Purpose | Topological Quantum Phenomena in Condensed Matter with Broken Symmetries

■ Leader's Address
Toward the Formation of "Topological Quantum Physics"

Topology is a concept and method enabling the classification of shape by continuous deformation. By widely applying such mathematical concept to novel phenomena in modern physics, we seek to deepen our understanding of the phenomena in a universal viewpoint. The objective of this research project is to further develop modern physics based on the topological aspect of matter. The shape subject to continuous deformation here is based on the symmetries and phases of the quantum mechanical wave functions.

Well known examples of quantum phenomena characterized by topology are quantization of vortices in superconductors and superfluids, Aharonov-Bohm effect of interference of electron wave functions, quantum Hall effect, fractional quantum Hall effects, spin-Hall effects in dissipative metals. Such quantum phenomena for which underlying topology plays fundamental roles paved a way to an important major frontier in modern physics. This trend has shown significant expansion today. In addition to semiconductors and normal metals, topological quantum phenomena have been recognized also in superconductors, superfluids, and even in insulators. The recognition that there must be a universal classification of these topological quantum phenomena in a variety of physical systems drives efforts to demonstrate it both theoretically and experimentally.

Since superconductivity is a kind of superfluid state of electrons, it is clearly useful in investigating its novel phenomena to utilize some analogies with superfluid helium and cold atoms. However, it has been rare that a major project is specifically organized to bring together experimental groups as well as theory groups investigating these different condensate systems. There are less obvious areas where collaborations among groups investigating different physical systems should prove useful. Among the recent topics of focused attention in condensed matter physics are the spin-triplet pairing state in non-centrosymmetric superconductors and the surface metallic state specific to topological insulators. Although apparently different, these phenomena have much in common: strong spin-orbit interaction of the electrons and broken inversion symmetry are required. In fact, a correspondence is recognized between these phenomena in the viewpoint of topological quantum phenomena.

The objective of project is to lead the world's effort in pursuing and deepening the physics of topological quantum phenomena over a vast variety of material systems. It is our hope and aim that after five years of intensive efforts in this project, the word "topological quantum physics" is widely recognized as a key to describe an important new area in physics.

■ Purpose

The purpose of the research area "Topological Quantum Phenomena in Condensed Matter with Broken Symmetries" is to investigate novel quantum phenomena characterized by topological aspects of broken symmetries realized in a variety of condensed matter systems such as superconductors, superfluids, and insulators. Through these investigations, it is aimed that unified treatment as "topological quantum phenomena" is established, and furthermore the new research areas of "Topological Quantum Physics" be created.

The physical systems investigated in this program are those superconductors and superfluids for which symmetry breaking in the "BULK" itself contains important outstanding issues, and also their surfaces and boundaries, which we designate as "EDGES", as stages where novel topological phenomena emerge. The thorough understanding of quantum phenomena in the "bulk" is the essential first step to understand those at the "edges" from the viewpoint of topology.

The main physical systems we focus on in the core programs in this project are:: (A); Superconductors with broken time-reversal symmetry,; (B); Spin-triplet superfluids, and; (C); Superconductors and insulators with broken inversion symmetries.
To bridge the physics of these systems, we organize the group developing; (D); Theories of Quantum Phenomena in Topological Condensates.

To complement and reinforce these core projects, we solicit open application for grants for domestic researchers.

■ Targets of Core Research Programs

□ Toward establishing the physics of topological quantum phenomena, we aim to demonstrate the following:: A; Determination of the vector order parameter of the ruthenate superconductor; A; Demonstration of proximity effects and quantum interference effects originating from odd-frequency superconductivity specific to junctions involving superconductors with broken time-reversal symmetry; B; Demonstration of intrinsic angular momentum and the associated edge mass current of superfluid 3He-A phase with broken time-reversal symmetry; B; Elucidation of Andreev surface bound states in various phases of superfluid 3He; C; Elucidation of singlet-triplet mixing and the roles of spin-orbit interaction in non-centrosymmetric superconductors and electric-field-induced surface superconductors.; C; Demonstration of helical edge state in topological insulators and elucidation of their physical properties.

□ Through the research activities above, we seek to achieve universalunderstanding of the topological quantum phenomena in a variety of systems.: D; Theoretical understanding and description of spontaneous flows of charge, mass, and spins at the surfacesand boundaries of quantum condensate systems with broken symmetries. Establishing unified treatment of these phenomena as a typical example of topological quantum phenomena.; D; Deepening the systematic understanding of quasi-particle excitations characteristic of surfaces and boundaries, thereby elucidating the universal mathematical structure underlying the topological quantum phenomena.

■ Organization and Program Activities

The physics of topological quantum phenomena is currently approaching the stage in which interdisciplinary interactions and collaborations can maximize their synergy effects. This project consist of four research groups A01 though D01 with 31 project members (18 core members and 13 adjunct members). The administrative committee lead by the project leader conducts a number of focused programs as described below in order to promote the interdisciplinary research as well as to foster young researchers.

1. Pursuit of Analogies through Collaborative and Interdisciplinary Research

Spin-triplet pairing condensate states, edge currents, spin-orbit interactions under inversion-symmetry breaking: these are some of the key concepts in the physics of topological quantum phenomena. We will expand the frontiers of topological quantum physics by collaborations among experts studying these common concepts in different material systems, ranging from superfluids, superconductors, to insulators. With the common viewpoint as "topological quantum phenomena", we will promote collaborations among different groups in the project through frequent small workshops on focused interdisciplinary subjects and other programs. We aim to acquire universal understanding of these phenomena as well as gaining revitalized viewpoints on individual phenomena. Annual Project Meetings (to be held as International Symposia in 2012 and 2014) will be structured from the sessions reflecting the interdisciplinary progress.

2. Fusion of Research through Fostering Young Researchers