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Register a new userMagnetic Phases in Periodically Rippled Graphene
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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.
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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.
In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These nonequilibrium states, at high driving frequencies, exhibit the quintessential robustness against local disorder similar to equilibrium topological phases. However, proving the existence of such topological phases in a general setting is an open problem. We propose a universal effective theory that leverages on modern free probability theory and ideas in random matrices to analytically predict the existence of the topological phase for finite driving frequencies and across a range of disorder. We find that, depending on the strength of disorder, such systems may be topological or trivial and that there is a transition between the two. In particular, the theory predicts the critical point for the transition between the two phases and provides the critical exponents. We corroborate our results by comparing them to exact diagonalizations for driven-disordered 1D Kitaev chain and 2D Bernevig-Hughes-Zhang models and find excellent agreement. This Letter may guide the experimental efforts for exploring topological phases.
Graphene epitaxially grown on Ru(0001) displays a remarkably ordered pattern of hills and valleys in Scanning Tunneling Microscopy (STM) images. To which extent the observed ripples are structural or electronic in origin have been much disputed recently. A combination of ultrahigh resolution STM images and Helium Atom diffraction data shows that i) the graphene lattice is rotated with respect to the lattice of Ru and ii) the structural corrugation as determined from He diffraction is substantially smaller (0.015 nm) than predicted (0.15 nm) or reported from X-Ray Diffraction or Low Energy Electron Diffraction. The electronic corrugation, on the contrary, is strong enough to invert the contrast between hills and valleys above +2.6 V as new, spatially localized electronic states enter the energy window of the STM. The large electronic corrugation results in a nanostructured periodic landscape of electron and holes pockets.
The exceptionally high mobility of carriers in graphene is one of its defining characteristics, especially in view of potential applications. Therefore it is of both practical and fundamental importance to understand the mechanisms responsible for limiting the values of mobility. The aim of the paper is to study theoretically one such mechanism, i.e. scattering on ripples. The transport properties of rippled graphene are studied using using single-band tight-binding model. Both the bond-length variation, corresponding to the vector potential in the effective mass picture, and fluctuating scalar potential are included in the formalism. The samples are modeled as self-similar surfaces characterized by the roughness exponent with values ranging from typical for graphene on SiO$_{2}$ to seen in suspended samples. The range of calculated resistivities and mobilities overlaps with experiment. The results presented here support the notion of rippling as one of the factors limiting the mobility.
We report measurements of the effects of a random vector potential generated by applying an in-plane magnetic field to a graphene flake. Magnetic flux through the ripples cause orbital effects: phase-coherent weak localization is suppressed, while quasi-random Lorentz forces lead to anisotropic magnetoresistance. Distinct signatures of these two effects enable an independent estimation of the ripple amplitude and correlation length.
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