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 the  and  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.
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Quasiparticle excitations and evidence for superconducting double transitions in monocrystalline U0.97Th0.03Be13. / Shimizu, Yusei; Kittaka, Shunichiro; Nakamura, Shota; Sakakibara, Toshiro; Aoki, Dai; Homma, Yoshiya; Nakamura, Ai; Machida, Kazushige.In: Physical Review B, Vol. 96, No. 10, 100505, 18.09.2017.
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TY - JOUR
T1 - Quasiparticle excitations and evidence for superconducting double transitions in monocrystalline U0.97Th0.03Be13
AU - Shimizu, Yusei
AU - Kittaka, Shunichiro
AU - Nakamura, Shota
AU - Sakakibara, Toshiro
AU - Aoki, Dai
AU - Homma, Yoshiya
AU - Nakamura, Ai
AU - Machida, Kazushige
N1 - Funding Information: et al. Shimizu Yusei * Kittaka Shunichiro Nakamura Shota Sakakibara Toshiro Institute for Solid State Physics, University of Tokyo , Kashiwa, Chiba 277-8581, Japan Aoki Dai Homma Yoshiya Nakamura Ai Institute for Materials Research (IMR), Tohoku University , Oarai, Ibaraki 311-1313, Japan Machida Kazushige Department of Physics, Ritsumeikan University , Kusatsu, Shiga 525-8577, Japan * Present address: Institute for Materials Research, Tohoku University, Oarai, Ibaraki, 311-1313, Japan; email@example.com September 2017 18 September 2017 96 10 100505 16 February 2017 13 July 2017 ©2017 American Physical Society 2017 American Physical Society Superconducting (SC) gap symmetry and magnetic response of cubic U 0.97 Th 0.03 Be 13 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 T c 2 in the SC state below T c 1 . The absence (presence) of an anomaly at T c 2 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; T c 2 ( H ) is isotropic, whereas T c 1 ( H ) exhibits a weak anisotropy between the  and  directions. In the low-temperature phase below T c 2 ( 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. Tohoku University http://dx.doi.org/10.13039/501100006004 http://sws.geonames.org/1861060/ Ministry of Education, Culture, Sports, Science and Technology http://dx.doi.org/10.13039/501100001700 MEXT http://sws.geonames.org/1861060/ 15H05883 15H05884 15K05882 marker B_SUGG 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  triggered exploration of an unconventional pairing mechanism in 5 f actinide compounds, and subsequently two uranium compounds, UPt 3  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 μ Ω cm ). Also unusual is the temperature variation of the upper critical field H c 2 : an enormous initial slope − ( d H c 2 / d T ) T c ∼ 42 T/K and an apparent absence of a Pauli paramagnetic limiting at low temperatures  . Extensive studies have been made to elucidate the SC gap symmetry [6,7] , with an expectation of an odd-parity pairing in this compound [8–11] . Recently, it has been found quite unexpectedly that nodal quasiparticle excitations in UBe 13 are absent as revealed by low- T angle-resolved heat-capacity measurements for a single crystalline sample  . A long-standing mystery regarding UBe 13 is the occurrence of a second phase transition 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 μ SR  and thermal-expansion  experiments using polycrystalline samples. The SC transition temperature T c is nonmonotonic 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 c 1 ), reaching a local maximum at x ∼ 0.03  . Below T c 1 , another phase transition accompanied by a large heat-capacity jump occurs at T c 2 in a narrow range of 0.019 < x < 0.045 [14,15] . Interestingly, only for this x region, weak magnetic correlations have been observed in zero-field μ SR measurements  . The previous thermal-expansion study  claimed that the low-temperature (“ T L ”) anomaly appearing below T c for 0 ≤ x < 0.02 , which can be connected to the “ B * anomaly” observed in pure UBe 13 [16–18] , is a precursor of the transition at T c 2 . Up to the present, the true nature of the transition at T c 2 remains controversial [19,20] . Two different scenarios have been discussed so far on the T c 2 transition: (i) an additional SC transition that breaks time-reversal symmetry  , and (ii) the occurrence of an antiferromagnetic ordering that coexists with the SC state [22,23] . Indeed, although it has been reported that the NMR spin-relaxation rate  , heat capacity  , and muon Knight shift  show unusual