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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) Conductance of the graphene flake taken at different temperatures. N and P regions are those related to voltages higher and lower than the charge neutrality point, respectively. (b) Conductance fluctuations obtained from the conductance curves. From top to bottom: 0.3 K, 2.67 K, 10 K, 20 K and 30 K. (c,d) Magnetoconductance fluctuations obtained with back gate voltages −5 V and +5 V measured from the charge neutrality point. From top to bottom: 0.3 K, 3.0 K, 12 K, 20 K, 28 K and 36 K. Offsets were added for better visualization. (e) Log-log plots of the RMS value of the fluctuations for p-type (green ) and n-type (cyan ) magnetoconductance fluctuations and p-type (red +) and n-type (blue ) transconductance fluctuations. Dashed lines indicate two distinct regions: a region with a T−1/2 dependence and a saturation region.
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f2: (a) Conductance of the graphene flake taken at different temperatures. N and P regions are those related to voltages higher and lower than the charge neutrality point, respectively. (b) Conductance fluctuations obtained from the conductance curves. From top to bottom: 0.3 K, 2.67 K, 10 K, 20 K and 30 K. (c,d) Magnetoconductance fluctuations obtained with back gate voltages −5 V and +5 V measured from the charge neutrality point. From top to bottom: 0.3 K, 3.0 K, 12 K, 20 K, 28 K and 36 K. Offsets were added for better visualization. (e) Log-log plots of the RMS value of the fluctuations for p-type (green ) and n-type (cyan ) magnetoconductance fluctuations and p-type (red +) and n-type (blue ) transconductance fluctuations. Dashed lines indicate two distinct regions: a region with a T−1/2 dependence and a saturation region.

Mentions: The conductance fluctuations (ΔG, CF) shown in Fig. 2b were calculated from the conduction curves found in Fig. 2a by subtracting a simple moving average with a window of 0.6 V. The amplitude of the CF is not constant, and oscillates by ~24% between 0.72 to 0.55 G0 (G0 is the quantum of conductance: 4e2/h, where e is the fundamental electric charge and h is Planck’s constant).


Conductance fluctuations in high mobility monolayer graphene: Nonergodicity, lack of determinism and chaotic behavior
(a) Conductance of the graphene flake taken at different temperatures. N and P regions are those related to voltages higher and lower than the charge neutrality point, respectively. (b) Conductance fluctuations obtained from the conductance curves. From top to bottom: 0.3 K, 2.67 K, 10 K, 20 K and 30 K. (c,d) Magnetoconductance fluctuations obtained with back gate voltages −5 V and +5 V measured from the charge neutrality point. From top to bottom: 0.3 K, 3.0 K, 12 K, 20 K, 28 K and 36 K. Offsets were added for better visualization. (e) Log-log plots of the RMS value of the fluctuations for p-type (green ) and n-type (cyan ) magnetoconductance fluctuations and p-type (red +) and n-type (blue ) transconductance fluctuations. Dashed lines indicate two distinct regions: a region with a T−1/2 dependence and a saturation region.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: (a) Conductance of the graphene flake taken at different temperatures. N and P regions are those related to voltages higher and lower than the charge neutrality point, respectively. (b) Conductance fluctuations obtained from the conductance curves. From top to bottom: 0.3 K, 2.67 K, 10 K, 20 K and 30 K. (c,d) Magnetoconductance fluctuations obtained with back gate voltages −5 V and +5 V measured from the charge neutrality point. From top to bottom: 0.3 K, 3.0 K, 12 K, 20 K, 28 K and 36 K. Offsets were added for better visualization. (e) Log-log plots of the RMS value of the fluctuations for p-type (green ) and n-type (cyan ) magnetoconductance fluctuations and p-type (red +) and n-type (blue ) transconductance fluctuations. Dashed lines indicate two distinct regions: a region with a T−1/2 dependence and a saturation region.
Mentions: The conductance fluctuations (ΔG, CF) shown in Fig. 2b were calculated from the conduction curves found in Fig. 2a by subtracting a simple moving average with a window of 0.6 V. The amplitude of the CF is not constant, and oscillates by ~24% between 0.72 to 0.55 G0 (G0 is the quantum of conductance: 4e2/h, where e is the fundamental electric charge and h is Planck’s constant).

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.


Related in: MedlinePlus