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Time-Reversal Symmetry Breaking Superconductivity in Sr2RuO4

a r X i v :c o n d -m a t /9808159v 1 [c o n d -m a t .s u p r -c o n ] 14 A u g 1998

Submitted to Nature 1

Time-Reversal Symmetry Breaking Superconductivity in Sr 2RuO 4

G.M.Luke ∗,Y.Fudamoto ∗,K.M.Kojima ∗,http://www.sodocs.net/doc/8f56d5e9551810a6f5248659.html rkin ∗,J.Merrin ∗,B.Nachumi ∗,Y.J.Uemura ∗,Y.Maeno †,Z.Q.Mao †,Y.Mori †,H.Nakamura ‡,M.Sigrist §

Dept.of Physics,Columbia University,New York,NY 10027,U.S.A.†

Dept.of Physics,Kyoto University,Kyoto 606-8502,Japan.‡

Dept.of Material Science and Engineering,Kyoto University,Kyoto 606-8501,Japan.§

Yukawa Instutute for Theoretical Physics,Kyoto University,Kyoto 606-8502,Japan.

In addition to its importance for existing and potential applications,superconductivity[1]is one of the most interesting phenomena in condensed matter physics.Although most superconducting materials are well-described in the context of the Bardeen Cooper and Schrieffer (BCS)theory[2],considerable effort has been de-voted to the search for exotic systems whose novel properties cannot be described by the BCS theory.Conventional superconductors break only gauge symmetry by selecting a def-inite phase for the Cooper pair wavefunction;a signature of an unconventional supercon-ducting state is the breaking of additional symmetries[3].Evidence for such broken symmetries include anisotropic pairing (such as d-wave in the high-T c cuprates)and the presence of multiple superconducting phases (UPt 3and superfluid 3He[4]).We have per-formed muon spin relaxation measurements of Sr 2RuO 4and observe a spontaneous internal magnetic field appearing below T c .Our measurements indicate that the supercon-ducting state in Sr 2RuO 4is characterized by broken time reversal symmetry which,when combined with symmetry considerations in-dicate that its superconductivity is of p-wave (odd-parity)type,analagous to superfluid 3

He.Despite the structural similarity with the high T c cuprates,the origin of the un-conventional superconductivity in Sr 2RuO 4is fundamentally different in nature.

Sr 2RuO 4,which is isostructural to the high-T c cuprate La 1.85Sr 0.15CuO 4,is to date the only known layered perovskite superconductor which does not contain copper.Although first synthesized in the 50’s,[5]its superconductivity was only found in

1994[6];T c ’s of early samples were roughly 0.7K but have increased to T c =1.5K in recent high quality single crystals[7].Despite its low transition temperature,Sr 2RuO 4is of great interest as there is growing evidence for an unconventional supercon-ducting state.In this system,strong correlation ef-fects enhance the effective mass seen in quantum oscillation[8]and Pauli spin susceptibility measure-ments,in the same way as in 3He[9].Combining this feature with Sr 2RuO 4’s expected tendency to display ferromagnetic spin fluctuations,Rice and Sigrist[10],and later Baskaran[11]argued that the pairing in Sr 2RuO 4could be of odd parity (spin triplet)type.The strong suppression of the superconducting T c by even non-magnetic impurities suggests non-s-wave pairing[7].Specific heat[12]and NMR 1/T 1[13]mea-surements indicate the presence of a large residual density of states (RDOS)at low temperatures (well within the superconducting state);in high quality samples,this RDOS as T →0seems to approach half of the normal state value.Several authors[14,15]have proposed so-called non-unitary p-wave super-conducting states for Sr 2RuO 4to account for this RDOS as well as the absence of a Hebel-Slichter peak in NMR measurements[13].A finite RDOS is not a unique signature of unconventional superconductiv-ity;for example it is observed in so-called gapless superconductors with isotropic s-wave pairing as a re-sult of impurity scattering (although this is unlikely in the specific case of Sr 2RuO 4where the finite RDOS apparently remains in the cleanest samples).It could also be explained with a multi-band hypothesis[16]where different gaps are associated with two types of bands.Therefore,further studies are required for a definitive determination of the pairing symmetry in Sr 2RuO 4.

One aspect of the pairing symmetry,the breaking of time reversal symmetry (TRS)can be probed di-rectly.If the superconducting state has a degenerate representation (as is possible for some triplet super-conducting states)then TRS can be broken,whereas it cannot be broken for non-degenerate representa-tions (the case for all singlet states).When spin or-bit coupling is small,the pair wave function can be written as a product of the orbital part and the spin part.Non-zero angular momentum of either the or-bital or the spin part could result in TRS breaking,although there are many such cases with conserved TRS,such as d-wave states in the high-T c cuprates.TRS breaking is also possible in the case of strong spin orbit coupling.In general,pairing states can be further classified in terms of gap functions attached to irreducible representations of a point group for a given crystal lattice symmetry of the system[3].TRS

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