Imaging the Breakdown of Ohmic Transport in Graphene

Abstract

Ohm's law describes the proportionality of current density and electric field. In solid-state conductors, Ohm's law emerges due to electron scattering processes that relax the electrical current.Here, we use nitrogen-vacancy center magnetometry to directly image the local breakdown of Ohm's law in a narrow constriction fabricated in a high mobility graphene monolayer. Ohmic flow is visible at room temperature as current concentration on the constriction edges, with flow profiles entirely determined by sample geometry. However, as the temperature is lowered below 200 K, the current concentrates near the constriction center. The change in the flow pattern is consistent with a crossover from diffusive to viscous electron transport dominated by electron-electron scattering processes that do not relax current.

Hydrodynamic approach to two-dimensional electron systems

“…6, and more recently corroborated in Ref. [44], where a novel imaging technique was applied to the point contact problem (see Section 2.4), see also Ref. [45].…”

“…The transition from the Ohmic to hydrodynamic flow observed in the point contact geometry in Refs. [39,44] is similar to the transition between the Knudsen and Poiseuille flows [17,68,58]. The tendency of the viscous flow to avoid [32].…”

“…At the same time, at T 150 K the electron-electron scattering length decreases to ee ≈ 0.1 ÷ 0.3 µm. Since the pioneering work on the nonlocal resistance [27] and Wiedemann-Franz law violation [28], several impressive experiments [39,41,42,43,44,45] aimed at uncovering the hydrodynamic behavior of the electronic system in graphene. In particular, it was suggested that a viscous hydrodynamic flow in electronic systems might exhibit enhanced, higher-than-ballistic conduction [39,44,45].…”

“…Since the pioneering work on the nonlocal resistance [27] and Wiedemann-Franz law violation [28], several impressive experiments [39,41,42,43,44,45] aimed at uncovering the hydrodynamic behavior of the electronic system in graphene. In particular, it was suggested that a viscous hydrodynamic flow in electronic systems might exhibit enhanced, higher-than-ballistic conduction [39,44,45]. More recently, several breakthrough experiments [30,34,44,45,46,47,48,49,50,51,52,53,54] demonstrated various distinct imaging techniques making it possible to "observe" the electronic flow in graphene "directly".…”

“…In particular, it was suggested that a viscous hydrodynamic flow in electronic systems might exhibit enhanced, higher-than-ballistic conduction [39,44,45]. More recently, several breakthrough experiments [30,34,44,45,46,47,48,49,50,51,52,53,54] demonstrated various distinct imaging techniques making it possible to "observe" the electronic flow in graphene "directly".…”