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

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.

Shubnikov–de Haas measurements on a high mobility monolayer graphene flake sandwiched between boron nitride sheets

“…Moreover, the carrier concentration can be found from the slope of these curves. This result has been discussed elsewhere [15]. A plot of the carrier concentration as a function of the gate voltage is shown in figure 3(b).…”

“…In order to estimate the mobility, the longitudinal conductivity of the structure was measured at different temperatures and different values of backgate voltage (V BG ), as shown in figure 1(b). In our case, the charge neutrality point (V CNP ) was at approximately −2 V. As the temperature is reduced, fractal conductance fluctuations become more intense and are associated to a chaotic transport of the carriers [15].…”

“…These deviations are common in many samples [3] and can occur as a consequence of the background disordered potential that affect the quality of the oscillations. [15] 2.3.2. Effective mass and Fermi velocity.…”

Tuning weak localization in single-layer disordered SnSe2/graphene/h-BN field-effect device

“…On the other hand, the exfoliated dielectric h-BN flake layer for the back gate is not as good as atomic layer deposition (ALD) hafnium oxide (HfO 2 ) for single-layer MoS 2 transistor [35], few-layer SnSe 2 transistor [11] and high-k (deionized water) top gate for few-layer SnS 2 [36] and SnSe 2 [11] transistors, which could be improved a lot by 2D materials stacking techniques, for example a stacked SnSe 2 /WSe 2 tunneling field-effect transistor device with a superior on/off ratio of 10 7 [22] and few-layer SnSe 2 transistor with a high on/off ratio of 10 5 [12]. There is no magnetic moment here based on our theoretical calculations, which is a great advantage for a quantum interference related device.…”