Superconductivity at 1 K in Y-Au-Si quasicrystal approximants

We report the structural and physical properties of two Y-Au-Si (YAS) compounds, Y 14 . 1 Au 69 . 2 Si 16 . 7 and Y 15 . 4 Au 68 . 6 Si 16 . 1 , which are 1 / 1 approximant crystals of a Tsai-type quasicrystal without intrinsic magnetic moments. The compounds differ by the presence of either a tetrahedron (Au,Si) 4 or a single Y atom at the center of their characteristic structural building unit consisting of concentric polyhedral shells. Both compounds exhibit bulk superconductivity, which seems to be of a conventional type-II BCS type. The compound with Y atoms at the cluster center has a slightly higher transition temperature with a sharper step in the speciﬁc heat than the compound with tetrahedral units. We discuss the occurrence of this superconducting state in the light of the speciﬁc structural and physical properties of these quasicrystal approximants.

Quasicrystals (QCs) are unique crystals that possess longrange aperiodic order with diffraction symmetries forbidden in conventional crystals [1]. The formation conditions of QCs and their stability with respect to their related periodic and compositionally similar approximant crystals (ACs) have been intensely investigated but are still not well understood. Likewise, a complete understanding of the effects of quasiperiodic long-range order on physical properties can be challenging [2]. In this context, ACs have played a pivotal role in the analysis of atomic structure of QCs by providing the common local structural information [3][4][5]. They are also crucial as reference systems in efforts to extract the potential unique physical properties emerging from quasiperiodicity. The recent discovery of bulk superconductivity in the Al-Zn-Mg QC [6] (together with its related 1/1 and 2/1 ACs) has attracted a great deal of attention as this was a convincing report on the emergence of long-range order in the physical properties of QCs. Surprisingly, to the best of our knowledge, there is only one other report of superconductivity for periodic AC: Yb-Au-Ge (YAG) AC [7]. In that report, the relationship between superconductivity and magnetism is discussed; our current Y-Au-Si (YAS) system has similar structures as YAG while having no intrinsic magnetic moments, which enables us to investigate superconductivity in the absence of magnetism. There also exist intriguing theoretical predictions for *  superconductivity on a quasiperiodic lattice [8,9], which have not been clarified in experiments yet.
The most prolific group of QCs are the icosahedral Tsaitype QCs, which are frequently accompanied by cubic 1/1 and 2/1 AC phases. Tsai-type QCs and their ACs can be described locally by the same atomic cluster building unit [3]. The conventional Tsai cluster, as shown in Fig. 1(a), is made up of four concentric polyhedral shells. The first shell is a dodecahedron, which is followed by an icosahedron. The third and fourth shell are an icosidodecahedron and a rhombic triacontahedron, respectively [3]. The clusters are arranged periodically in ACs and aperiodically in QCs. There is a tetrahedral unit at the cluster center [see Fig. 1(b)], which is orientationally disordered for the QCs and the cubic ACs. Recently, it has been shown that RE-Au-Si systems (RE = Gd, Tb, Ho) contain a second type of Tsai-type 1/1 approximant in which the orientationally disordered (Au/Si) 4 central tetrahedron is replaced by a single RE atom [10]; see Fig. 1(c). In the following, we refer to the former as IT phase (for inner-tetrahedron) and to the latter as CC phase (for cluster-center atom). The CC approximant phases, built from orientationally identical units that locally exhibit perfect icosahedral symmetry, provide additional opportunity to explore the ways in which aperiodicity may influence physical properties.
In this paper, we show that IT-and CC-type Y-Au-Si (YAS) 1/1 AC can be selectively synthesized, as has been demonstrated for the RE-Au-Si (RE = Gd, Tb, Ho) in Ref. [10]. We observe zero-resistance behavior at T ∼ 1 K for YAS(IT) and YAS(CC). We checked the bulk nature of the superconductivity from their specific heat. The effect of a magnetic field on the resistivity and specific heat was also studied. The result indicates type-II Bardeen-Cooper-Schrieffer (BCS) superconductivity for both phases. We discuss the effect of the presence/absence of the disordered tetrahedral unit on the emergence of superconductivity.  [3]. (c) Cluster center of the CC phase. The cluster centers in (b) and (c) are presented as electron density isosurfaces (isosurface level is set at 13 e/Å 3 ), revealing either an orientationally disordered M4 tetrahedral unit (M ≈ 55% Au, 45% Si) or a single Y atoms for the IT and CC phase, respectively. The diameter of the surrounding dodecahedral shell reduces from 7.3 to 6.8 Å. The orientational disorder of M4 is modeled as a twelve-vertex cuboctahedron (i.e.,averaging three orientations) using the space group Im3 position 24g and constraining the occupancy to 1/3 [5].