temperature dependence in the SC state, little is known concerning the gap structure in U 1 − x Th x Be 13 due to the lack of information about the anisotropy of its quasiparticle excitations in magnetic fields. In order to resolve the controversy regarding the second transition at T c 2 , and to uncover its gap symmetry, in this Rapid Communication we report the results of high-precision heat-capacity and dc magnetization measurements on U 0.97 Th 0.03 Be 13 . Single-crystalline U 0.97 Th 0.03 Be 13 samples were obtained using a tetra-arc furnace; the ingot was remelted several times and then quenched. By this procedure, we have succeeded in obtaining small monocrystalline samples with no additional heat treatment as confirmed by sharp x-ray Laue spots in Fig. 1(b) . Heat capacity ( C ) was measured at low temperatures down to 60 mK by means of a standard quasiadiabatic heat-pulse method in a He 3 - He 4 dilution refrigerator. Field-orientation dependences C ( H , ϕ ) were obtained under rotating magnetic fields in the ( 1 1 ¯ 0 ) crystal plane that includes the [ 001 ] , [ 111 ] , and [ 110 ] axes, using a 5 T × 3 T vector magnet. We define the angle ϕ measured from the [ 001 ] direction. dc magnetization measurements were performed along the [ 1 1 ¯ 0 ] axis down to T ∼ 0.28 K for the same single crystal using a capacitive Faraday magnetometer  installed in a He 3 refrigerator. A magnetic-field gradient of 9 T/m was applied to the sample, independently of the central field at the sample position. 10.1103/PhysRevB.96.100505.f1 1 FIG. 1. (a) T - x phase diagram of U 1 − x Th x Be 13 [15,16] , where the solid lines are based on Ref.  . There are four phases (A, B, C, and D) in its SC state, according to the previous μ SR  and thermal-expansion  studies. The red circles indicate the transition temperatures at zero field for the sample used in the present experiment ( x = 0.03 ). Here T c 1 and T c 2 are determined from C ( T ) by considering the entropy conservation at each transition. (b) Laue x-ray photographs for the cubic fourfold ( 100 ) (upper panel) and twofold ( 1 1 ¯ 0 ) (lower panel) planes. (c) C ( T ) / T of U 0.97 Th 0.03 Be 13 at zero and in magnetic fields up to 5 T, measured every 0.5 T step for two directions H ∥ [ 001 ] (circles) and H ∥ [ 111 ] (triangles). Figure 1(c) shows C ( T ) / T curves measured at zero and various fields up to 5 T applied along the [ 001 ] and [ 111 ] axes. At zero field, two prominent jumps occur at T c 1 ∼ 0.56 K and T c 2 ∼ 0.41 K, where the transition temperatures [red circles in Fig. 1(a) ] are determined by transforming the broadened transitions into idealized sharp ones by an equal-areas construction. The results are in agreement with the previous reports [13,14] . With increasing field, both transitions shift to lower temperature, getting closer to each other [27,28] . Above 3.5 T, the two transitions become very close to each other and are difficult to resolve separately. There is a notable feature in the anisotropy of C ( T ) in magnetic fields. At low fields below ∼ 1.75 T, the shifts of the two transition temperatures are almost isotropic. At higher fields above 2.5 T, however, the T c 1 ( H ) becomes slightly anisotropic, T c 1 ( H | | [ 001 ] ) > T c 1 ( H | | [ 111 ] ) , while T c 2 ( H ) remains isotropic. In general, an anisotropy of T c ( H ) and H c 2 results from those of SC gap function and/or Fermi velocity. If the double transitions come from two inhomogeneous SC states with the same gap symmetry, they should show the same anisotropic (or isotropic) field response. Our experimental results exclude such an extrinsic possibility. Thus the difference between field anisotropy in T c 1 ( H ) and T c 2 ( H ) is an essential effect which strongly suggests that the order parameters of these two phases have qualitatively different field-orientation dependences. A key question, then, is whether the second transition at T c 2 is a SC transition into a different gap symmetry. To address this question, we performed precise dc magnetization [ M ( T ) ] measurements across the double transitions. Figure 2 shows the temperature dependence of M ( T ) measured at 1.5 T together with the C ( T ) / T data for the same field on the same sample. FC and ZFC denote the data taken in the field-cooling and zero-field-cooling protocols, respectively. The FC-ZFC branching occurs below ∼ 0.5 K close to