Electron-induced rippling in graphene

Abstract

We show that the interaction between flexural phonons, when corrected by the exchange of electron-hole excitations, may place the graphene sheet very close to a quantum critical point characterized by the strong suppression of the bending rigidity of the membrane. Ripples arise then due to spontaneous symmetry breaking, following a mechanism similar to that responsible for the condensation of the Higgs field in relativistic field theories. In the presence of membrane tensions, ripple condensation may be reinforced or suppressed depending on the sign of the tension, following a zero-temperature buckling transition in which the order parameter is given essentially by the square of the gradient of the flexural phonon field.

4 pages, 3 figures

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Cited by in corpus (35)

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• Conductivity of suspended graphene at the Dirac point
• Strain dependent elastic modulus of graphene
• Electronic structure of spontaneously strained graphene on hexagonal Boron Nitride
• Graphene's morphology and electronic properties from discrete differential geometry
• Rippling and crumpling in disordered free-standing graphene
• The effect of rippling on the mechanical properties of graphene
• Thermodynamics of quantum crystalline membranes
• Helicoidal Graphene Nanoribbons: Chiraltronics
• Fluctuation-induced current from freestanding graphene: toward nanoscale energy harvesting
• Buckling of thermalized elastic sheets
• Quantized transport, strain-induced perfectly conducting modes and valley filtering on shape-optimized graphene Corbino devices
• Density functional theory analysis of flexural modes, elastic constants, and corrugations in strained graphene
• Collective excitations in a large-d model for graphene
• The flat phase of quantum polymerized membranes
• Critical radius and temperature for buckling in graphene
• Model of ripples in graphene
• Ripples in a string coupled to Glauber spins
• Ripples in a graphene membrane coupled to Glauber spins
• Interplay between in-plane and flexural phonons in electronic transport of two-dimensional semiconductors
• Ripples in hexagonal lattices of atoms coupled to Glauber spins
• Bifurcation analysis and phase diagram of a spin-string model with buckled states
• Measuring strain and rotation fields at the dislocation core in graphene
• Bending rigidity, sound propagation and ripples in flat graphene
• STM driven transition from rippled to buckled graphene in a spin-membrane model
• Rippling transition from electron-induced condensation of curvature field in graphene
• Thermo-electromechanical effects in relaxed shape graphene and bandstructures of graphene quantum dots
• A numerical study of the rippling instability driven by electron-phonon coupling in graphene
• Buckling in a rotationally invariant spin-elastic model
• Magnetically Controlling the Explosion of Dirac Fermions during the Oxidation of Graphene
• Nature of Spontaneous Curvature in Suspended Graphene
• Perturbative renormalization and thermodynamics of quantum crystalline membranes
• Quantum Buckling