Quasiparticle excitations and evidence for superconducting double transitions in monocrystalline U0.97Th0.03Be13

Abstract

Superconducting (SC) gap symmetry and magnetic response of cubic U0.97Th0.03Be13 are studied by means of high-precision heat-capacity and dc magnetization measurements using a single crystal, in order to address the long-standing question of its second phase transition at Tc2 in the SC state below Tc1. The absence (presence) of an anomaly at Tc2 in the field-cooling (zero-field-cooling) magnetization indicates that this transition is between two different SC states. There is a qualitative difference in the field variation of the transition temperatures; Tc2(H) is isotropic whereas Tc1(H) exhibits a weak anisotropy between [001] and [111] directions. In the low temperature phase below Tc2(H), the angle-resolved heat-capacity C(T, H, φ) reveals that the gap is fully opened over the Fermi surface, narrowing down the possible gap symmetry.The nature of superconductivity in heavy-fermion compounds is of primary importance because an unconventional pairing mechanism is generally expected to occur due to strong electron correlation between heavy quasiparticles. The discovery of heavy-fermion superconductivity in UBe 13 [1] triggered exploration of unconventional pairing mechanism in 5f actinide compounds, and subsequently two uranium compounds, UPt 3 [2] and URu 2 Si 2 [3, 4], were found to show superconductivity. These U-based heavy-fermion superconductors have attracted considerable interest because of their unusual superconducting (SC) and normal-state properties. Among these, superconductivity in UBe 13 is highly enigmatic; it emerges from a strongly non-Fermi-liquid state with a large resistivity (ρ ∼ 150 µΩcm). Also unusual is the temperature variation of the upper critical field H c2 : an enormous initial slope −(dH c2 /dT ) Tc ∼ 42 T/K and an apparent absence of a Pauli paramagnetic limiting at low temperatures [5]. Extensive studies have been made to elucidate the SC gap symmetry [6,7], with an expectation of an oddparity pairing in this compound [8][9][10][11]. Recently, it has been found quite unexpectedly that nodal quasiparticle excitations in UBe 13 are absent as revealed by low-T angle-resolved heatcapacity measurements for a single crystalline sample [12].A long-standing mystery regarding UBe 13 is the occurrence of a second phase transitions in the SC state when a small amount of Th is substituted for U [ Fig. 1(a)] [13,14]. It has been reported that there exist four phases (A, B, C, and D) in its SC state, according to the previous µSR [16] and thermalexpansion [24] experiments using polycrystalline samples. The SC transition temperature T c is non-monotonic as a function of the Th concentration x in U 1−x Th x Be 13 , and exhibits a sharp minimum near x = 0.02. Further doping of Th results in an increase of the bulk SC transition temperature (T c1 ), reaching a local maximum at x ∼ 0.03 [13]. Below T c1 , another phase transition accompanied by a large heat-capacity jump occurs at T c2 in a narrow range of 0.019< x <0.045 [14,16]. Interestingly, only for this x region, weak magnetic correlations hav...

Unconventional superconducting gap structure protected by space group symmetry

“…For UBe 13 , the E u state [101,102] and the accidental A 1u + A 2u mixed state [101] have been proposed, consistent with the double transition in U 1−x Th x Be 13 . In the former E u state, j z -dependent point nodes emerge: the superconducting gap opens for γ k = E 1/2 , while point nodes appear for γ k = E 3/2 [see Eqs.…”

“…(33a) and (33b)]. Previous studies based on the E u scenario simply assumed the E 1/2 Bloch state and obtained the full gap superconducting state in the time-reversal symmetric A and C phases [101]. Their results are not valid when the FS crossing the Γ-L line is formed by the E Next, we consider the gap structures in PrOs 4 Sb 12 .…”

Topology and symmetry of surface Majorana arcs in cyclic superconductors

“…The limit of β = 0 corresponds to the pure A 1u state with the nodeless gap which is consistent to the full gap behavior in pure UBe 13 (x = 0). For β ∈ (0, π/2), the nonunitary chiral A 1u ± iA 2u state can explain both the broken time reversal symmetry and full gap behavior in 0 < T < T c2 at x ∼ 0.03, 25 where β remains as the fitting parameter. The pure f -wave state with β = π/2 occupies the higher T phase in 0.019 ≤ x ≤ 0.045.…”

“…8, we display the angle-resolved surface density of states, N S (k x , k y , E) defined in Eq. (25), in cyclic p-wave states for different surface orientations. The gapless linear dispersion appears at k x = k y = 0, which reflects the nontrivial topological invariant w s 1d = 2 in Eq.…”

“…20,32 Another senario is the oddparity E u state. 25 This suggests the cyclic state in T < T c2 , biaxial nematic states in T c2 < T < T c1 for 0.019 < x < 0.045, and the uniaxial nematic state for x < 0.019.…”