameter between carbon atoms. A tight binding Hamiltonian including a Hubbard interaction term is solved self consistently for ripples with different amplitudes and periods. We find that, for values of the Hubbard interaction $U$ above a critical value $U_C$, the system displays a superposition of local ferromagnetic and antiferromagnetic ordered states. Nonetheless the global ferromagnetic order parameter is zero. The $U_C$ depends only on the product of the period and hopping amplitude modulation. When the Hubbard interaction is close to the critical value of the antiferromagnetic transition in pristine graphene, the antiferromagnetic order parameter becomes much larger than the ferromagnetic one, being the ground state similar to that of flat graphene.
A recently proposed curvature renormalization group scheme for topological phase transitions defines a generic `curvature function as a function of the parameters of the theory and shows that topological phase transitions are signalled by the divergence of this function at certain parameters values, called critical points, in analogy with usual phase transitions. A renormalization group procedure was also introduced as a way of flowing away from the critical point towards a fixed point, where an appropriately defined correlation function goes to zero and topological quantum numbers characterising the phase are easy to compute. In this paper, using two independent models - a model in the AIII symmetry class and a model in the BDI symmetry class - in one dimension as examples, we show that there are cases where the fixed point curve and the critical point curve appear to intersect, which turn out to be multi-critical points, and focus on understanding its implications.
Single-layer graphene sheets are typically characterized by long-wavelength corrugations (ripples) which can be shown to be at the origin of rather strong potentials with both scalar and vector components. We present an extensive microscopic study, based on a self-consistent Kohn-Sham-Dirac density-functional method, of the carrier density distribution in the presence of these ripple-induced external fields. We find that spatial density fluctuations are essentially controlled by the scalar component, especially in nearly-neutral graphene sheets, and that in-plane atomic displacements are as important as out-of-plane ones. The latter fact is at the origin of a complicated spatial distribution of electron-hole puddles which has no evident correlation with the out-of-plane topographic corrugations. In the range of parameters we have explored, exchange and correlation contributions to the Kohn-Sham potential seem to play a minor role.
The textbook thermophoretic force which acts on a body in a fluid is proportional to the local temperature gradient. The same is expected to hold for the macroscopic drift behavior of a diffusive cluster or molecule physisorbed on a solid surface. The question we explore here is whether that is still valid on a 2D membrane such as graphene at short sheet length. By means of a non-equilibrium molecular dynamics study of a test system -- a gold nanocluster adsorbed on free-standing graphene clamped between two temperatures $Delta T$ apart -- we find a phoretic force which for submicron sheet lengths is parallel to, but basically independent of, the local gradient magnitude. This identifies a thermophoretic regime that is ballistic rather than diffusive, persisting up to and beyond a hundred nanometer sheet length. Analysis shows that the phoretic force is due to the flexural phonons, whose flow is known to be ballistic and distance-independent up to relatively long mean-free paths. Yet, ordinary harmonic phonons should only carry crystal momentum and, while impinging on the cluster, should not be able to impress real momentum. We show that graphene, and other membrane-like monolayers, support a specific anharmonic connection between the flexural corrugation and longitudinal phonons whose fast escape leaves behind a 2D-projected mass density increase endowing the flexural phonons, as they move with their group velocity, with real momentum, part of which is transmitted to the adsorbate through scattering. The resulting distance-independent ballistic thermophoretic force is not unlikely to possess practical applications.
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