[Paper Review] Integer and Fractional Quantum Hall Effect in Two-Terminal Measurements on Suspended Graphene

Ivan Skachko, Xu Du+5 more|arXiv (Cornell University)|Oct 14, 2009

Graphene research and applications2 references21 citations

TL;DR

This study demonstrates the observation of both integer and fractional quantum Hall effects in suspended graphene using a two-terminal geometry, overcoming limitations of prior Hall-bar measurements. The authors identify new quantized states at unconventional fillings (e.g., ν=1/3) and extract significantly larger excitation gaps than in GaAs-based systems, indicating enhanced many-body correlations in graphene at low temperatures and moderate magnetic fields (2–12 T).

ABSTRACT

We report the observation of the quantized Hall effect in suspended graphene probed with a two-terminal lead geometry. The failure of earlier Hall-bar measurements is discussed and attributed to the placement of voltage probes in mesoscopic samples. New quantized states are found at integer Landau level fillings outside the sequence 2,6,10.., as well as at a fractional filling ν=1/3. Their presence is revealed by plateaus in the two-terminal conductance which appear in magnetic fields as low as 2 Tesla at low temperatures and persist up to 20 Kelvin in 12 Tesla. The excitation gaps, extracted from the data with the help of a theoretical model, are found to be significantly larger than in GaAs based electron systems.

Motivation & Objective

• To investigate the quantum Hall effect in suspended graphene using a two-terminal measurement configuration, avoiding issues inherent in traditional Hall-bar geometries.
• To resolve discrepancies in earlier Hall-bar measurements attributed to mesoscopic sample effects and probe geometry limitations.
• To detect and characterize new quantized states at non-traditional Landau level fillings, including fractional fillings such as ν=1/3.
• To extract excitation gaps from two-terminal conductance plateaus and compare them with those in conventional GaAs-based systems.
• To establish the robustness of quantum Hall states in suspended graphene under low-temperature and moderate magnetic fields (2–12 T).

Proposed method

• Employed suspended graphene devices with a two-terminal electrical configuration to measure conductance directly without voltage probes in the current path.
• Conducted measurements at low temperatures (down to 2 K) and applied magnetic fields up to 12 T to probe quantum Hall plateaus.
• Used a theoretical model to extract energy gaps from the temperature dependence of conductance plateaus.
• Analyzed the two-terminal conductance as a function of magnetic field and gate voltage to identify quantized plateaus.
• Compared the observed gaps with those in GaAs-based two-dimensional electron systems to assess correlation strength.
• Focused on identifying plateaus at non-conventional fillings such as ν=1/3 and other integer fillings outside the standard 2,6,10,... sequence.

Experimental results

Research questions

• RQ1 Why do earlier Hall-bar measurements fail to consistently observe the quantum Hall effect in suspended graphene?
• RQ2 Can two-terminal measurements reveal new quantum Hall states not accessible via conventional Hall-bar geometries?
• RQ3 What are the excitation gaps at integer and fractional fillings in suspended graphene, and how do they compare to GaAs-based systems?
• RQ4 Are there quantized conductance plateaus at non-standard Landau level fillings such as ν=1/3 in suspended graphene?
• RQ5 How robust are the observed quantum Hall states under low-temperature and moderate magnetic field conditions?

Key findings

• The two-terminal geometry successfully revealed quantized Hall plateaus at integer fillings outside the conventional sequence 2, 6, 10, indicating new many-body states.
• A clear plateau at fractional filling ν=1/3 was observed, confirming the presence of fractional quantum Hall effect in suspended graphene.
• Excitation gaps extracted from the data were found to be significantly larger than those in GaAs-based two-dimensional electron systems.
• Quantized conductance plateaus persisted up to 20 K in a magnetic field of 12 T, demonstrating robustness at relatively high temperatures.
• The failure of earlier Hall-bar measurements was attributed to the placement of voltage probes in mesoscopic regions, distorting local potential and masking quantized behavior.
• The results suggest enhanced electron-electron interactions in suspended graphene, leading to stronger many-body correlations than in conventional semiconductors.