T c 1 at this field, indicating the appearance of bulk superconductivity. We find a small but distinct kink in the ZFC data near T c 2 , while no such anomaly can be seen in the FC curve. This fact implies a substantial change in the vortex pinning strength at this temperature, consistent with the previous vortex creep measurements [29,30] . Regarding the possible origin of the enhanced flux pinning in the low- T phase, we find no signatures that can be ascribed to a magnetic transition in the FC curve near T c 2 . Our magnetization data, therefore, strongly suggest that the transition at T c 2 is of a kind such that the SC order parameter changes. Indeed, it has been argued that such an enhancement of the vortex pinning occurs in a SC state with broken time-reversal symmetry  . This conclusion is also consistent with the previous neutron scattering measurements  which show no evidence for magnetic ordering in U 0.965 Th 0.035 Be 13 down to 0.15 K. 10.1103/PhysRevB.96.100505.f2 2 FIG. 2. Temperature dependence of the dc magnetization M ( T ) measured at 1.5 T for H | | [ 1 1 ¯ 0 ] . The data of C ( T ) / T measured in the same magnetic field are also plotted for comparison. Next we examine the magnetic-field dependence of the heat capacity and its anisotropy in more detail, whose behavior in low fields reflects quasiparticle excitations in the SC state and provides a hint for the gap symmetry [32–34] . Figure 3(a) shows C ( H ) / T measured at b l a c k T = 0.12 , 0.18, 0.24, 0.30, 0.36, and 0.40 K for the cubic [ 001 ] and [ 111 ] directions, and the inset shows the enlarged C ( H ) / T plot obtained at 0.08 K. Note that C ( H ) below 1 T is quite linear to H at the lowest temperature of 0.08 K. This behavior is in striking contrast with a convex upward H dependence expected for nodal superconductors  . Moreover, there is n o anisotropy in C ( H ) ∝ H between H | | [ 001 ] and [ 111 ] in low fields below ∼ 2 T. The absence of the anisotropy is further demonstrated by angle-resolved C ( ϕ ) / T in Fig. 4(a) , obtained in a field of 1 T rotated in the ( 1 1 ¯ 0 ) crystal plane at T = 0.08 and 0.42 K, together with the result measured in the normal state at 0.60 K. The absence of any angular dependence in C ( ϕ ) / T in a low- T low- H region again excludes the possibility of a nodal-gap structure in which a characteristic angular oscillation should be expected in C ( ϕ ) / T  . The present C ( H , ϕ ) data thus indicate that nodal quasiparticles are absent in U 0.97 Th 0.03 Be 13 , similarly to the behaviors observed in pure UBe 13  . 10.1103/PhysRevB.96.100505.f3 3 FIG. 3. (a) Magnetic-field dependence of C ( H ) / T up to 5 T for H | | [ 001 ] (circles) and H | | [ 111 ] (triangles) measured at T = 0.12 , 0.18, 0.24, 0.30, 0.36, 0.40, and 0.42 K. The inset shows the C ( H ) / T in low magnetic fields measured at the base temperature of T = 0.08 K. C ( H ) / T and its differential as a function of magnetic field around the double transitions at (b) 0.30 and (c) 0.40 K. The transition fields of the A and B phases, i.e., H c 2 A and H c 2 B , are determined as magnetic fields where the differential, d [ C ( H ) / T ] / d H , shows a local minimum. At higher fields, double-steplike anomalies are observed in C ( H ) / T at 0.42, 0.40, and 0.36 K [Fig. 3(a) ]. Here the double transitions can be clearly defined by the differential data, d [ C ( H ) / T ] / d H , as shown in Figs. 3(b) and 3(c) . The lower-field step occurs when the boundary T c 2 ( H ) is crossed, while the higher-field one corresponds to the transition at T c 1 ( H ) , i.e., the upper critical field H c 2 ( T ) ≡ H c 2 A . Note that the position of the lower-field anomaly ( H c 2 B ) is fully isotropic , whereas the higher-field one ( H c 2 A ) shows an appreciable anisotropy, indicating that H c 2 becomes anisotropic: H c 2 A ∥ [ 001 ] > H c 2 A ∥ [ 111 ] . The anisotropy of H c 2 A becomes larger at lower temperatures. With decreasing T , both of the transition fields shift to higher fields, getting close to each other, and are difficult to discriminate below ∼ 0.24 K [Fig. 3(a) ]. These features of the transition fields are fully consistent with those observed for T c 1 ( H ) and T c 2 ( H ) shown in Fig. 1(c) . Note that the isotropic behaviors in C ( H ) / T as well as T c 2 ( H ) (Fig. 3 ) contrast starkly with the anisotropic behavior of B * anomaly found in pure UBe 13  , suggesting that these phenomena may result from different origins. Figure 4(b) shows the H - T phase diagram of U 0.97 Th 0.03 Be 13 determined from the present C ( T , H ) measurements, where the two SC phases are denoted as A and B phases. The overall features of the phase diagram are essentially the same as those obtained previously [27,28,38] . In Fig. 4(a) , C ( ϕ ) / T data measured at T = 0.36 K in μ 0 H = 3 T (A phase) rotated in the ( 1 1 ¯ 0 ) are also shown; C ( ϕ ) / T shows a distinct angular oscillation with the maximum (minimum) along the  () direction, reflecting the anisotropy in H c 2 A . 