Geometric oscillations of local Hall and Nernst effects in ballistic graphene at weak magnetic fields

Abstract

We predict a novel class of magnetotransport oscillations in ballistic graphene specific for a ring-shape geometry. Using the Büttiker-Landauer formalism, we analytically obtain the local Hall and Nernst coefficients in the weak-field ballistic regime. These coefficients exhibit pronounced oscillations as functions of both the magnetic field and the angular positions of the measurement probes. The oscillations originate from the discrete set of skipping orbits that geometrically connect the contacts, with resonances occurring when the angular separation between contacts times the radius of the disk equals an integer number of cyclotron diameters. Unlike conventional quantum oscillations in conductivity, this effect is robust at room temperature and can dominate local thermoelectric signals. This geometric control of ballistic flow provides a platform for studying electron hydrodynamics and engineering phase-coherent devices, with potential applications in sensitive terahertz detectors and thermal management systems.

Figures (5)

• Figure 1: (a) Ballistic graphene sheet connected to top (cold, blue) and bottom (hot, red) reservoirs. Electrons (filled circles) and holes (empty circles), driven by the temperature gradient, are deflected oppositely by perpendicular magnetic field B, producing spatially separated edge currents. (b) Fermi-Dirac distributions for undoped graphene at low and high temperatures. The hot reservoir generates a larger carrier population than the cold one. Magnetic field separates these carriers spatially, yielding a pronounced Nernst effect and a finite local Seebeck voltage at each edge. Crucially, the local Seebeck coefficient has opposite signs on opposite edges.
• Figure 2: (a) Four-terminal Büttiker setup for ballistic disk transport measurements. Contacts l, R, u, L are arbitrarily positioned at the edge, enabling local electrical (longitudinal, Hall) and thermoelectric (Seebeck, Nernst) measurements via applied bias imbalances. (b) Configuration used in our calculations. (c) Simulated electron trajectories in a graphene disk for $\beta = E/(\upsilon_F B)=0$ (red) and $0.1$ (blue). Panels show trajectories completing 1–4 full revolutions along the edge. $\beta = 0.1$ corresponds to a strong electric field regime experimentally accessible with typical laboratory fields ($\beta \sim 0.01-0.1$).
• Figure 3: Dependencies of the values $\mathcal{T}_{lR}^e$, $\mathcal{T}_{lu}^e$, and $\mathcal{T}_{lL}^e$ on the chemical potential at $T = 0$ for a fixed emission angle $\theta = \pi/2$ (a) and for all emission angles $\theta \in [0,\pi]$ (b). We put $R=2.5~\mu\text{m}$ and $\delta R=315~\text{nm}$, where $\delta R=R\delta\alpha$ is the width of contacts. The panel (c) shows the angular dependences of the quantities $\tilde{\mathcal{T}}_{lR},~\tilde{\mathcal{T}}_{lL},~\tilde{\mathcal{T}}_{uR},~\tilde{\mathcal{T}}_{uL}$ at $\mu=100~\text{meV}$ and $\delta R=160~\text{nm}$.
• Figure 4: Local Hall conductivity as a function of the contact position at fixed magnetic field (a) and vs. field at fixed contact position (b). For $\mu < 50~\text{meV}$, conductivity is $e^2/2h$—a plateau with virtually no oscillations. As field increases, oscillations give way to plateaus.
• Figure 5: Local Nernst coefficient as a function of the contact position at fixed field (a) and vs. field at fixed contact position (b). At the charge neutrality point, the Nernst effect is maximal, with $\alpha_N(\mu=0)\approx0.712$. With doping, oscillations emerge around zero.