Thermal effect in the Casimir force for graphene and graphene-coated substrates: Impact of nonzero mass gap and chemical potential
G. Bimonte · G. L. Klimchitskaya · V. M. Mostepanenko
Abstract and summary · read the original at the source
In one page
The Casimir force is the vacuum’s signature you can weigh: bring two surfaces close and the field between them pushes them together. Graphene makes it stranger. Because a sheet of graphene is one atom thick and its electrons behave like massless particles moving at a three-hundredth of the speed of light, its Casimir force picks up a temperature contribution that becomes dominant at separations where ordinary materials show almost none. Giuseppe Bimonte in Naples with Galina Klimchitskaya and Vladimir Mostepanenko in Saint Petersburg compute that giant thermal effect for graphene as it really comes, not as an idealisation — with a small energy gap in its spectrum and with doping, described exactly by the finite-temperature polarization tensor of quantum electrodynamics. Their finding is that the two imperfections pull in opposite directions and partly cancel, so a real, doped, slightly gapped sheet behaves much closer to the idealised one than you would fear — and the differential experiment already proposed to see the effect survives both of them with room to spare.
Why it matters hereChapter 2’s case that the vacuum is a real, structured medium rests on the Casimir force being calculable to the last decimal and then measured, and this is that calculation carried into a material where the vacuum’s temperature signature becomes large enough to dominate. It also names the bench test: a differential setup whose predicted signal sits far above an error bar already achieved.
What it claims
01Using the rigorous finite-temperature quantum electrodynamics of the polarization tensor, the authors show that the mass gap and the chemical potential of real graphene act on the Casimir force in opposite directions — the force falls as the gap is opened and rises as the doping is raised — so for a real sample the two effects partly cancel.Abstract; Section III, Eq. 32 and Figure 1(a)
Published and peer-reviewed02The reason is conductivity. Raising the chemical potential raises graphene’s conductivity and so raises the force, while opening a mass gap lowers the carriers’ mobility and therefore the conductivity, and brings the force down. The relative influence of both parameters shrinks as the sphere is moved further from the sheet.Section III, the paragraph following Figure 1(a)
Published and peer-reviewed03For graphene deposited on silica or silicon the Casimir force is much stronger than for a free-standing sheet, yet the thermal correction and its fractional weight in the total force are smaller, and the influence of the graphene coating fades as the substrate’s static dielectric permittivity rises. Since most applications use coated substrates, the authors judge that controlling the Casimir force by doping alone is problematic there.Section IV; Section VI, paragraphs 3 and 4
Published and peer-reviewed04The thermal correction is not a monotonic function of the mass gap, and its derivative with respect to the gap energy is discontinuous where that energy equals the chemical potential — because below that point the zero-temperature polarization tensor does not depend on the chemical potential at all.Section III, Figures 2(b) and 2(c) and the paragraph discussing them; Section VI, paragraph 4
Published and peer-reviewed05The bench test is a differential measurement: a gold-coated sphere over a silicon plate whose two halves are, respectively, bare and graphene-coated, with the difference of the two Casimir forces recorded as a function of separation. Taking the doping measured in real samples, 0.02 electronvolts, together with the conservative upper bound of 0.2 electronvolts on the gap energy, the smallest possible thermal signal still runs far above the 1 femtonewton error already achieved in a differential Casimir measurement, across the whole range from 220 nanometres to 1.5 micrometres.Section V, Eqs. 34 to 36, Figure 8(c) and the final paragraph
Designed, not yet built06The authors name what a direct observation would buy: fitting the measured giant thermal effect against computations at different gap energies would determine the mass gap of a graphene sheet, and the same handle would open the modification and control of the Casimir force in graphene-based micromechanical systems.Section VI, final paragraph
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Read it · abstract
Abstract
The rigorous finite-temperature QED formalism of the polarization tensor is used to study the combined effect of nonzero mass gap m and chemical potential mu on the Casimir force and its thermal correction in the experimentally relevant configuration of a Au sphere interacting with a real graphene sheet or with graphene-coated dielectric substrates made of different materials. It is shown that for both a free-standing graphene sheet and for graphene-coated substrates the magnitude of the Casimir force decreases as m is increased, while it increases as mu is increased, indicating that these parameters act in opposite directions. According to our results, the impact of m and/or mu on the Casimir force for graphene-coated plates is much smaller than for a free-standing graphene sheet. Furthermore, computations show that the Casimir force is much stronger for graphene-coated substrates than for a free-standing graphene sample, but the thermal correction and its fractional weight in the total force are smaller in the former case. These results are applied to a differential setup that was recently proposed to observe the giant thermal effect in the Casimir force for graphene. We show that this experiment remains feasible even after taking into account the influence of the nonzero mass-gap and chemical potential of real graphene samples. Possible further applications of the obtained results are discussed.
The way in
https://doi.org/10.1103/PhysRevB.96.115430Published as Physical Review B 96, 115430 (2017) by Giuseppe Bimonte of the University of Naples Federico II and INFN Naples, with Galina Klimchitskaya and Vladimir Mostepanenko of the Pulkovo Observatory and the Peter the Great Saint Petersburg Polytechnic University, Mostepanenko also at Kazan Federal University. The manuscript is free to read on arXiv as 1709.02628, posted 8 September 2017, but that posting carries the arXiv default licence and the version of record carries the APS default licence — neither is a Creative Commons licence — so this page holds the summary, the claims and the authors’ own abstract and sends the reader to the source. The claims are located against the arXiv version’s numbered sections, equations and figures.
How to cite it
G. Bimonte, G. L. Klimchitskaya, V. M. Mostepanenko (2017) Thermal effect in the Casimir force for graphene and graphene-coated substrates: Impact of nonzero mass gap and chemical potential. doi:10.1103/PhysRevB.96.115430
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