10.1103/PhysRevB.96.100505.f4 4 FIG. 4. (a) Angular dependence of C ( ϕ ) / T , measured at T = 0.08 (B phase), 0.42 (A phase), and 0.60 K (normal state), in a magnetic field of 1 T. C ( ϕ ) / T , measured at T = 0.36 K in 3 T (A phase), near H c 2 is also plotted. (b) H - T phase diagram for the SC state of U 0.97 Th 0.03 Be 13 for [ 001 ] and [ 111 ] , where T and H denote data obtained from temperature and field scans, respectively. Here, T c 1 and T c 2 were determined by considering entropy conservation at transitions in the C ( T ) / T curves. The present experiment thus provides strong evidence that U 0.97 Th 0.03 Be 13 exhibits double SC transitions with two different SC order parameters. Let us discuss possible SC gap symmetries in this system. A key experimental fact is that the SC gap is fully open over the Fermi surface in both the B and C phases, as suggested by the present and previous  studies, respectively. This would imply either (i) the SC gap function itself to be nodeless, or (ii) the SC gap function to have nodes only in the directions in which the Fermi surface is missing. Regarding the latter, band calculations tell us that the Fermi surface is missing along the 〈 111 〉 direction, except for a tiny electron band [39,40] . Given the fact that spontaneous magnetism is observed from zero-field μ SR only below T c 2  , in addition, it would be natural to assume that the B phase is a time-reversal-symmetry-broken SC state. Under these constraints, two plausible scenarios can be proposed to explain the multiple SC phases in U 1 − x Th x Be 13 . One is to employ a degenerate order parameter belonging to higher dimensional representations of the O h symmetry (degenerate scenario). The other is to assume two order parameters belonging to different representations of the O h group, nearly degenerate to each other (accidental scenario)  . Degenerate scenario. The group-theoretic classification of the gap functions under the cubic symmetry O h has been given by several authors [21,41–43] . Among them, the two-dimensional odd-parity E u state is a promising candidate for the order parameter which naturally explains the existing experimental data of both pure and Th-doped UBe 13  . The possibility of the odd-parity state has also been suggested from the μ SR Knight shift experiments  . As for the odd-parity E u state, we have two basis functions, l 1 ( k ) = 3 ( x ̂ k x − y ̂ k y ) and l 2 ( k ) = 2 z ̂ k z − x ̂ k x − y ̂ k y , and their combinated state, d ( k ) = l 1 + i l 2 = x ̂ k x + ε y ̂ k y + ε 2 z ̂ k z with ε = e i 2 π / 3 ( ε 3 = 1 ) . The nonunitary state d ( k ) = l 1 + i l 2 has point nodes only along the 〈 111 〉 direction, therefore, the nodal quasiparticle excitations can be missing considering the calculated Fermi surface [39,40] . The condition of the occurrence of each two-dimensional SC state can be examined using the Ginzburg-Landau free-energy density, F = α ( T ) ( | l 1 | 2 + | l 2 | 2 ) + β 1 ( | l 1 | 2 + | l 2 | 2 ) 2 + β 2 ( l 1 l 2 * + l 1 * l 2 ) 2 with α ( T ) = α 0 ( T c − T ) , where β 1 > 0 is required for the stability. If β 2 > 0 , the nonunitary state with the broken time-reversal symmetry becomes stable in lower T as a ground state (the B phase). With increasing temperature the degeneracy of the order parameters is lifted at T c 2 , and one of them appears in the A phase ( T c 2 < T < T c 1 ). Logically, the other one appears in the C phase by changing dopant x . In pure UBe 13 (the C phase), a nodeless gap function, i.e., l 2 ( k ) = 2 z ̂ k z − x ̂ k x − y ̂ k y , which is a unitary state, is likely, explaining the absence of nodal quasiparticle excitations  without invoking the Fermi-surface topology. Accidental scenario. We briefly discuss the possibility of the accidental scenario, starting