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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.

No MeSH data available.


Theoretical GOE (red dashed curves) and the estimated probability density functions (solid curves) for the N (left) and P regions (right) as a function of the spacing ‘s’ obtained at 0.3 K.
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f5: Theoretical GOE (red dashed curves) and the estimated probability density functions (solid curves) for the N (left) and P regions (right) as a function of the spacing ‘s’ obtained at 0.3 K.

Mentions: It has been postulated that the spectra of time-reversal invariant systems whose classical counterparts show chaotic behavior should have the same fluctuation properties of a Gaussian orthogonal ensemble (GOE) or a Gaussian symplectic ensemble (GSE)2021. When the system does not exhibit time reversal symmetry, a Gaussian unitary ensemble (GUE) better models it22. The distributions of the eigenvalue spacing were estimated as a probability density function as shown in Fig. 5, together with the theoretical distributions (the evolution of the distributions at different temperatures is shown in supplementary Fig. S3). A Kolmogorov-Smirnov (K-S) test2324 was performed to check which probability density function better fits the experimental data and the results are given in Fig. 6. At lower temperatures the distributions for both the P and N regions tend towards a GOE.


Conductance fluctuations in high mobility monolayer graphene: Nonergodicity, lack of determinism and chaotic behavior
Theoretical GOE (red dashed curves) and the estimated probability density functions (solid curves) for the N (left) and P regions (right) as a function of the spacing ‘s’ obtained at 0.3 K.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f5: Theoretical GOE (red dashed curves) and the estimated probability density functions (solid curves) for the N (left) and P regions (right) as a function of the spacing ‘s’ obtained at 0.3 K.
Mentions: It has been postulated that the spectra of time-reversal invariant systems whose classical counterparts show chaotic behavior should have the same fluctuation properties of a Gaussian orthogonal ensemble (GOE) or a Gaussian symplectic ensemble (GSE)2021. When the system does not exhibit time reversal symmetry, a Gaussian unitary ensemble (GUE) better models it22. The distributions of the eigenvalue spacing were estimated as a probability density function as shown in Fig. 5, together with the theoretical distributions (the evolution of the distributions at different temperatures is shown in supplementary Fig. S3). A Kolmogorov-Smirnov (K-S) test2324 was performed to check which probability density function better fits the experimental data and the results are given in Fig. 6. At lower temperatures the distributions for both the P and N regions tend towards a GOE.

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.