Time-Reversal Symmetry Breaking States in High-Temperature Superconductors

Progress of Theoretical Physics, Jun 1998

The dx2−y2-wave symmetry of the order parameter leads to various physical phenomena of high-temperature superconductors which are not present in standard superconductors. A particularly interesting new aspect occurs in connection with the behavior of the order parameter in the vicinity of interfaces (Josephson junctions) between superconductors and close to surfaces. In this review we discuss the appearance of localized states with broken time-reversal symmetry in these regions, using various different schemes of analysis: the tunneling formalism, the Bogolyubov-de Gennes equation, and the generalized Ginzburg-Landau theory. We demonstrate that this kind of state is connected with the opening of a gap in the quasiparticle density of states which lowers the local free energy density. A direct consequence of time-reversal symmetry breaking can be seen in the presence of spontaneous supercurrents. Other features, such as the possibility of vortices with fractional flux quanta and unusual phase slip effects in Josephson junctions are examined as possible experimental indications for a time-reversal symmetry breaking state. Furthermore, quasiparticle tunneling has been recently discussed and applied to probe the surface of such a superconductor for the violation of time-reversal symmetry. Concerning the magnetic properties surfaces supporting such a state can yield a paramagnetic contribution to the magnetic response of the superconductor. Finally, some examples of superconductors which break time-reversal symmetry in the bulk are discussed. Clear signals in the zero-field relaxation rate of muons leave little doubt that such superconducting states are realized in UPt3, U1−xThxBe13 and Sr2RuO4.

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Time-Reversal Symmetry Breaking States in High-Temperature Superconductors

Time-Reversal Symmetry Breaking States in High-Temperature Superconductors 0 Manfred SIGRIST 0 0 Yukawa Institute for Theoretical Physics, Kyoto University , Kyoto 606-8502 , Japan The dx 2 _ y2 - wave symmetry of the order parameter leads to various physical phenomena of high-temperature superconductors which are not present in standard superconductors. A particularly interesting new aspect occurs in connection with the behavior of the order parameter in the vicinity of interfaces (Josephson junctions) between superconductors and close to surfaces. In this review we discuss the appearance of localized states with broken time-reversal symmetry in these regions, using various different schemes of analysis: the tunneling formalism, the Bogolyubov-de Gennes equation, and the generalized GinzburgLandau theory. We demonstrate that this kind of state is connected with the opening of a gap in the quasiparticle density of states which lowers the local free energy density. A direct consequence of time-reversal symmetry breaking can be seen in the presence of spontaneous supercurrents. Other features, such as the possibility of vortices with fractional flux quanta and unusual phase slip effects in Josephson junctions are examined as possible experimental indications for a time-reversal symmetry breaking state. Furthermore, quasiparticle tunneling has been recently discussed and applied to probe the surface of such a superconductor for the violation of time-reversal symmetry. Concerning the magnetic properties surfaces supporting such a state can yield a paramagnetic contribution to the magnetic response of the superconductor. Finally, some examples of superconductors which break time-reversal symmetry in the bulk are discussed. Clear signals in the zero-field relaxation rate of muons leave little doubt that such superconducting states are realized in UPt3, U I-x Thx BeI3 and Sr2Ru04. - underlying mechanism. 3), 4) Today a great deal of experimental data give convinc­ ing evidence that the pair wavefunction has dx 2_ y2-wave character, most commonly written as (1·1) where cks denotes the electron creation operator. Nevertheless, the mechanism remains a matter hotly debated among various groups. Pairing with dx 2_ y2-wave symmetry is a property common to several theories. One such theory is based on the idea that the pairing interaction is mediated through the exchange of antifer­ romagnetic spin fluctuations among the quasiparticles. 5), 6) Another describes the superconducting states as pairing resulting from the doping of a spin liquid state, the so-called resonating valence bond (RVB) state. 7) - 9) An alternative view pre­ sented recently proposes the existence of a large continuous symmetry 80( 5 ) which establishes a connection between the antiferromagnetic and the superconducting or­ der parameters. 10) These competing scenarios in addition to others are still a matter of controversy. It is not the goal of this article to elaborate on these microscopic theories further. Rather, we would like to give here a review of some implications of d-wave pairing in high-temperature superconductors, in particular, in connection with the internal phase structure of the pair wave function (Eq. (1·1)). The phenomena best inves­ tigated theoretically, as well as experimentally, in this respect are related with the Josephson effect, which provides a very powerful means to study the phase of the su­ perconducting order parameters. 11),12) The Josephson effect turned out to be crucial in the experimental tests of the pairing symmetry, because it allows for the detec­ tion of the sign difference in the pair wave function along the x- and y-coordinate. The presence of nodes in the quasiparticle excitation gap seen by number of other important experiments are in this respect less decisive for the identification of the pairing symmetry, because this feature is shared by various pairing states. 3), 4) This article is mainly concerned with the possibility of order parameter con­ figurations which break time-reversal symmetry, for example on certain Josephson junctions, at surfaces or other inhomogeneities. We show that such states can lead to unusual magnetic properties. The possibility of time-reversal symmetry breaking superconducting states is not unlikely in view of the strong evidence for such states in the heavy Fermion superconductors UPta and U1- xThxBe13 and the more recently discovered compound Sr2Ru04, as we discuss in the last section. §2. Order parameter symmetry All high-temperature superconductors consist of Cu02-planes stacked on top of each other and separated by layers of other elements. . The prevailing view is that the physics essential to the superconductivity occurs in these Cu02-planes, while the intermediate layers act as charge reservoirs to remove or add electrons to the planes. Therefore the discussion of the symmetry of the superconducting state must be based on the lattice struc­ ture of the plane (...truncated)


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Manfred Sigrist. Time-Reversal Symmetry Breaking States in High-Temperature Superconductors, Progress of Theoretical Physics, 1998, pp. 899-929, 99/6, DOI: 10.1143/PTP.99.899