Nippon Telegraph and Telephone: Detection of Divergent Orbital Diamagnetism of Graphene at the Dirac Point-Opening the Way to Reveal New Properties and Features in Graphene-
Nippon Telegraph and Telephone Corporation (NTT), Université Paris-Saclay, CEA-Saclay, Institut Néel and the National Institute of Materials Science (NIMS) have collaboratively succeeded in detecting divergent orbital diamagnetism in graphene monolayer at neutral load point (Dirac). It corroborates an important role of the topological phase*1 (Berry phase) in condensed matter physics.
Diamagnetism is a phenomenon where a magnetization emerges in a material opposite to the externally applied magnetic field. Graphene is a boundary of graphite one atom thick, and it has a unique relationship between energy and momentum of an electron, forming a conical shape between them (Fig. 1). Above all, there is a point called “Dirac point”, where the two cones touch. The Dirac point behaves like a topologically abnormal point and has been theoretically predicted to be essential for generating divergent diamagnetism.
In this study, extremely clean graphene encapsulated by hexagonal boron nitride (hBN) and highly sensitive magnetic sensors using the giant magnetoresistance (GMR) effect*2 allowed to detect a strong diamagnetic signal at the Dirac point. Since the divergent diamagnetism arises from the topological phase at the Dirac point, this experimental observation demonstrates a crucial role of the topological phase in graphene. Moreover, our experimental techniques are applicable to various materials other than graphene, and thus should contribute to explore new phenomena driven by a non-trivial topological phase in topological materials.*3.
The diamagnetism of graphene has been intensively studied for more than 60 years. Theoretically, the diamagnetic response is predicted to become infinite at the Dirac point in the ideal disorder-free graphene at zero temperature. On the contrary, because of a finite level of disorder and a finite temperature, the experimental demonstration of divergent diamagnetism in graphene remained difficult. Recent theoretical studies have revealed that the topological phase, which arises from the unique band structure*4 of a material, is essential to determine its electrical and optical properties. Because divergent diamagnetism in graphene is one of the representative examples to show the role of topological phase in realistic material, its detection is long awaited.
The joint research group succeeded in making extremely clean graphene by encapsulating it with two atomically flat hBNs. We mounted this graphene heterostructure on top of GMR-based magnetic sensors and attempted to measure a diamagnetic signal (schematic illustration of the study). When a diamagnetic response emerges, a loop of an electron orbit in graphene generates a magnetic field. The in-plane component of this magnetic field affects the direction of magnetization in a ferromagnetic layer in the GMR device. Due to the variation of the resistance according to the relative direction of the magnetization between the two ferromagnetic layers of the GMR device, it is possible to electrically detect the diamagnetic response (Fig. 2). In the actual experiments, an external magnetic field was applied normally to graphene, and by detecting the change in the resistance of GMR devices, we measured a magnetic field generated by a diamagnetic response. From the electrical signals obtained, we succeeded in showing that a large diamagnetic response emerges at the Dirac point (Fig. 3). These experimental results are in good agreement with the theoretical calculations taking into account the geometries of our devices.
3. Technical remarks
Our successful experimental observation became possible using ultraclean graphene encapsulated by atomically flat hBN (Fig. 4). Moreover, the elaborate detection setup is a key: since a magnetic field generated by a diamagnetic response is normal to the graphene plane, it seems appropriate to try to detect the normal component of the generated magnetic field. However, since a large perpendicular external magnetic field is required to obtain a diamagnetic response itself, the normal component of a small diamagnetic field is overwhelmed by the large external field and difficult to detect. In this study, we focused not on the normal but on the in-plane component of the diamagnetic field and detected it by the GMR devices, which allowed the detection of the diamagnetic response in graphene.
4. Future developments
Our experimental observation of divergent diamagnetism in graphene unequivocally shows the importance of the topological phase in condensed matter physics. The application of this experimental technique to other new materials is accelerating to reveal unique properties in topologically non-trivial materials.
5. Publication details
“Detection of divergent orbital diamagnetism of graphene at the Dirac point”
J. Vallejo, NJ Wu, C. Fermon, M. Pannetier-Lecoeur, T. Wakamura, K. Watanabe, T. Taniguchi, T. Pellegrin, A. Bernard, S. Daddinounou, V. Bouchiat, S. Guéron, 1 M. Ferrier, G. Montambaux, H. Bouchiat
6．Glossary of terms
It is also called “Berry phase”. Electrons have both particle and wave nature, and the wave function of electrons has the phase component. Suppose the state of an electron is adiabatically transformed from the initial state A to the same state (let’s define it as A’) by changing a parameter on which the wave function of the electron depends. In this case, while the electron has finally returned to the same state, its wave function acquires an additional phase which depends on the trajectory between A and A’ in the parameter space. In our experimental situation, the transformation of A into A’ corresponds to the closed orbit of the wave function of the electron due to the rotational movement of the cyclotron driven by the external magnetic field. In graphene, an electron acquires the pi phase when it circulates once around the Dirac point.
2.Giant magnetoresistance effect
This is the effect where the perpendicular resistance of the ferromagnetic/paramagnetic/ferromagnetic three-layer structures changes depending on the relative direction of magnetization in the two ferromagnetic layers. Usually the magnetization of one of the ferromagnets is pinned and the other is left free to change.
Groups of materials with topologically non-trivial band structures (see 4). Their topological nature is categorized by the topological number. Topological insulators epitomize topological materials, which have insulating mass and conductive surfaces or edges.
It represents the relationship between energy and momentum of electrons and determines the electrical properties of materials. Since materials are made up of a periodic lattice of atoms, the periodic potential induced by these atoms provides the band structure of each material.
Schematic illustration of the study: Detection of divergent orbital diamagnetism in monolayer graphene by GMR-based magnetic sensors.
Fig. 1: Dispersion relationship between electron energy and momentum (wavenumber) in graphene. The electron density and the charge polarization (electron or hole) can be modulated by the gate voltage. The Dirac point is located in the middle of the electron and hole doped region.
Fig. 2: Diagram of the electrical detection of diamagnetism using magnetic sensors based on GMR.
Fig. 3: Magnetic field due to the diamagnetic response detected by the GMR device and the magnetization converted from the magnetic field.
Fig. 4: Optical microscope image of the device. Graphene is encapsulated by hBN and deposited on top of GMR-based magnetic sensors.