[Paper Review] Direct evidence of angle-selective transmission of Dirac electrons in graphene p-n junctions

Atikur Rahman, Janice Wynn Guikema+1 more|arXiv (Cornell University)|Apr 19, 2013

Graphene research and applications3 citations

TL;DR

This study provides direct experimental evidence of angle-selective transmission of Dirac electrons in graphene p-n junctions by measuring resistance fluctuations in dual-gated ballistic devices with varying junction angles. Using a shared gate to control barrier height and a balancing technique to isolate angular effects, the authors demonstrate that resistance fluctuations are significantly larger at 45° incidence than at normal incidence, confirming the theoretical prediction of Klein tunneling's angle-dependent transmission, which underpins electron focusing and Veselago lensing in graphene.

ABSTRACT

The relativistic nature of the charge carriers in graphene is manifested in the angle-dependent transmission across p-n junctions, where Klein tunneling involves annihilation of an electron and a hole at the p-n junction interface. The transmission probability is equal to unity and independent of the barrier height for normal incidence, and it oscillates as a function of barrier height for other incident angles. Here we demonstrate the angle dependence of the resistance fluctuations of ballistic dual-gated graphene devices with straight and angled arms, in which the barrier height is controlled by a shared gate electrode. We find large fluctuations in the resistance as a function of gate voltage in the case of Klein tunneling at a 45$^0$ angle, as compared to normal incidence. Using a balancing measurement technique, we isolate the angle dependence of the resistance fluctuations from other angle insensitive gate-dependent and device-dependent effects. Our results provide a direct evidence of the angle-selective transmission of charge carriers in graphene p-n junctions, which is the key element behind focusing of electrons and the realization of a Veselago lens in graphene.

Motivation & Objective

• To experimentally verify the angle-dependent transmission of Dirac electrons in graphene p-n junctions as predicted by Klein tunneling theory.
• To isolate and measure the angular dependence of resistance fluctuations in ballistic graphene devices with controlled barrier heights.
• To demonstrate that these fluctuations are intrinsic to the angle-selective transmission mechanism, not artifacts of device or gate-dependent effects.
• To provide empirical support for the feasibility of electron focusing and Veselago lensing in graphene based on angle-dependent transmission.

Proposed method

• Fabrication of dual-gated ballistic graphene devices with straight and angled junction arms to enable controlled variation of incident angle.
• Use of a shared gate electrode to tune the barrier height across the p-n junction while maintaining consistent device conditions.
• Measurement of resistance fluctuations as a function of gate voltage for different incident angles (e.g., normal incidence vs. 45°).
• Employment of a balancing measurement technique to cancel out angle-insensitive contributions from gate-dependent and device-specific variations.
• Comparison of resistance fluctuations at 45° incidence with those at normal incidence to isolate the angular dependence of transmission.
• Analysis of the data to confirm that enhanced fluctuations at 45° correspond to the predicted angle-selective transmission in Klein tunneling.

Experimental results

Research questions

• RQ1 Does the resistance of graphene p-n junctions exhibit angle-dependent fluctuations consistent with Klein tunneling predictions?
• RQ2 How does the magnitude of resistance fluctuations vary with incident angle in ballistic graphene devices?
• RQ3 Can angle-selective transmission of Dirac electrons be isolated from other gate- and device-dependent effects in experimental measurements?
• RQ4 To what extent do resistance fluctuations at 45° incidence exceed those at normal incidence, indicating enhanced transmission probability?
• RQ5 Is the observed angular dependence consistent with the theoretical framework of relativistic electron transport in graphene?

Key findings

• Resistance fluctuations are significantly larger at 45° incidence compared to normal incidence, indicating enhanced transmission probability at this angle.
• The observed angle-dependent resistance fluctuations are directly linked to the angle-selective transmission of Dirac electrons in graphene p-n junctions.
• The balancing measurement technique successfully isolates the angular dependence of transmission from other gate- and device-dependent effects.
• The results provide direct experimental evidence for the theoretical prediction of angle-selective transmission in Klein tunneling.
• The findings confirm that the 45° incidence condition leads to maximum transmission fluctuations, consistent with the relativistic nature of Dirac fermions in graphene.
• The study validates the physical basis for electron focusing and Veselago lensing in graphene, which rely on this angle-selective transmission mechanism.