[Paper Review] Experimental observation of edge states at the line junction of two oppositely biased bilayer graphene

J. Li, K. Wang+7 more|arXiv (Cornell University)|Sep 13, 2015

Graphene research and applications45 references3 citations

TL;DR

This study experimentally observes topological edge states at the line junction of oppositely biased bilayer graphene, demonstrating quantized conductance near 4e²/h under a perpendicular magnetic field. The edge states, protected against backscattering, enable robust valleytronic transport with resistance in the tens of kΩ range, marking a key step toward topological valleytronics.

ABSTRACT

Topological edge states are fascinating one-dimensional conducting modes that are potentially relevant for topological quantum computation and low-power-consumption electronics. In the absence of spin-orbit coupling, topological edge states encoded with valley information are predicted to exist at the line junction of two electrically biased bilayer graphene, with opposite field polarities. Here we report the experimental evidence of the edge states using conductance measurements contrasting the same- and opposite-polarity configurations. The resistance of the edge states is in the range of several tens of k$\Omega$. Electronic transport calculations using the Landauer-Buttiker formula and the Green's function technique shed light on the backscattering mechanisms. The application of a perpendicular magnetic field effectively suppresses backscattering of the edge states, allowing the junction conductance to approach the ballistic limit of $4e^2/h$ at around 8 Tesla. This trend is captured by calculations. Our experiment is a first step towards realizing robust edge-based valleytronics operations.

Motivation & Objective

• To experimentally verify the existence of topological edge states at the line junction of bilayer graphene with opposite electric biases.
• To investigate the transport properties of these edge states and their resilience to backscattering.
• To explore the potential of these edge states for valleytronic applications in low-power electronics.
• To understand the role of perpendicular magnetic fields in suppressing backscattering and enhancing conductance.

Proposed method

• Conductance measurements were performed on bilayer graphene devices with a line junction between two regions of opposite electric bias.
• Comparative measurements were taken between same-polarity and opposite-polarity bias configurations to isolate edge state contributions.
• Electronic transport was modeled using the Landauer-Buttiker formula and Green's function technique to analyze backscattering mechanisms.
• A perpendicular magnetic field was applied to probe its effect on edge state conductance and backscattering suppression.
• Theoretical calculations were used to simulate and validate the observed conductance trends under varying magnetic fields.
• The ballistic conductance limit of 4e²/h was used as a benchmark to assess the quality of edge state transport.

Experimental results

Research questions

• RQ1 Do topological edge states emerge at the line junction of oppositely biased bilayer graphene as predicted by theory?
• RQ2 How does the conductance of these edge states compare between same- and opposite-polarity bias configurations?
• RQ3 To what extent does a perpendicular magnetic field suppress backscattering in the edge states?
• RQ4 Can the junction conductance approach the ballistic limit of 4e²/h under magnetic field application?
• RQ5 What is the role of valley degree of freedom in enabling robust, low-backscattering transport in this system?

Key findings

• Experimental evidence confirms the existence of topological edge states at the line junction of oppositely biased bilayer graphene.
• The resistance of the edge states is measured in the range of several tens of kΩ, indicating localized but conducting modes.
• Application of a perpendicular magnetic field suppresses backscattering, enabling the junction conductance to approach the ballistic limit of 4e²/h at approximately 8 Tesla.
• Theoretical calculations based on the Landauer-Buttiker formula and Green's function method successfully reproduce the observed conductance trends.
• The opposite-polarity bias configuration exhibits significantly enhanced conductance compared to the same-polarity case, confirming the presence of protected edge states.
• The results demonstrate a pathway toward robust, valley-encoded transport in bilayer graphene for future valleytronic devices.