Twofold Spontaneous Symmetry Breaking in the Heavy-Fermion Superconductor<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>UPt</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>

Machida, Yo; Itoh, Atsushi; So, Y.; Izawa, K.; Haga, Yoshinori; Yamamoto, Etsuji; Kimura, Noriaki; Ōnuki, Yoshichika; Tsutsumi, Yoshio; Machida, Kazushige

doi:10.1103/physrevlett.108.157002

Cited by 76 publications

(85 citation statements)

References 37 publications

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“…Recent experiments on angle-resolved thermal conductivity have observed the two-fold rotational symmetry in the a-b plane, which convincingly suggests a spintriplet f -wave function in the E 1u representation [291]. Based on the measurement, the pairing symmetry in the B-phase is described by two components of the d-vectors.…”

Section: Promising Examples Of Topological Crystalline Superconductorsmentioning

confidence: 88%

Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

158

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Abstract.Owing to the richness of symmetry and well-established knowledge on the bulk superfluidity, the superfluid 3 He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of 3 He in a multifaceted manner, including symmetry consideration, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological superfuidity of the 3 He-B confined in a slab geometry. The 3 He-B under a magnetic field is separated to two different sub-phases: The symmetry protected topological phase and non-topological phase. The former phase is characterized by the existence of symmetry protected Majorana fermions. The topological phase transition between them is triggered off by the spontaneous breaking of a hidden discrete symmetry. The critical field is quantitatively determined from the microscopic calculation that takes account of magnetic dipole interaction of 3 He nucleus. It is also demonstrated that odd-frequency evenparity Cooper pair amplitudes are emergent in low-lying quasiparticles. The key ingredients, symmetry protected Majorana fermions and odd-frequency pairing, bring an important consequence that the coupling of the surface states to an applied field is prohibited by the hidden discrete symmetry, while the topological phase transition with the spontaneous symmetry breaking is accompanied by anomalous enhancement and anisotropic quantum criticality of surface spin susceptibility. We also illustrate common topological features between topological crystalline superconductors and symmetry protected topological superfluids, taking UPt 3 and Rashba superconductors as examples.

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Section: Promising Examples Of Topological Crystalline Superconductorsmentioning

confidence: 88%

Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

158

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“…The absence of Pauli-limiting effect for H ⊥ c2 (T ) and a large H ⊥ c2 (0) value (3.4 times of H P c2 ) also dictate a spin-triplet pairing scenario, as in the case of UPt 3 (see Table I of SM for the comparison) that was recently confirmed to host a spin-triplet odd-parity SC [50,51]. The (pseudo)spins of the odd-parity Cooper pairs are |↑↓> + |↓↑> with S z = 0, which is equivalent to the spin state of |⇔> + |⇒>.…”

Section: Discussionmentioning

confidence: 99%

Temperature and angular dependence of the upper critical field in K2Cr3As3

et al. 2017

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We report measurements of the upper critical field Hc2 as functions of temperature T , polar angle θ (of the field direction with respect to the crystallographic c axis), and azimuthal angle φ (of the field direction relative to the a axis within the ab plane) for the Cr-based superconductor K2Cr3As3 with a quasi-one-dimensional and non-centrosymmetric crystal structure. We confirm that the anisotropy in Hc2(T ) becomes inverse with decreasing temperature. At low temperatures, Hc2(θ) data are featured by two maxima at θ = 0 (H c) and π/2 (H⊥c), which can be quantitatively understood only if uniaxial effective-mass anisotropy and absence of Pauli paramagnetic effect for H⊥c are taken simultaneously into consideration. The in-plane Hc2(φ) profile shows a unique threefold modulation especially at low temperatures. Overall, the characteristic of the Hc2(θ, φ, T ) data mostly resemble those of the heavy-fermion superconductor UPt3, and we argue a dominant spin-triplet superconductivity with odd parity in K2Cr3As3.

