Faculty Profiles - TANAKA, Yukio

Papers - TANAKA, Yukio

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Symmetry and Topology in Superconductors, odd-frequency pairing and edge states Invited Reviewed

Y. Tanaka, M. Sato and N.Nagaosa

Journal of the Physical Society of Japan Vol. ８１ ( １ ) page： 011013_1-34 2012

Authorship：Lead author Language：English Publishing type：Research paper (scientific journal)

Superconductivity is a phenomenon where the macroscopic quantum coherence appears due to the pairing of electrons. This offers a fascinating arena to study the physics of symmetry breaking, i.e., broken gauge symmetry. However, the important symmetries in superconductors are not only the gauge invariance. Especially, the symmetry properties of the pairing, i.e., the parity and spin-singlet/spin-triplet, determine the physical properties of the superconducting state. Recently it has been recognized that there is the important third symmetry of the pair amplitude, i.e., even or odd parity with respect to the frequency. The conventional uniform superconducting states correspond to the even-frequency pairing, but the recent finding is that the odd-frequency pair amplitude arises in the spatially non-uniform situation quite ubiquitously. Especially, this is the case in the Andreev bound state (ABS) appearing at the surface/interface of the sample. The other important recent development is on the nontrivial topological aspects of superconductors. As the band insulators are classified by topological indices into (i) conventional insulator, (ii) quantum Hall insulator, and (iii) topological insulator, also are the gapped superconductors. The influence of the nontrivial topology of the bulk states appears as the edge or surface of the sample, i.e., bulk-edge correspondence. In the superconductors, this leads to the formation of zero energy ABS (ZEABS). Therefore, the ABSs at the surface/interface of the superconductors are the place where the symmetry and topology meet each other which offer the stage of rich physics. In this review, we discuss the physics of ABS from the viewpoint of the odd-frequency pairing, the topological bulk-edge correspondence, and the interplay of these two issues. It is described how the symmetry of the pairing and topological indices determine the absence/presence of the ZEABS, its energy dispersion, and properties as the Majorana fermions. Various related issues such as the Helium 3, transport of Majorana fermions, and tunneling spectroscopies are also briefly discussed.

DOI： 10.1143/JPSJ.81.011013

Web of Science

Topology of Andreev bound states with flat dispersion Reviewed

M. Sato, Y. Tanaka, K. Yada and T. Yokoyama

Physical Review B Vol. 83 ( 22 ) page： 224511_1-22 2011

Language：English Publishing type：Research paper (scientific journal)

Theory of dispersionless Andreev bound states on surfaces of time-reversal-invariant unconventional superconductors is presented. The generalized criterion for the dispersionless Andreev bound state is derived from the bulk-edge correspondence, and the chiral spin structure of the dispersionless Andreev bound states is argued from which the Andreev bound state is stabilized. We then summarize the criterion in a form of index theorems. The index theorems are proved in a general framework to certify the bulk-edge correspondence. As concrete examples, we discuss the (i) d xy -wave superconductor, (ii) p x -wave superconductor, and (iii) noncentrosymmetric superconductors. In the last example, we find a peculiar time-reversal-invariant Majorana fermion. The time-reversal-invariant Majorana fermion shows an unusual response to the Zeeman magnetic field, which can be used to identify it experimentally.

DOI： 10.1103/PhysRevB.83.224511

Topological superconductivity in CuxBi2Se3. Reviewed

S. Sasaki, M. Kriener, K. Segawa, K. Yada, Y. Tanaka, M.Sato, and Y. Ando.

Physical Review Letters Vol. 107 ( 21 ) page： 217001_1-5 2011

Language：English Publishing type：Research paper (scientific journal)

A topological superconductor (TSC) is characterized by the topologically protected gapless surface state that is essentially an Andreev bound state consisting of Majorana fermions. While a TSC has not yet been discovered, the doped topological insulator CuxBi2Se3, has been predicted to possess a topological superconducting state. We report that the point-contact spectra on the cleaved surface of superconducting Cu x Bi 2 Se 3 present a zero-bias conductance peak (ZBCP) which signifies unconventional superconductivity. Theoretical considerations of all possible superconducting states help us conclude that this ZBCP is due to Majorana fermions and gives evidence for a topological superconductivity in Cu x Bi 2 Se 3.

DOI： 10.1103/PhysRevLett.107.217001

Odd-frequency superconducting states with different types of Meissner response: Problem of coexistence Reviewed

Y. V. Fominov, Y. Tanaka, Y. Asano and M. Eschrig

Physical Review B Vol. 91 page： 144514_1-14 2015