The samples were synthesized by a self-flux method as described in detail in Ref. [10]. The starting nominal compositions were Y 8 (Au 0.79 Si 0.21 ) 92 for YAS(IT) and Y 11 (Au 0.79 Si 0.21 ) 89 for YAS(CC). More details about synthesis conditions and pictures of crystal specimens are presented in the Supplemental Material [11], which include Ref. [12].
Sample characterization was performed using powderx-ray diffraction (PXRD), single-crystal-X-ray diffraction (SCXRD), differential scanning calorimetry, scanning electron microscopy (SEM) coupled with energy-dispersive x-ray spectroscopy (EDX). We refined the structure of the two phases from SCXRD data [see Figs. 1(a)-1(c), and crystallographic supporting information (cif files) [11]]. The determined mass density is 13.88 g/cm 3 for YAS(IT) and 13.70 g/cm 3 for YAS(CC). Figure 2 shows and compares their PXRD patterns. The shift of the peak positions manifests the significant change in lattice parameter, a =  (4) for YAS(IT) and YAS(CC), respectively. The compositional difference was also confirmed from a contrast difference in the backscattered SEM image (see the left inset in Fig. 2).
The electrical resistivity and specific heat measurements were performed using a Bluefors dilution refrigerator equipped with a superconducting magnet. The electrical resistivity was measured using the conventional four-probe method. The specific heat data was collected using a differential membrane-based nanocalorimeter [13] down to ∼100 mK. The size of samples for specific heat measurement was approximately 50 × 50 × 20 μm 3 for YAS(IT) and 50 × 50 × 10 μm 3 for YAS(CC). The sample weight could not be measured due to the small sample sizes. For the dc magnetization measurements, we used a Physical Property Measurement System with the VSM option and an MPMS XL superconducting quantum interference device magnetometer (both from Quantum Design Inc.). We used polycrystalline samples for physical property measurements in this study. Figure 3(a) shows the M-H curve for YAS(IT) and YAS(CC) measured at T = 2 K. We observe a diamagnetic behavior which should be of bulk origin. Note that there is a paramagnetic contribution of magnetic impurities probably contained in the starting materials. Figure 3(b) shows the temperature dependence of magnetization M with the external field H = 10 kOe. We observe a nearly constant diamagnetic behavior down to ∼80 K. The increase of M at low temperature should be due to a paramagnetic contribution of magnetic impurities detected also in the M-H measurement.  specific heat coefficient in the normal state (γ n ); see below for γ n . See also the Supplemental Material [11]. We find that C/T deviates from the model (γ n + C D /T ) below T ∼ 50 K; see the deviation curve defined as the non-Debye contribution C ND /T ≡ C/T − (γ n + C D /T ) in Figs. 5(a) and 5(b). This deviation should not be attributed to the disordered tetrahedra, since it appears in both systems; YAS(CC) does not have the tetrahedral unit. Our open question is whether C ND is associated with acoustic excitations (characterized by ω ∼ q 4 dispersion) mentioned in Ref. [15] and/or possible soft phonons speculated from the ellipsoidal distribution of atoms (see Fig. 1).
The bulk nature of superconductivity was checked by measuring the specific heat. Figures 5(c) and 5(d) show the temperature dependence of C el /T , where C el indicates the electronic contribution to the specific heat. To obtain C el , we 054510-3 TABLE I. Specific heat coefficients and superconducting parameters of YAS(IT) and YAS(CC). The value of T c is determined from the midpoint of the resistivity drop. The lower critical field H c1 (0) at absolute zero is estimated from the following equation, which is valid for large κ value [16,18]: H c1 = H c ln(κ )/ √ 2κ. The coherence length ξ (0) and penetration depth λ(0) at absolute zero are estimated using the following relations: H c2 (0) = 0 /2πξ (0) 2 [16] and κ = λ/ξ (the definition of κ) where 0 is the magnetic flux quanta. employed linear fitting to the C/T vs T 2 curve above T c (see the Supplemental Material [11]). From the fitting of the zero-field data, we estimate the electronic (γ n ) and phonon (β) specific heat coefficients in the normal state. The values of specific-heat coefficients are listed in Table I. To extract the electronic part (C el ), we subtracted phonon contribution (i.e., βT 3 ) from the measured specific heat (C): i.e., C el = C − βT 3 . Our YAS(CC) sample exhibits a sharper step in C than the YAS(IT) sample. We observe a residual Sommerfeld term (denoted as γ 0 = 0.28 mJ/K 2 mol) for YAS(IT), which gives an offset in the C el /T vs T plot as shown in Fig. 5(a); this could indicate the presence of disorder/inhomogeneity in the system. In order to compare these two systems, we define C * el ≡ C el − γ 0 T and γ * n ≡ γ n − γ 0 ; note that in this approach, γ 0 = 0 (thus C * el = C el and γ * n = γ n ) for YAS(CC). In Fig. 5(e), we plot C * el /γ * n T against T /T c (for H = 0) to compare with the weak-coupling BCS theory. We set T c = 0.87 and 1.1 K for YAS(IT) and YAS(CC), respectively. For YAS(IT), we used a T c value that is ∼8% smaller than one estimated from the midpoint of resistivity drop. The solid line indicates the theoretical curve expected from the weak-coupling BCS model. There seems to be only a slight deviation from the model, suggesting that the superconductivity of YAS(IT) and YAS(CC) is of a conventional (phonon-mediated) BCS type. The normalized specific heat step at T c is estimated to be C * el /γ * n T c = 1.11 and 1.36 for YAS(IT) and YAS(CC), respectively. The value of YAS(CC) is close to 1.43, as expected from the weak-coupling theory [16]. allows us to estimate the orbital critical field at zero temperature using the Werthamer-Helfand-Hohenberg formula (in the dirty limit) [17]: H orb c2 (0) = −0.693T c dH c2 /dT ≈ 5.6 and 6.1 kOe for YAS(IT) and YAS(CC), respectively. The H orb c2 value is close to H c2 (0) for both phases, and thus the orbital effect mainly contributes to H c2 rather than the spin paramagnetic effect [17]. The estimated values of superconducting parameters are listed in Table I. From the zero-field data in Figs. 5(c) and 5(d), we estimate the thermodynamic critical field H c from the condensation energy −H 2 c (T )/8π and the specific heat data (see Supplementary Materials [11] and Ref. [12] therein). The Ginzburg-Landau parameter κ at absolute zero is estimated from the relation H c2 = √ 2κH c [16]. Since κ 1/ √ 2, the superconductivity for both phases should be of type II. See the caption of Table I for the other parameters.
According to the weak-coupling BCS theory, T c can be expressed as T c = 1.14 θ where V is the effective electron-electron interaction energy and D(E F ) is the density of states at the Fermi energy [6]. Since θ D ∝ β −1/3 [18], there should be no significant difference for θ D between YAS(IT) and YAS(CC). Thus the slightly higher T c of YAS(CC) indicates that YAS(CC) may have larger V D(E F ) value than YAS(IT). Assuming that γ * n ∝ D(E F ), the magnitude of V D(E F ) should reflect γ * n . We compare the superconductivity of YAS samples with that of YAG analogues [7], which are the only previously reported superconducting ACs having both the IT-and CC-type structures. Note that these structures are named AGY(I) and AGY(II) in Ref. [7] and correspond to IT-type and CC-type, respectively. Interestingly, the cluster-center Yb atoms in the CC-type YAG seems to have a magnetic moment, while the icosahedral Yb atomic shell does not. It is discussed in Ref. [7] that the relationship between the magnetic property and the superconductivity could be important in the YAG system. The CC-type YAG exhibits a lower T c than the IT-type one. However, in the case of YAG systems it is unclear how the presence/absence of a disordered tetrahedral unit affects the nature of superconductivity in ACs due to the intrinsic magnetic Yb ions in the CC-type YAG. The present YAS system does not have an intrinsic magnetic moment and shows the opposite behavior: YAS(CC) has a slightly higher T c (with the sharper step in C) than YAS(IT). The difference in the emergence of superconductivity between YAS(IT) and YAS(CC) could be attributed to the existence/absence of the cluster-center disordered-tetrahedral unit. We speculate that the absence of the disordered-tetrahedral unit enhance the homogeneity and atomic order, resulting in the sharper step in C at T c . Since YAS(IT) and YAS(CC) have nearly the same value of T c , it is suggested that the superconducting mechanism is common between the IT-and CC-phase. This allows us to conjecture that the superconductivity of the CC-type YAG is destabilized by the Yb magnetism, rather than induced by a Yb-related mechanism. We also note that the resistivity (at T > T c ) is higher in YAS samples than in YAG, which could be related to a stronger electron-phonon coupling in the YAS case.
In conclusion, we have synthesized the AC compounds YAS(IT) and YAS(CC) that differ by their cluster center. Both YAS(IT) and YAS(CC) show bulk superconductivity, 054510-4 confirmed from specific-heat and transport measurements. Note that the observation of the Meissner effect is needed to complete the proof of the superconductivity. Both systems exhibit nearly the same T c , suggesting that the mechanisms behaind superconductivity are the same for IT and CC phases. However, YAS(CC) has a slightly higher T c with a sharper step in C than YAS(IT), which could be reflecting the absence of disordered tetrahedra breaking the internal icosahedral symmetry in the local Tsai-type cluster. Since both YAS(IT) and YAS(CC) do not have intrinsic magnetic moments, our results could reflect an intrinsic effect of the presence/absence of disordered tetrahedral units on the emergence of superconductivity in AC. Our results pave the road to further investigation of superconductivity in AC and QC.