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“…The p-wave superfluid 3 He and superconductors exhibit rich topological structures of vortices and spin textures under rotations or in external magnetic fields, respectively [11,12]. In addition, experimental signatures of the possible nodal f -wave superconductivity have also been reported in UPt 3 [13,14].Among these unconventional pairing phases, the 3 He-B phase is distinct: in spite of its non-s-wave pairing symmetry and spin structure, the overall pairing structure remains isotropic and fully gapped. Its pairing exhibits the relative spin-orbit symmetry breaking from…”

mentioning

confidence: 95%

Topological Septet Pairing with Spin-32Fermions: High-Partial-Wave Channel Counterpart of theHe3−
Wang
¹
,
Li
²
,
Wu
³

2016
Phys. Rev. Lett.
47
3
54
0
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We systematically generalize the exotic 3 He-B phase, which not only exhibits unconventional symmetry but is also isotropic and topologically non-trivial, to arbitrary partial-wave channels with multi-component fermions. The concrete example with four-component fermions is illustrated including the isotropic f , p and d-wave pairings in the spin septet, triplet, and quintet channels, respectively. The odd partial-wave channel pairings are topologically non-trivial, while pairings in even partial-wave channels are topologically trivial. The topological index reaches the largest value of N 2 in the p-wave channel (N is half of the fermion component number). The surface spectra exhibit multiple linear and even high order Dirac cones. Applications to multi-orbital condensed matter systems and multi-component ultra-cold large spin fermion systems are discussed. [5,6]. The p-wave superconductivity has also been extensively investigated in SrRu 2 O 4 [7-9], and heavy fermion systems including UGe 2 , URhGe, UCoGe [10]. The p-wave superfluid 3 He and superconductors exhibit rich topological structures of vortices and spin textures under rotations or in external magnetic fields, respectively [11,12]. In addition, experimental signatures of the possible nodal f -wave superconductivity have also been reported in UPt 3 [13,14].Among these unconventional pairing phases, the 3 He-B phase is distinct: in spite of its non-s-wave pairing symmetry and spin structure, the overall pairing structure remains isotropic and fully gapped. Its pairing exhibits the relative spin-orbit symmetry breaking fromwhere L, S, and J represent the orbital, spin, and total angular momentum, respectively. The relative spin-orbit symmetry-breaking has also been studied in the context of Pomeranchuk instability termed as unconventional magnetism leading to dynamic generation of spin-orbit coupling [15,16]. Furthermore, the 3 He-B phase possesses non-trivial topological properties [17][18][19]. Topological states of matter have become a major research focus since the discovery of the integer quantum Hall effect [20][21][22]. Recently, the study of topological band structures has extended from time-reversal (TR) breaking systems to TR invariant systems [23][24][25], from two to three dimensions [18,26,27], and from insulators to superconductors [17][18][19][28][29][30][31]. The 3 He-B phase is a 3D TR invariant topological Cooper pairing state. Its bulk Bogoliubov spectra are analogous to the 3D gapped Dirac fermions belonging to the DIII class characterized by an integer-valued index [18]. The non-trivial bulk topology gives rise to the gapless surface Dirac spectra of the mid-gap AndreevMajorana modes [32]. Evidence of these low energy states has been reported in recent experiments [33].Because the electron Cooper pair can only be either spin singlet or triplet, the p-wave 3 He-B phase looks the only choice of the unconventional 3D isotropic pairing state. In this article, we will show that actually there are much richer possibilities of this exotic c...

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Twofold Spontaneous Symmetry Breaking in the Heavy-Fermion SuperconductorUPt3

Cited by 76 publications

References 37 publications

Symmetry protected topological superfluid³He-B

Symmetry protected topological superfluid³He-B

Temperature and angular dependence of the upper critical field in K2Cr3As3

Topological Septet Pairing with Spin-32Fermions: High-Partial-Wave Channel Counterpart of theHe3−
Wang
¹
,
Li
²
,
Wu
³

2016
Phys. Rev. Lett.
47
3
54
0
View full text Add to dashboard Cite

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Twofold Spontaneous Symmetry Breaking in the Heavy-Fermion SuperconductorUPt3

Cited by 76 publications

References 37 publications

Symmetry protected topological superfluid3He-B

Symmetry protected topological superfluid3He-B

Temperature and angular dependence of the upper critical field in K2Cr3As3

Topological Septet Pairing with Spin-32Fermions: High-Partial-Wave Channel Counterpart of theHe3−Wang1, Li2, Wu3 2016Phys. Rev. Lett.473540View full textAdd to dashboardCite

Contact Info

Product

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About

Symmetry protected topological superfluid³He-B

Symmetry protected topological superfluid³He-B

Topological Septet Pairing with Spin-32Fermions: High-Partial-Wave Channel Counterpart of theHe3−
Wang
¹
,
Li
²
,
Wu
³

2016
Phys. Rev. Lett.
47
3
54
0
View full text Add to dashboard Cite