The thermopower and Nernst Effect in graphene in a magnetic field

Abstract: We report measurements of the thermopower $S$ and Nernst signal $S_{yx}$ in graphene in a magnetic field $H$. Both quantities show strong quantum oscillations vs. the gate voltage $V_g$. Our measurements for Landau Levels of index $n\ne 0$ are in quantitative agreement with the edge-current model of Girvin and Jonson (GJ). The inferred off-diagonal thermoelectric conductivity $\alpha_{yx}$ comes close to the quantum of Amps per Kelvin. At the Dirac point ($n=0$), however, the width of the peak in $\alpha_{yx}$ is very narrow. We discuss features of the thermoelectric response at the Dirac point including the enhanced Nernst signal.

• The paper demonstrates significant quantum oscillations in non-zero Landau levels that align with Girvin-Jonson model predictions.
• The paper finds an enhanced Nernst signal at the Dirac point, highlighting unexpectedly strong thermoelectric behavior compared to higher Landau levels.
• The study employs precise lithographic techniques and high magnetic fields to yield robust measurements, informing future advances in graphene thermoelectric devices.

Thermopower and Nernst Effect in Graphene under Magnetic Fields

This paper presents an empirical study of the thermopower ($S$) and Nernst signal ($S_{yx}$) in graphene when subjected to a magnetic field. The primary focus is on observing the quantum oscillations of these thermoelectric properties as a function of the gate voltage ($V_g$) and establishing a quantitative alignment with the edge-current model proposed by Girvin and Jonson (GJ) for non-zero Landau Levels (LLs).

Summary of Findings

• Quantitative Agreement with GJ Model: The study demonstrates notable quantum oscillations for $n \ne 0$ LLs, which align well with GJ's theoretical predictions. The thermoelectric conductivity, $\alpha_{yx}$, achieves values nearing the universal quantum of $k_Be/h \ln 2$ Ampere per Kelvin in these regimes.
• Unique Characteristics at the Dirac Point: At the Dirac point ($n=0$ LL), the behavior of the system deviates significantly from the predictions of conventional models. The observed Nernst signal in this case is significantly enhanced, marking a stark contrast to the modest values seen at other LL indices.
• Implications of Observed Data: The study's findings refresh the understanding of thermoelectric transport in graphene across quantized LLs. Particularly, the distinct thermal response at the Dirac point requires revisions to existing models, potentially involving novel edge state dynamics.

Theoretical Relevance

Graphene's unique electronic properties contribute to its unexpectedly pronounced thermoelectric effects in quantized magnetic fields. The linear energy dispersion shifts typical thermoelectric responses, prompting modifications to established models like that of GJ for non-zero LLs. The $n=0$ level in graphene appears to involve novel thermoelectric phenomena that suggest complex interactions and may inform theoretical advances in the understanding of 2D materials under quantum Hall conditions.

Experimental Approach

The methodology centers around precise lithographic techniques to create microscale heaters and thermometers, enabling fine evaluation of the temperature gradients and subsequent thermoelectric responses in graphene. The utilization of high magnetic fields (up to 14 T) aids in exploring these effects deep into the quantum regime, enhancing the robustness and accuracy of $\alpha_{xy}$ measurements.

Implications and Recommended Future Work

The paper's results provoke further interest in the exploration of edge-state phenomena in graphene, especially at its Dirac point under magnetic fields. The intriguing peak width variations at $n=0$ highlight potential for further experimental refinement, particularly with cleaner samples and stronger fields, to expound upon these findings.

The distinctive nature of thermopower and Nernst effects in graphene portend avenues for developing innovative technologies exploiting quantum thermoelectric properties. These insights could guide advances in graphene-based thermoelectric devices and inform broader applications in nanoelectronics and material science.

Further theoretical studies could focus on reconciling the discrepancies observed at the Dirac point, potentially prompting refined models that integrate edge state variabilities and Berry-phase phenomena.

In summary, this investigation presents critical insights into graphene's thermoelectric behavior under magnetic fields, suggesting both theoretical and experimental paths to fully capture the nuanced quantum mechanics at play.