on the other hand, Fermi arcs are a precursor
signature of d-wave superconductivity, Sr2IrO4
may superconduct at lower temperatures. Further inquiries into these questions will shed new
light on the long-sought connection between the
pseudogap and HTSC.
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We thank J. H. Shim, K. Haule, G. Kotliar, C. Kim, M. Norman, and
G. Khaliullin for helpful discussions. Work at the University of
Michigan was supported by the U.S. NSF under grant no.
DMR-07-04480. B.J.K. acknowledges the Institute for Complex
Adaptive Matter for a travel grant that enabled a visit and helpful
discussions at Rutgers University. Work in the Materials Science
Division of Argonne National Laboratory (sample preparation
and characterization) was supported by the U.S. Department of
Energy (DOE) Office of Science, Basic Energy Sciences, Materials
Science and Engineering Division. The Advanced Light Source
is supported by the Director, Office of Science, Office of Basic
Energy Sciences of the U.S. DOE under contract no.
DE-AC02-05CH11231. Y.K.K. is supported through the National
Research Foundation (grant no. 20100018092).
Materials and Methods
Figs. S1 and S2
22 January 2014; accepted 28 May 2014
Observation of broken time-reversal
symmetry in the heavy-fermion
E. R. Schemm,1,2,3 W. J. Gannon,4† C. M. Wishne,4
W. P. Halperin,4 A. Kapitulnik1,2,3,5
Models of superconductivity in unconventional materials can be experimentally
differentiated by the predictions they make for the symmetries of the superconducting
order parameter. In the case of the heavy-fermion superconductor UPt3, a key question is
whether its multiple superconducting phases preserve or break time-reversal symmetry
(TRS). We tested for asymmetry in the phase shift between left and right circularly
polarized light reflected from a single crystal of UPt3 at normal incidence and found that
this so-called polar Kerr effect appears only below the lower of the two zero-field
superconducting transition temperatures. Our results provide evidence for broken TRS in
the low-temperature superconducting phase of UPt3, implying a complex two-component
order parameter for superconductivity in this system.
The heavy-fermion metal UPt3 (1) is one of only a handful of unconventional super- conductors (2, 3) exhibiting multiple super- conducting phases (4–6). In the normal state, strong hybridization between itinerant platinum 5d electrons and localized uranium 5f
moments results in an effective mass that is ~50
times that of free electrons (2). Below the Néel
temperature TN 5 K, the local U moments order
antiferromagnetically in the a-b plane (7). In zero
magnetic field, two peaks in the specific heat at
Tc+ 550 mK and Tc– 480 mK indicate the
presence of two superconducting states of differ-ing symmetry, called the A and B phases, respectively (4–6). Pressure studies suggest that these
two phases couple to, and are stabilized by, the
antiferromagnetic order parameter (8). In finite
magnetic fields, three distinct vortex phases are
also observed (9–11). The phase diagram of UPt3
therefore presents a particular challenge for models of unconventional superconductivity.
In the absence of a detailed understanding of
the microscopic origins of unconventional superconductivity, theoretical and experimental efforts
center on identifying the structure of the macroscopic superconducting order parameter—the pair
wavefunction, or gap. In the case of UPt3, acceptable candidate order parameters should respect
the D6h point-group symmetry of the underlying
crystal lattice and should therefore transform
under one or more representations of this group.
In this framework, many—but not all—experimental
studies of the superconducting states (1) favor an
E2u odd-parity triplet representation in which the
gap is given by
DðkFÞ ¼ ž½h1 ð T Þðk2 x − k2 yÞkz þ− 2i ⋅ h2 ð T Þkxkykz ;
in a coordinate system where ž‖ c. Here, h1ð TÞº ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1−ð T=Tcþ Þ2
is the real component of the superconducting order parameter, marking the onset of the A phase at Tc+, whereas h2ðTÞº ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
introduces an additional imaginary
component in the B phase at Tc– (12, 13). An order parameter of this form first breaks gauge
symmetry in the A phase, in which it also exhibits
fourfold rotational symmetry in the a-b plane distinct from the hexagonal symmetry of the crystal
lattice. In the B phase, the order parameter becomes isotropic in the a-b plane as T → 0 K, and
the phase difference between the real and imaginary components imparts an overall angular
momentum to the pair wave function. Hence,
time-reversal symmetry (TRS) is broken in this
phase, with the sign of the imaginary component
determining the orientation (chirality) of the internal angular momentum of the pair along T ž.
The results of Josephson interferometry experiments (13, 14) are consistent with the spatial
symmetries of the E2u order parameter of Eq. 1.
However, attempts to observe TRS-breaking (TRSB)
in UPt3 via muon spin relaxation measurements
have yielded conflicting results (15, 16). Moreover, recent thermal conductivity data (17) have
been interpreted to support a gap function belonging to an E1u representation that precludes
TRSB in the B phase. Thus, the unresolved question of whether TRS is indeed broken in the B
phase has become critical to determining the symmetry and hence the proper classification of the
superconducting order parameter of UPt3.
A general consequence of a TRSB order parameter (with a net moment oriented along the c
1Department of Physics, Stanford University, Stanford, CA
94305, USA. 2Geballe Laboratory for Advanced Materials,
Stanford University, Stanford, CA 94305, USA. 3Stanford
Institute for Materials and Energy Sciences (SIMES), SLAC
National Accelerator Laboratory, 2575 Sand Hill Road, Menlo
Park, CA 94025, USA. 4Department of Physics and
Astronomy, Northwestern University, Evanston, IL 60208,
USA. 5Department of Applied Physics, Stanford University,
Stanford, CA 94305, USA.
*Corresponding author. E-mail: email@example.com
†Present address: Department of Physics and Astronomy, Stony
Brook University, Stony Brook, NY 11794, USA.