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- Activity Report 2017 -

Nakatsuji Group

Strongly Correlated Zero-Gap Semiconductor Pr2Ir2O7

Fig. 1. Band structure of a Luttinger semimetal, which is a zero-gap semiconductor. The valence band, which is filled with electrons (blue spheres) and the empty conduction band both have a three-dimensional parabolic shape, and are in contact with each other at a single point close to the Fermi level.

Fig. 2. Temperature dependence of the dielectric constant. The low-temperature value is several tens of times larger than that of known zero-gap semiconductors (e.g. α–Sn and HgTe). The dielectric constant becomes larger when the Fermi level approaches the band touching point.

In the field of the solid state physics, materials exhibiting novel physical properties are vigorously explored. Zero-gap semiconductors are one fascinating group of materials where topological functionalities lead to high carrier mobility and the quantum Hall effect. It is known that electrons behave as if they are massless in materials such as graphene because of the linear band dispersion near the point where the valence and the conduction bands come in contact with each other. For graphene, new phenomena were discovered one after another and it became the subject of the Nobel Prize in Physics in 2010. So far, the physics of zero-gap semiconductors have only been studied in materials where the interaction between electrons is weak.

An example of a zero-gap structure is a Luttinger semimetal with quadratic band touching whose band dispersion is parabolic near the band touching point as illustrated in Fig. 1. It was predicted more than 40 years ago that materials in a Luttinger semimetal state would show novel electronic states because of the strong electronic correlations that are unobtainable in conventional metals. However, in materials known so far, such as α–Sn and HgTe, it has been difficult to identify experimentally the effects of electronic correlations because the effective mass of electrons is small and hence the electronic correlations are weak.

To clarify the effect of the strong electronic correlations, we focused on Pr2Ir2O7 [1]. It is already known that Pr2Ir2O7 is a Luttinger semimetal with quadratic band touching and that the effective mass of electrons is about 6 times larger than the mass of the free electron in vacuum [2]. We therefore carried out a terahertz spectroscopy study on the Pr2Ir2O7 thin films and observed a very large dielectric constant of about 180 at a temperature of 5 K as shown in Fig. 2 [3]. This value is several tens of times larger than that of zero-gap semiconductors (e.g. α–Sn and HgTe) known so far. Additionally, in a Luttinger semimetal state, the dielectric constant is a measure of the scale of electronic correlations. By using this fact, when the magnitude of the electronic correlations is estimated from the dielectric constant, the scale of electronic correlations is about 2 orders of magnitude larger than the kinetic energy.

We have thus demonstrated that electronic correlations are indeed very strong in a Luttinger semimetal with quadratic band touching. In the future, it is expected that further understanding of the role of electronic correlations in determining the physical properties of zero-gap semiconductors will lead to the creation of novel metallic states and new functional materials.


  • [1] T. Ohtsuki, Z. Tian, A. Endo, M. Halim, S. Katsumoto, Y. Kohama, K. Kindo, S. Nakatsuji, and M. Lippmaa, arXiv:1711.07813 (2017).
  • [2] T. Kondo, M. Nakayama, R. Chen, J. J. Ishikawa, E.-G. Moon, T. Yamamoto, Y. Ota, W. Malaeb, H. Kanai, Y. Nakashima, Y. Ishida, R. Yoshida, H. Yamamoto, M. Matsunami, S. Kimura, N. Inami, K. Ono, H. Kumigashira, S. Nakatsuji, L. Balents, and S. Shin, Nat. Commun. 6, 10042 (2015).
  • [3] B. Cheng, T. Ohtsuki, D. Chaudhuri, S. Nakatsuji, M. Lippmaa, and N. P. Armitage, Nat. Commun. 8, 2097 (2017).


  • T. Ohtsuki, B. Chenga, D. Chaudhuria, S. Nakatsuji, M. Lippmaa, and N. P. Armitagea
  • aJohns Hopkins University