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Supported by the Swedish National Science Council and the
Swedish National Space Board (A.G., R.A., and E.M.); U.S.
Department of Energy (DOE) grant DE-AC02-05CH11231 (P. E. N.);
European Research Council grant 615929 (M.S.); NASA (S.R.K.);
and NSF grant 1545949. The iPTF Swedish collaboration is funded
through a grant from the Knut and Alice Wallenberg foundation. This
research used resources of the National Energy Research Scientific
Computing Center, supported by DOE contract DE-AC02-05CH11231.
Some of the data presented here were obtained at the W. M. Keck
Observatory, which is operated as a scientific partnership among the
California Institute of Technology, the University of California, and
NASA grant HST-GO-14862.002. The Observatory was made
possible by the generous financial support of the W. M. Keck
Foundation. Some of the data presented here were obtained with
ALFOSC, which is provided by the Instituto de Astrofisica de
Andalucia (IAA) under a joint agreement with the University of
Copenhagen and NOTSA. The Space Telescope Science Data
Analysis System (STSDAS) and the command language PyRAF
are products of the Space Telescope Science Institute, which
is operated by the Association of Universities for Research in
Astronomy (AURA) for NASA. Part of the processing was carried out
off-line using the commercial software package MATLAB and
Statistics Toolbox Release 2013a, The Math Works Inc., Natick, MA.
Photometric data used in this paper are available in tables S1, S2,
and S5, spectroscopic data are available at public repository
WISeREP (33) ( http://wiserep.weizmann.ac.il) under the ID “SN
2016geu”; the positions of the SN images used in the lensing model
are provided in table S4.
Materials and Methods
Figs. S1 to S3
Tables S1 to S5
25 October 2016; accepted 24 March 2017
A parity-breaking electronic nematic
phase transition in the spin-orbit
coupled metal Cd2Re2O7
J. W. Harter,1,2 Z. Y. Zhao,3,4 J.-Q. Yan,3,5 D. G. Mandrus,3,5 D. Hsieh1,2*
Strong electron interactions can drive metallic systems toward a variety of well-known
symmetry-broken phases, but the instabilities of correlated metals with strong spin-orbit
coupling have only recently begun to be explored. We uncovered a multipolar nematic
phase of matter in the metallic pyrochlore Cd2Re2O7 using spatially resolved second-harmonic optical anisotropy measurements. Like previously discovered electronic nematic
phases, this multipolar phase spontaneously breaks rotational symmetry while preserving
translational invariance. However, it has the distinguishing property of being odd under
spatial inversion, which is allowed only in the presence of spin-orbit coupling. By examining
the critical behavior of the multipolar nematic order parameter, we show that it drives
the thermal phase transition near 200 kelvin in Cd2Re2O7 and induces a parity-breaking
lattice distortion as a secondary order.
In the presence of strong Coulomb inter- actions, the fluid of mobile electrons in a metal can spontaneously break the point group symmetries of the underlying crystal attice, realizing the quantum analog of a
nematic liquid crystal (1). Like their classical
counterparts, quantum nematic phases generally
preserve spatial inversion symmetry and are there-
fore anisotropic but centrosymmetric fluids. Ex-
perimental evidence of such nematic order was
first detected in a two-dimensional (2D) GaAs/
AlGaAs quantum well interface on the basis of
a pronounced resistivity anisotropy between the
two principal directions of the underlying square
lattice (2, 3). Subsequently, similar behavior has
been reported in a number of quasi-2D square
lattice compounds, including Sr3Ru2O7 (4), URu2Si2
(5), and several families of both copper- (6, 7) and
iron-based (8–11) high-temperature superconduc-
tors, suggesting possible connections between
even-parity nematic fluctuations and unconven-
tional s- and d-wave Cooper pairing (12).
Extending earlier work on Fermi liquid in-
stabilities in the p-wave spin interaction channel
(13), it has recently been predicted that corre-
lated metals with strong spin-orbit coupling may
realize a fundamentally new class of electronic
nematic phases with spontaneously broken spa-
tial inversion symmetry (14), including a quantum
analog of the unusual NT nematic phase discussed
in the context of classical bent-core liquid crystals
(15). Theoretical models have shown that parity-
breaking nematic fluctuations can induce odd-
parity p- or f-wave Cooper pairing and thus provide
a route to topological superconductivity (16, 17).
In addition, because inversion symmetry-breaking
necessarily lifts the spin degeneracy of bulk energy
bands in a spin-orbit coupled system, odd-parity
nematic order offers a potential mechanism for
generating topologically protected Weyl and nodal-
line semimetals and for designing highly tunable
charge-to-spin current conversion technologies
for spintronics applications.
The order parameter for this predicted new
class of spin-orbit–coupled parity-breaking electronic nematic phases—so-called “multipolar”
nematics (14)—can be represented by a symmetric
traceless second-rank pseudotensor Qij that is odd
under spatial inversion. This order parameter
induces a deformation and spin splitting of the
Fermi surface via the spin-orbit interaction
Hamiltonian HSO ¼
Qijsikj, where si are
the Pauli matrices and kj is the crystal momen-
tum (14, 18). In a cubic material, for example, this
order parameter can have either Eu or T2u sym-
metry. An example of a spin-polarized Fermi sur-
face distortion induced by T2u multipolar nematic
order is shown in Fig. 1A.
The correlated metallic pyrochlore Cd2Re2O7
has been proposed as a candidate for hosting
multipolar nematic order because of the strong
spin-orbit coupling of Re 5d valence electrons.
Detailed Raman scattering (19), x-ray (20, 21)
and neutron (22) diffraction, and optical second-harmonic generation (SHG) (23) studies have
shown that at critical temperature (Tc) 200 K,
the material undergoes a continuous phase transition from a centrosymmetric cubic structure (space
group Fd3m) to a noncentrosymmetric tetragonal
structure (space group I 4m2) that breaks threefold
rotational symmetry about the 111 axis (Fig. 1, B
and C). This phase transition has traditionally
been attributed to the freezing of a soft phonon
mode with Eu symmetry, dominated by the displacement of O(1) atoms (19, 24, 25). However, the observation of extremely small changes in lattice
1Department of Physics, California Institute of Technology,
Pasadena, CA 91125, USA. 2Institute for Quantum
Information and Matter, California Institute of Technology,
Pasadena, CA 91125, USA. 3Materials Science and
Technology Division, Oak Ridge National Laboratory, Oak
Ridge, TN 37831, USA. 4Department of Physics and
Astronomy, University of Tennessee, Knoxville, TN 37996,
USA. 5Department of Materials Science and Engineering,
University of Tennessee, Knoxville, TN 37996, USA.
*Corresponding author. Email: firstname.lastname@example.org