Nippon Telegraph And Telephone : Graphene p-n junction as an electronic beam splitter — Key component of electron quantum optics using graphene —

(Press release material)

September 4, 2015

Quantum optics is a field of research that investigates the wave-particle nature of light based on quantum mechanisms, using interferometers consisting of optical elements, such as mirrors and beam splitters. Knowledge obtained by quantum optics has been applied to quantum cryptography and quantum teleportation. An electron is also a quantum having wave-particle nature like a photon and thus can interfere. A difference between an electron and a photon is whether it is a Fermion or Boson. This difference appears in the two-particle interference. Another important difference is the presence/absence of the Coulomb interaction. The presence of the Coulomb interaction for electrons has both positive and negative aspects: through the interaction, electron quantum state can be controlled but its coherence is easily destroyed.

The resultant short coherence length makes electron quantum optics experiments difficult. So far, electron quantum optics has been performed in the quantum Hall state, which appears in two-dimensional electron systems under magnetic field, formed in gallium arsenide (GaAs)/aluminum gallium arsenide (AlGaAs) heterostructures. In this system, a narrow channel called quantum point contact with the electron transmission probability of 1/2 (Figure 1, left) is used as a beam splitter. A fundamental problem of this system is that the coherence length of approximately 10 µm is as long as the typical size of the interferometer, limiting experiments to the basic level. A way to solve this problem and carry out more advanced experiments is to use graphene, in which the coherence length is expected to be longer. However, since graphene is a gapless material, beam splitters based on quantum point contacts made by depleting local electrons do not work.

In this work, a team comprised of members from NTT Basic Research Laboratories and CEA Saclay proposed a new architecture of a beam splitter using a graphene p-n junction. In graphene, electrons injected from the n and p regions are mixed in the p-n junction and then partitioned at the exit of the junction (Figure 1, right). The electron mixing and the subsequent partitioning processes can serve as a beam splitter. The beam splitter behavior has been verified by the measurements of the current noise (shot noise).

If the p-n junction acts as a beam splitter, electrons are randomly distributed to the n and p current channels, generating the shot noise. We showed that, when the p-n junction is short, the shot noise is generated as expected. As it becomes longer, the noise becomes smaller. Our results indicate that the energy relaxation length, which is an indicator of the loss of the quantum information, is 15 µm and shorter p-n junction can serve as a beam splitter.

1. We used graphene grown on SiC. A p-n junction was made using a top gate covering half of the graphene. The ungated region was n doped, while p carriers were introduced in the gated region. Therefore, a p-n junction was formed at the interface between the gated and ungated regions. We prepared five samples with different p-n junction lengths between 5 and 100 µm (Figure 2).
2. All measurements were carried out in a quantum Hall effect regime, which is caused by applying a magnetic field perpendicular to graphene. We measured the shot noise for the system with and without a p-n junction and showed that the shot noise is generated by the p-n junction (Figure 3). This indicates that electron mixing and partitioning indeed occur at the p-n junction.
3. Measurements for samples with different p-n junction lengths revealed that the noise decreases with increasing p-n junction length (Figure 4). This result indicates that a p-n junction shorter than the estimated energy relaxation length of 15 µm can serve as a beam splitter.

In general, graphene is obtained by exfoliation from graphite. A drawback of this technique is that the graphene size is limited to several 10 µm. Whereas, the graphene we used were grown by thermal decomposition of SiC substrate. By exploiting the wafer-size graphene, we fabricated devices with different p-n junction lengths. This enables us to measure the energy relaxation length.

The architecture of graphene p-n junction is simpler than that of quantum point contact, which is used as a beam splitter in conventional semiconductors, allowing us to integrate several beam splitters within a mesoscopic scale. Utilizing these beam splitters and the long coherence length in graphene, it would be possible to fabricate complicated electronic interferometers, which have not been able to be fabricated. Experiments in these devices would reveal effects of the Coulomb interaction on decoherence. Furthermore, generation of quantum entangled electron pair is expected to be achieved in such devices.

N. Kumada, F. D. Parmentier, H. Hibino, D. C. Glattli, and P. Roulleau
"Shot noise generated by graphene p-n junctions in the quantum Hall effect regime"
Nature Communications (2015).

Complementary results from a group of Osaka University, Kyoto University, and NIMS will be published simultaneously in Nature Communications.