New Explorer at Exotic Boundary: How Superconductivity and Quantum Hall Effect Go Together

Superconductivity and the quantum Hall (QH) effect are representative quantum effects realized in electron systems in solids. Each has been an important topic studied for many years in low temperature physics and semiconductor physics, respectively. Now, what happens if the two effects couple?

First, consider the interface between normal metal and superconductor (metal/superconductor junction). When an electron with an energy lower than the superconducting gap travels from the metal to the superconductor, a unique effect occurs. The incident electron creates a Cooper pair in the superconductor and, at the same time, a hole appears in the metal side to fulfill charge and spin conservation. Remarkably, this hole reflects along the same trajectory of the incident electron (“retro-reflection”), because the momentum should also be conserved before and after the reflection. Figure 1(a) schematically shows this situation. This phenomenon, peculiar to the metal/superconductor junction, is known as Andreev reflection [1].

»View larger version

Fig. 1. Schematics of (a) Andreev reflection at the nonmagnetic metal/superconductor interface. (b) 2DES/superconductor interface under the quantum Hall effect (QHE). Andreev reflection is possible through multiple Andreev and normal reflections at the 2DES/superconductor interface. (Courtesy of Dr. Y. Kozuka)

Next, what happens at the metal/QH junction? A two-dimensional electron system (2DES) shows the QH effect in strong magnetic fields, where the orbital motion of the electron is quantized, and the energy level degenerates to a discrete value, forming the Landau level. In the QH regime, chiral edge modes emerge along the edge of the 2DES, while the bulk of the 2DES is insulating. In the classical picture, the edge modes originate from the skipping orbitals at the edge of the sample due to the Lorentz force. Solid curves in Fig. 1(b) show an example of the skipping orbitals. The edge modes are responsible for electron transport between the metal and the 2DES in the QH regime.

Now, let us consider the QH/superconductor junction. In the presence of a magnetic field, Andreev reflection might seem impossible because the Lorentz force inhibits the created hole from retracing the trajectory of the incident electron. Nevertheless, through “multiple” Andreev reflections at the junction, the electron incident on an interface of the 2DES/superconductor junction can come out from the other edge as an electron or a hole. The dashed curves in Fig. 1(b) schematically depict this situation in the classical view. Researchers have studied Andreev reflection in the QH regime since the 1990s [2]. Furthermore, the recent theoretical prediction on the emergence of non-abelian quasiparticles at the interface between superconductivity and chiral or helical edge states [3] is invoking further interest in this topic and experimentalists are now enthusiastically pursuing this possibility.

Experimentally, however, it is not easy to realize a well-defined QH/superconductor junction. Of course, the superconductivity must survive in a magnetic field high enough to cause the QH effect. More seriously, the Schottky barrier arises between the metal and the semiconductor and hinders sufficient proximity between the QH edge modes and Cooper pairs. For this reason, AlGaAs/GaAs 2DES, the most conventional 2DES, is not suitable for investigating this topic. Instead, InAs-based heterostructure has been studied [4] and recently a graphene-based system has been reported [5, 6].

Kozuka and coworkers have reported a completely new material system [7]. They fabricated a ZnO-2DES/MoGe junction from Mg_xZn_1−xO/ZnO 2DES coupled to amorphous MoGe, a superconductor with a high upper critical field. Their ZnO-based 2DES shows pronounced integer and fractional quantum Hall effects [8]. Also importantly, unlike conventional semiconductors, such as GaAs, ideal ohmic contacts without a Schottky barrier could be easily realized in ZnO-based 2DES with low-workfunction metals such as Ti [9]. They showed that their system exhibited clear signatures of Andreev reflection from zero magnetic field up to the QH regime. They analyzed the conductance through the junction with the aid of the Blonder–Tinkham–Klapwijk model and interpreted that multiple Andreev reflection at the 2DES/superconductor interface occurred in the QH regime.

The above fascinating experimental achievement stands on the long expertise of the authors with ZnO systems. Following the InAs- and graphene-based exemplars, the new junction will serve as an attractive platform to explore new physics in the QH/superconductor junction, such as non-abelian particles.

References

• [1] A. F. Andreev, J. Exp. Theor. Phys. 46, 1823 (1964) [Sov. Phys. JETP 19, 1228 (1964)]. Google Scholar
• [2] M. P. A. Fisher, Phys. Rev. B 49, 14550 (1994). 10.1103/PhysRevB.49.14550 Crossref, Google Scholar
• [3] L. Fu and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008). 10.1103/PhysRevLett.100.096407 Crossref, Google Scholar
• [4] H. Takayanagi and T. Akazaki, Physica B 249–251, 462 (1998). 10.1016/S0921-4526(98)00164-1 Crossref, Google Scholar
• [5] K. Komatsu, C. Li, S. Autier-Laurent, H. Bouchiat, and S. Guéron, Phys. Rev. B 86, 115412 (2012). 10.1103/PhysRevB.86.115412 Crossref, Google Scholar
• [6] F. Amet, C. T. Ke, I. V. Borzenets, J. Wang, K. Watanabe, T. Taniguchi, R. S. Deacon, M. Yamamoto, Y. Bomze, S. Tarucha, and G. Finkelstein, Science 352, 966 (2016). 10.1126/science.aad6203 Crossref, Google Scholar
• [7] Y. Kozuka, A. Sakaguchi, J. Falson, A. Tsukazaki, and M. Kawasaki, J. Phys. Soc. Jpn. 87, 124712 (2018). 10.7566/JPSJ.87.124712 Link, Google Scholar
• [8] J. Falson, D. Maryenko, B. Friess, D. Zhang, Y. Kozuka, A. Tsukazaki, J. H. Smet, and M. Kawasaki, Nat. Phys. 11, 347 (2015). 10.1038/nphys3259 Crossref, Google Scholar
• [9] Y. Kozuka, A. Tsukazaki, and M. Kawasaki, Appl. Phys. Rev. 1, 011303 (2014). 10.1063/1.4853535 Crossref, Google Scholar

Author Biographies