Non-centrosymmetric superconductivity

Transcription

1 Non-centrosymmetric superconductivity Huiqiu Yuan ( 袁辉球 ) Department of Physics, Zhejiang University 拓扑,

2 OUTLINE Introduction Mixture of superconducting pairing states in weak coupling non-centrosymmetric SCs: Li 2 (Pd 1-x Pt x ) 3 B and Y 2 C 3 Discussion

3 Symmetry and Cooper pairing

4 Broken inversion symmetry Antisymmetric spin-orbit coupling H p t = α g σ c c ( g, preserve time reversal symmetry) k = g k k, s, s' k s,s' ks ks' Lift the twofold spin degeneracy. Spins in each sub-band rotate around the Fermi surface. Inversion-symmetric case With Rashba-type ASOC Saxena and Monthoux, Nature 427, 799 (2004)

5 Superconductivity without inversion symmetry (e.g., P. A. Frigeri, cond-mat/ ) Mixed states having both singlet and triplet components Intrinsically forms two bands with different admixtures: + ( k) = ψ + t g( k) and ( k) = ψ t g( k) (ψ: spin-singlet; t : spin-triplet) _(k) changes sign when ASOC is strong enough (i.e., ν=t/ψ 1) The spin d-vector must be parallel to g(k) for spin-triplet state. + _ ψ t ψ dominates: pure singlet t dominates: pure triplet ψ < t: nodes in one gap The relative magnitudes of ψ and t depend on the strength of the ASOC

6 Non-centrosymmetric superconductors Superconductivity at interfaces the interface breaks parity symmetry Dirty SC, e.g., distorted SC, doped SC Cd 2 Re 2 O 7, Mo 3 Al 2 C, La 5 B 2 C 6, and Mo 3 P: weak ASOC effect CePt 3 Si (P4mm): But magnetic and heavy Fermion SC Yogi et al., PRL (2004) NMR: Hebel-Slichter peak, powerlaw T 3 for T 0 Banalde et al., PRL (2005) Penetration depth λ ~T for T 0 CePt 3 Si: SC is complicated by its coexistence with AFM and its HF nature.

7 Non-centrosymmetric superconductors Superconductivity at interfaces the interface breaks parity symmetry Dirty SC, e.g., distorted SC, doped SC Cd 2 Re 2 O 7, Mo 3 Al 2 C, La 5 B 2 C 6, and Mo 3 P: weak ASOC effect CePt 3 Si (P4mm): But magnetic and heavy Fermion SC UIr and CeRhSi 3, CeIrSi 3 : SC under pressure UIr CeRhSi 3 SC Akazawa et al., JPCM (2004) Kimura et al., PRL (2005)

8 Non-centrosymmetric superconductors Superconductivity at interfaces the interface breaks parity symmetry Dirty SC, e.g., distorted SC, doped SC Cd 2 Re 2 O 7, Mo 3 Al 2 C, La 5 B 2 C 6, and Mo 3 P: weak ASOC effect CePt 3 Si (P4mm): But magnetic and heavy Fermion SC UIr and CeRhSi 3, CeIrSi 3 : SC under pressure N. Kimura et al, PRL (2007) Y. Okuda et al, JPSJ (2007) Extremely large H c2 (0). No paramagnetic limit: attributed to the spin triplet pairing?

9 Non-centrosymmetric superconductors Superconductivity at interfaces the interface breaks parity symmetry Dirty SC, e.g., distorted SC, doped SC Cd 2 Re 2 O 7, Mo 3 Al 2 C, La 5 B 2 C 6, and Mo 3 P: weak ASOC effect CePt 3 Si (P4mm): But magnetic and heavy Fermion SC UIr and CeRhSi 3, CeIrSi 3 : SC under pressure Li 2 Pd 3 B and Li 2 Pt 3 B (P4 3 32): T c = 7.5K and 2.5K. No magnetism, different SO coupling. Y 2 C 3 (cubic structure, I43d): T c =16K. No strong el-el correlation and magnetism. Model systems to study ASOC in SC without inversion symmetry

10 Li 2 Pd 3 B and Li 2 Pt 3 B: a model system to study parity broken superconductivity Li 2 Pd 3 B: T c ~ 7K; Li 2 Pt 3 B: T c ~ 2.5K Cubic structure (space group P4 3 32, No. 212) Lack inversion symmetry. No evidence of magnetic order or strong el.-el. Interaction. ASOC strength increases threefold from Pd- to Pt- compound [α Pt /α Pd ~ (Z Pt /Z Pd ) 2 =2.9]. Crystal structure of Li 2 Pd 3 B and Li 2 Pt 3 B: SC is solely tuned by the ASOC between the two compounds.

11 Li 2 Pd 3 B and Li 2 Pt 3 B: distinct SC properties Cubic P Li 2 Pt 3 B λ(t) shows T-linear behavior λ (nm) FC ZFC 5 Oe 0 2 T (K) 3-5 Li 2 Pt 3 B (#3) M( 10-5 emu) Li 2 Pd 3 B (#2) λ (nm) Li 2 Pd 3 B λ(t) shows exponential behavior T/T c Spin-Orbit coupling is in ratio (Z Pt /Z Pd ) 2 =3 larger ASOC in Li 2 Pt 3 B H.Q. Yuan, et al., PRL (2006) 97,

12 Li 2 Pd 3 B: BCS-like SC with anisotropic gap A 4 λ(t)/λ _ T c =7 K for sample #1 and 6.7 K for sample #2. Experimental data agree well with the ASOC theoretical model. B ρ s Order parameter [T c ] 2 ψ t 0 0 T/T c 1 Li 2 Pd 3 B theory fit sample #1 sample # T/T c The order parameter component ψ (spin singlet) dominates over t (spin triplet). + (k) and - (k) are nonzero over the entire Fermi surface, but anisotropic. H.Q. Yuan, et al., PRL (2006) 97,

