Historical research guide · 0731 · 2020
Fluctuation-induced current from freestanding graphene
P. M. Thibado · P. Kumar · Surendra Singh · M. Ruiz-Garcia · A. Lasanta · L. L. Bonilla
In one minute
Paul Thibado’s group at the University of Arkansas put a scanning tunnelling microscope tip above a sheet of graphene suspended over a hole and watched it move. At room temperature the sheet never stops: its nanometre ripples flip between concave and convex, and the carbon atoms ride them. With the tip pulled back far enough that no electrons tunnel, that motion still pushes charge around the circuit — a displacement current, which the team routes through a pair of diodes so each flip drives current one way and the return flip the other. Rigid graphene on copper gives nothing, which rules out contamination and field emission. Power reaching one diode reached 40 picowatts. With Luis Bonilla and colleagues in Madrid they then model the ripple as a Brownian particle in a double-well potential wired to the diode circuit, and work the accounting through: the system sits at a single temperature in equilibrium, the graphene supplies exactly the power the load resistor dissipates, and the changing diode resistance lifts the output above Nyquist’s noise-power formula.
Connection
Chapter 6 wants devices that turn fluctuations straight into current, and this is the cleanest published example of one: no temperature difference across the device, no radioactive source, just a membrane that will not hold still and a circuit that rectifies it. Chapter 2 supplies the reason it will not hold still. The same group’s molecular-dynamics study of how those ripples invert is on this site at /library/stm-b278fb0be1.
From the source
At room temperature the out-of-plane fluctuations of freestanding graphene are about a hundred times larger than those of graphene supported on copper — 10 picoamps of tunnelling-current fluctuation against 0.1 picoamps — and extrapolated to zero tunnelling current the motion still contributes about 20 picoamps of displacement current.Figure 1, panels d and e, and the accompanying text
With the tip withdrawn until no electrons tunnel, a DC bias of 15 or 45 volts produces a spiky, time-dependent current through diode 2, and the power dissipated in that diode reaches 40 picowatts; identically prepared rigid graphene produces no such current, which the authors take as confirmation that contamination and field emission are not the source.Figure 2, panels a to d, and the paragraph on backing the tip away
Modelling the nearest ripple as a Brownian particle in a double-well potential coupled to the diode circuit by Langevin-Ito equations, the whole system reaches thermal equilibrium at one temperature and the rates of heat, work and entropy production go to zero — yet the time-averaged power dissipated in the resistor equals the time-averaged power supplied by the thermal bath, so electrical work is carried out on the load without violating the second law.Equations 1 to 8; Figure 3, panel a; summary paragraph
The exact thermal power formula reduces to Nyquist’s noise power, temperature divided by the resistance-capacitance product, only if the resistance is constant; because the diode resistance changes with time the true result is a large power enhancement over Nyquist.Figure 3, panel b, and the text following Equation 8
Because the power includes the Brownian motion of the graphene ripple and not only that of the electrons, the barrier-crossing rate of the double well introduces a new and much slower time scale: lowering that rate leaves the total power unchanged but redistributes it to very low frequencies, which the authors note adds technological value for harvesting.Figure 3, panel f, and the paragraph on the power spectral density
Driving the system out of equilibrium — extra noise sources, or different temperatures in different parts of the circuit — would produce entropy and measurable deviations from detailed balance, and the authors name this as the next thing worth investigating in freestanding graphene.Closing paragraph of the summary section
The way in
https://doi.org/10.1103/physreve.102.042101How to cite it
P. M. Thibado, P. Kumar, Surendra Singh, M. Ruiz-Garcia, A. Lasanta, L. L. Bonilla (2020) Fluctuation-induced current from freestanding graphene doi:10.1103/physreve.102.042101