Exotic Multigap Structure in UPt3 Unveiled by a First-Principles Analysis

Abstract

A heavy-fermion superconductor UPt3 is a unique spin-triplet superconductor with multiple superconducting phases. Here we provide the first report on the first-principles analysis of the microscopic superconducting gap structure. We find that the promising gap structure is an unprecedented E2u state, which is completely different from the previous phenomenological E2u models. Our obtained E2u state has in-plane twofold vertical line nodes on small Fermi surfaces and point nodes with linear dispersion on a large Fermi surface. These peculiar features cannot be explained in the conventional spin 1/2 representation, but is described by the group-theoretical representation of the Cooper pairs in the total angular momentum j = 5/2 space. Our findings shed new light on the long-standing problems in the superconductivity of UPt3.PACS numbers: 74.20.Mn, 74.20.Pq, 74.20.Rp,74.70.Tx Identifying the pairing state and the pairing mechanism is one of the most interesting and important issues in the field of unconventional superconductivity. In particular, a spin-triplet type of pairing state attracts much attention, since there are few examples except for the superfluid helium 3. In the strongly correlated electron systems, the heavy-fermion superconductor UPt 3 is one of the rare candidates for spin-triplet superconductors [1,2]. The most impressive feature of this material is the multiple superconducting phase diagram. At zero magnetic field, there appears the superconducting double transition into the A phase at the upper critical temperature T + c ∼ 540mK, and then into the B phase at the lower T − c ∼ 490mK [3]. Moreover, the C phase appears at high field and low temperature in the H − T phase diagram [4,5]. In each phase, nodal quasiparticle excitations have been observed [6][7][8][9], and also the time-reversal symmetry breaking has been reported in B phase [10][11][12]. In spite of these prominent features, the superconducting gap structure still remains to be solved. Many scenarios have been proposed based on the phenomenological approach so far [13][14][15][16]. Among them, the most promising gap symmetry has been widely believed to be E 2u models [1,[17][18][19]. However, recent measurement of the fieldangle resolved thermal transport has detected in-plane twofold oscillations in the C phase [20]. This result is inconsistent with the proposed E 2u models, because in the group-theoretical argument, it is believed that the E 2u models do not have such in-plane twofold symmetry. Such twofold symmetry seems to be rather compatible with the E 1u models proposed in Refs. [21][22][23]. This is also supported by the following observations. A small residual thermal conductivity [24] suggests the presence of point nodes with linear dispersion in the E 1u models. The Josephson effect [25] with s-wave superconductor is compatible with E 1u planar states. Thus, recently, the * nomoto.takuya@scphys.kyoto-u.ac.jp E 1u models [21][22][23] have been revisited. This strongly promoted the field-angle resolved specific heat measur...

Experimental consequences of Bogoliubov Fermi surfaces

“…The pairing of electrons with additional internal degrees of freedom resulting, e.g., from different orbitals or basis sites, can lead to qualitatively new pairing states. Such pairing states have for example been proposed for iron-based superconductors [2][3][4][5][6][7][8][9], Cu x Bi 2 Se 3 [10,11], cubic systems such as half-Heusler compounds [12][13][14][15][16][17][18][19][20][21], UPt 3 [22,23], transition-metal dichalcogenides [24,25], and twisted bilayer graphene [26][27][28]. It has been shown that in centrosymmetric multiband superconductors that break TRS, point and line nodes are generically "inflated," by interband pairing, into Fermi surfaces of Bogoliubov quasiparticles [29,30].…”

The Role of Odd‐Frequency Pairing in Multiband Superconductors

“…The superconducting order parameter in UPt 3 is widely believed to belong to the irreducible representation with spin‐triplet pairing . Following recent work explicitly accounting for the symmetries of the lattice, the order parameter is given by a linear combination of d ‐wave and f ‐wave basis functions: where and are Pauli matrices in spin and sublattice space, respectively, and , and are complex numbers parameterizing the phase diagram . Notice the unusual combination of spin‐triplet f ‐wave terms being odd in spatial parity and spin‐triplet d ‐wave terms being even in parity.…”

Bogoliubov Fermi Surfaces in Superconductors with Broken Time-Reversal Symmetry

“…Our conclusions are relevant for a wide range of candidate TRSB superconductors, such as UPt 3 [9][10][11][12], Thdoped UBe 13 [13,14], PrOs 4 Sb 12 [15], Sr 2 RuO 4 [16,17], URu 2 Si 2 [18,19], SrPtAs [20], and Bi/Ni bilayers [21]. Remarkably, signatures of these Fermi surfaces may have already been observed in Th-doped UBe 13 [14] (and possibly in UPt 3 [11]), where there is evidence for a nonzero density of states at zero temperature, which appears not to be due to impurities.…”

“…Another example is the nematic superconductivity of Cu x Bi 2 Se 3 [7], where the odd parity of the gap is encoded in the orbital degrees of freedom. Furthermore, theories of pairing in YPtBi and UPt 3 based on j = 3/2 and j = 5/2 fermions, respectively, have greatly enriched the allowed superconducting states [8,9].…”