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Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding

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Flexural phonons in free-standing graphene.

Eros Mariani¹, Felix von Oppen

¹Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany.

Physical Review Letters

|March 21, 2008

Summary

Flexural phonons in graphene membranes exhibit quadratic dispersion, leading to an anomalous T(5/2)lnT resistivity dependence below a crossover temperature. This behavior arises from coupled bending and stretching in the membrane.

Area of Science:

Condensed Matter Physics
Materials Science
Nanotechnology

Background:

Freestanding graphene membranes possess unique phononic properties due to their 2D structure.
Understanding phonon behavior is crucial for predicting electronic properties like electrical resistivity.
Symmetries in graphene dictate the nature of phonon dispersion relations.

Purpose of the Study:

To investigate the role of out-of-plane (flexural) phonons in the electrical resistivity of graphene membranes.
To determine the temperature dependence of resistivity arising from flexural phonon interactions.
To elucidate the microscopic origins of anomalous temperature dependencies in graphene's electrical transport.

Main Methods:

Theoretical analysis of flexural phonon dispersion relations in freestanding graphene membranes, considering rotation and reflection symmetries.

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Calculation of the phonon contribution to electrical resistivity (rho) by analyzing phonon-charge carrier interactions.

Investigation of the coupling between bending and stretching degrees of freedom and its effect on phonon renormalization.

Main Results:

Flexural phonons exhibit quadratic dispersion at long wavelengths, consistent with symmetry constraints.
Charge carriers excite flexural phonons in pairs, influencing their contribution to resistivity.
An anomalous temperature dependence, rho proportional to T(5/2)lnT, is observed below a crossover temperature T(x).
The logarithmic factor in resistivity arises from the renormalization of flexural phonon dispersion due to coupled in-plane and out-of-plane motions.

Conclusions:

Flexural phonons are the dominant contributors to resistivity in graphene membranes below T(x).
The observed anomalous temperature dependence provides insight into electron-phonon coupling mechanisms in 2D materials.
The coupling between bending and stretching modes significantly modifies phonon properties and electron transport in graphene.