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Conductance fluctuations in high mobility monolayer graphene: Nonergodicity, lack of determinism and chaotic behavior

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ABSTRACT

We have fabricated a high mobility device, composed of a monolayer graphene flake sandwiched between two sheets of hexagonal boron nitride. Conductance fluctuations as functions of a back gate voltage and magnetic field were obtained to check for ergodicity. Non-linear dynamics concepts were used to study the nature of these fluctuations. The distribution of eigenvalues was estimated from the conductance fluctuations with Gaussian kernels and it indicates that the carrier motion is chaotic at low temperatures. We argue that a two-phase dynamical fluid model best describes the transport in this system and can be used to explain the violation of the so-called ergodic hypothesis found in graphene.

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(a) Hausdorff dimension and (b) determinism as a function of temperature for the P () and N () regions. As a comparison, for a typical graphene sample fabricated on a SiO2 substrate in our group, the Hausdorff dimension is ~1.3 and the determinism is ~97% at 0.3 K.
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f4: (a) Hausdorff dimension and (b) determinism as a function of temperature for the P () and N () regions. As a comparison, for a typical graphene sample fabricated on a SiO2 substrate in our group, the Hausdorff dimension is ~1.3 and the determinism is ~97% at 0.3 K.

Mentions: The Hausdorff dimension, obtained for changes in gate voltage smaller than ~295 mV, is shown in Fig. 4a. Determinism is a measure of complexity that can be used to quantitatively estimate the predictability of a signal. We use this measure to check how random or periodic a fluctuation is. The determinisms, considering the Fermi level sweep for the N and P regions shown in Fig. 4b, are statistically equivalent down to approximately 10 K. For lower temperatures, however, the determinism for the CF of the N region drops much faster than that for the P region. From this, we can estimate an activation energy near 10 · kB (~0.86 meV).


Conductance fluctuations in high mobility monolayer graphene: Nonergodicity, lack of determinism and chaotic behavior
(a) Hausdorff dimension and (b) determinism as a function of temperature for the P () and N () regions. As a comparison, for a typical graphene sample fabricated on a SiO2 substrate in our group, the Hausdorff dimension is ~1.3 and the determinism is ~97% at 0.3 K.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5016828&req=5

f4: (a) Hausdorff dimension and (b) determinism as a function of temperature for the P () and N () regions. As a comparison, for a typical graphene sample fabricated on a SiO2 substrate in our group, the Hausdorff dimension is ~1.3 and the determinism is ~97% at 0.3 K.
Mentions: The Hausdorff dimension, obtained for changes in gate voltage smaller than ~295 mV, is shown in Fig. 4a. Determinism is a measure of complexity that can be used to quantitatively estimate the predictability of a signal. We use this measure to check how random or periodic a fluctuation is. The determinisms, considering the Fermi level sweep for the N and P regions shown in Fig. 4b, are statistically equivalent down to approximately 10 K. For lower temperatures, however, the determinism for the CF of the N region drops much faster than that for the P region. From this, we can estimate an activation energy near 10 · kB (~0.86 meV).

View Article: PubMed Central - PubMed

ABSTRACT

We have fabricated a high mobility device, composed of a monolayer graphene flake sandwiched between two sheets of hexagonal boron nitride. Conductance fluctuations as functions of a back gate voltage and magnetic field were obtained to check for ergodicity. Non-linear dynamics concepts were used to study the nature of these fluctuations. The distribution of eigenvalues was estimated from the conductance fluctuations with Gaussian kernels and it indicates that the carrier motion is chaotic at low temperatures. We argue that a two-phase dynamical fluid model best describes the transport in this system and can be used to explain the violation of the so-called ergodic hypothesis found in graphene.

No MeSH data available.