13 Li 2 Pt 3 B: triplet SC with s-wave orbital symmetry A 4 λ(t)/λ _ T c =2.43 K for sample #3 and 2.3K for sample #5. The spin-triplet component is the dominant order parameter. ρ s B Order parameter [T c ] t ψ Li 2 Pt 3 B theory fit sample #3 sample # T/T c T/T c (k) changes sign from the large lobes (+) to the small lobes (-) in the 3D polar plot. Existence of line nodes in superconducting energy gap. Only gauge invariance symmetry is broken below T c S-wave character. H.Q. Yuan, et al., PRL (2006) 97,

14 Triplet State in Li 2 Pt 3 B: evidence from NMR M. Nishiyama et al, PRL (2007) 98, Knight shift remains unchanged below T c in Li 2 Pt 3 B Evidence of line nodes: 1/T 1 ~ T 3 Consistent with our conclusion.

15 Y 2 C 3 : Large upper critical field f (MHz) Κ 13Κ 11Κ 9Κ 7Κ 5Κ Κ µ 0 H (T) f (MHz) Κ 5Κ 3Κ Κ 0.5Κ 2Κ 0.5Κ µ 0 H (T) µ 0 H c2 (T) #2-1 #2-2 WHH GL theory Y 2 C T(K) Unusual T-dependence of H c2 (T c ), showing an upturn at low-t; Larger H c2 (0) ~ 29T close to the Pauli paramagnetic limit H P (0). H. Q. Yuan, et al. JPCS (2011) 72,

16 Y 2 C 3 : evidence of line nodes f(10 4 Hz) f(10 4 Hz) f(10 4 Hz) (a) f(hz) (b) f(hz) (c) f(hz) Y 2 C 3 (#2-1) T(K) Y 2 C 3 (#2-2) T(K) Y 2 C 3 (#4-2) T(K) T(K) Linear T-dependence at the lowest-t: evidence of line nodes. ρ s ρ s (a) T/T c (b) H = 9.85T T c = 12.2K T(K) TDO (#4-2) µsr Two-gap model T 3 T c T/T c T 1 T=const. Weakly linear behavior at the lowest-t, deviating from two-gap model; Line nodes: admixture of singlet-triplet pairing states due to broken inversion symmetry? Spin triplet state dominant? E-3 1/T 1 (sec -1 ) J. Chen, et al. PRB (2011) 83,

17 Analogy between QSH and NCS SC? NCS SC with Rashba-type SOC 2D Topological insulator + +

18 Topological classification of non-centrosymmetric superconductor Pure 2D P-wave in C 4v : A 2u i ( kx y x y ik ) > + i( k + ik ) > vacuum NCS SC s-wave + A 2u ( k yˆ k xˆ) x y + > 0 : t < ψ, no edge states, Z2 trivial ± ( k) = ψ ± t gk ( ) : + < 0 : t > ψ, helical edge states, Z2 non-trivial Majorana modes in vortex cores, Time-reversal symmetry, non-abelian statistics C.K. Lu, S. Yip, PRB (2010) 82,

19 Surface states in NCS superconductor s-wave + A 2u ( k yˆ k xˆ ) x y = 2 t ψ π 6 π 6 ε / ψ ε / ψ Momentum- and spin-resolved surface densities of states Existence of Andreev Bound States (ABS) : the helical edge states Time-reversal symmetry: Spin current J y z ρz, ± ( ky, ε) = ρz, ( ky, ε) C.K. Lu, S. Yip, PRB (2010) 82,

20 Surface states in NCS superconductor s-wave + A 2u ( k yˆ k xˆ ) x y = t 0.5 ψ π 6 No edge states, only bulk states Spin current J y z I z y dφ dε z R = N FvF dx (sinφ) ImTr[ σ g ( kˆ, ε, x)]tanh 2 2π 2π 2 Total surface spin current density vs. order parameter ratio C.K. Lu, S. Yip, PRB (2010) 82,

21 Experimental challenges in NCS SCs No convincing experimental evidence of topological surface states in NCS SCs until now! Many of the current NCS SCs show p < s : not good for the formation of topological states. Those NCS SCs showing p > s : air sensitive; difficult for grow single crystals; complicated by magnetic fluctuations. How to detect the surface states at such a low T? Point contact tunneling or STM? Further efforts are definitely required for investigating the novel features of NCS SCs, both the bulk and the surface states!

22 Summary and outlook SC lacking inversion symmetry exhibit qualitatively distinct properties from those with an inversion center. Broken inversion symmetry admits antisymmetric spin-orbit coupling (ASOC), admixing spin-singlet and spin-triplet pairing. The triplet contribution is weak in Li 2 Pd 3 B, a BCS-like superconductor with an anisotropic gap. With increased ASOC the spin-triplet component dominates in Li 2 Pt 3 B, producing line nodes in the energy gap. Evidence of nodal gap structure in weak coupling Y 2 C 3. Triplet superconductivity in an s-wave SC due to broken parity symmetry. Topological surface states in NCS superconductors? NCS SC: showing rich and fantastic properties!

23 Collaborators Measurements and analyses Jian Chen, Lin Jiao, Jinglei Zhang (ZJU) J. Singleton (LANL) M. B. Salamon (UTD) Sample preparations P. Badica (Tohoku U.) S. Akutagawa, J. Akimitsu (Aoyama Gakuin Uni.) Theory D. F. Agterberg (U. Wisconsin-Milwaukee) N. Hayashi (JAEA, Japan) M. Sigrist (ETHZ)

24 THANK YOU!