with the simplest and most symmetric A 1 u , namely, d A 1 u ( k ) = x ̂ k x + y ̂ k y + z ̂ k z with an isotropic full gap as the C phase for x = 0 . From x = 0.019 to x = 0.045 , we consider the combined state of one-dimensional representations, the above p wave A 1 u and f wave A 2 u with d A 2 u ( k ) = x ̂ k x ( k y 2 − k z 2 ) + y ̂ k y ( k z 2 − k x 2 ) + z ̂ k z ( k x 2 − k y 2 ) . The combined state of A 1 u and A 2 u , namely, nonunitary d ( k ) = d A 1 u + i d A 2 u is nodeless irrespective of the Fermi-surface topology, although d A 2 u alone has point nodes along the 〈 100 〉 and 〈 111 〉 directions. Thus nodeless A 1 u and the A 1 u + i A 2 u states can explain the absence of nodal quasiparticles in pure and Th-doped UBe 13 , respectively  . Similarly, the other order parameters belonging to different irreducible representations are possible, e.g., A 1 u + i E u ; the determination of the two order parameters is not easy due to the arbitrariness of their combinations. Finally, it is worth discussing the topology of the H - T phase diagram. In Fig. 4(b) , it may appear that the lines of T c 1 ( H ) and T c 2 ( H ) merge into a single second-order transition line in a high-field region. Such case is, however, not allowed in the thermodynamic argument of the multicritical point [46,47] . Instead, a crossing of the two second-order transition lines at a tetracritical point is possible  . This argument imposes the existence of another second-order transition below H c 2 for T ≲ 0.25 K, but no evidence for such a transition line has been obtained so far in our measurements as well as in previous thermal-expansion studies  . It might be natural to consider an anticrossing of the two second-order transition lines  . The crossing of T c 1 ( H ) and T c 2 ( H ) in U 1 − x Th x Be 13 will be examined further in future studies. To conclude, low-energy quasiparticle excitations and magnetic response of U 0.97 Th 0.03 Be 13 were studied by means of heat-capacity and dc magnetization measurements. The magnetization results evidence that the second transition at T c 2 is between two different SC states. Strikingly, the present C ( T , H , ϕ ) data strongly suggest that the SC gap is fully open over the Fermi surface in U 0.97 Th 0.03 Be 13 , excluding a number of gap functions possible in the cubic symmetry. Our new thermodynamic results entirely overturn a widely believed idea that nodal quasiparticle excitations occur in the odd-parity SC state with broken time-reversal symmetry. The absence (presence) of anisotropy for T c 2 ( T c 1 ) in fields clearly demonstrates that the gap symmetry in the B phase ( T < T c 2 ) is distinguished from that of the A phase ( T c 2 < T < T c 1 ). Moreover, the isotropic behavior of the T c 2 ( H ) in U 1 − x Th x Be 13 contrasts starkly to the anisotropic field response of the B * anomaly found in pure UBe 13 . These findings lead to a new channel to deepen its true nature of the ground state of U 1 − x Th x Be 13 , clarifying the origin of the unusual transition inside the SC phase. Acknowledgments. We greatly appreciate valuable discussions with M. Yokoyama, Y. Kono, Y. Haga, H. Amitsuka, and T. Yanagisawa. We also would like to thank K. Mochidzuki and K. Kindo for the use of the magnetic properties measurement system (Quantum Design, Inc.) and their support. Y.S. would like to acknowledge all the support from Institute for Materials Research, Tohoku University in growing monocrystalline U 1 − x Th x Be 13 samples using the joint research facility at Oarai. The present work was supported in part by a Grant-in-Aid for Scientific Research on Innovative Areas “J-Physics” (Grants No. 15H05883, No. 15H05884, and No. 15K05882) from MEXT, and KAKENHI (Grants No. 15H03682, No. 15H05745, No. 15K05158, No. 16H04006, No. 26400360, and No. 17K14328). Publisher Copyright: © 2017 American Physical Society.
PY - 2017/9/18
Y1 - 2017/9/18
N2 - 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 the  and  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.
AB - 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 the  and  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.
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U2 - 10.1103/PhysRevB.96.100505
DO - 10.1103/PhysRevB.96.100505
M3 - Article
AN - SCOPUS:85029932611
VL - 96
JO - Physical Review B
JF - Physical Review B
SN - 2469-9950
IS - 10
M1 - 100505