Correlation between Charge Inhomogeneities and Structure in Graphene and Other Electronic Crystalline Membranes

Abstract

Only one atom thick and not inclined to lattice defects, graphene represents the ultimate crystalline membrane. However, its structure reveals unique features not found in other crystalline membranes, in particular the existence of ripples with wavelength of 100-300 Angstroms. Here, I trace the origin of this difference to the free electrons in the membrane. The deformation energy of the lattice creates a coupling between charge fluctuations and the structure, resulting in ripples on the membrane, correlated with charge inhomogeneities. In graphene this mechanism reproduces the experimental result for both charge puddles and ripples.

Accepted for publication in PRB as Rapid Communication

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Cited by in corpus (32)

• Novel effects of strains in graphene and other two dimensional materials
• Suppression of anharmonicities in crystalline membranes by external strain
• Electron-hole puddles in the absence of charged impurities
• Mermin-Wagner theorem, flexural modes, and degraded carrier mobility in 2D crystals with broken horizontal mirror (${\sigma }_{\mathrm{h}}$) symmetry
• Generalized effective hamiltonian for graphene under non-uniform strain
• Electron density distribution and screening in rippled graphene sheets
• The Structure of Physical Crystalline Membranes within the Self-Consistent Screening Approximation
• Electron-induced rippling in graphene
• Self-Consistent Screening Approximation for Flexible Membranes: Application to Graphene
• Thermal fluctuations of free standing graphene
• Stress-controlled Poisson ratio of a crystalline membrane: Application to graphene
• The effect of rippling on the mechanical properties of graphene
• Rippling and crumpling in disordered free-standing graphene
• Thermodynamics of quantum crystalline membranes
• Fluctuation-induced current from freestanding graphene: toward nanoscale energy harvesting
• Flexuron, a self-trapped state of electron in crystalline membranes
• Buckling of thermalized elastic sheets
• Collective excitations in a large-d model for graphene
• The flat phase of quantum polymerized membranes
• Model of ripples in graphene
• Ripples in a graphene membrane coupled to Glauber spins
• Thermal stiffening of clamped elastic ribbons
• Ripples in hexagonal lattices of atoms coupled to Glauber spins
• Bending rigidity, sound propagation and ripples in flat graphene
• Rippling transition from electron-induced condensation of curvature field in graphene
• Transport properties of rippled graphene
• Thermal ripples in bilayer graphene
• Anomalous thermal expansion in Ising-like puckered sheets
• A numerical study of the rippling instability driven by electron-phonon coupling in graphene
• Large-scale critical behavior of the rippling phase transition for graphene membranes
• Quantum Buckling
• Perturbative renormalization and thermodynamics of quantum crystalline membranes