Antisymmetric Spin-orbit Coupling Research Articles

Anisotropic superconductivity in noncentrosymmetric BiPd

We report measurements of London penetration depth $\lambda(T)$ for the noncentrosymmetric superconductor BiPd by using a tunnel diode oscillator. Pronounced anisotropic behavior is observed in the low-temperature penetration depth; the in-plane penetration depth $\lambda_{ac}(T)$ follows an exponential decrease, but the interplane penetration depth $\lambda_b(T)$ shows power-law-type behavior. The superfluid density $\rho_s(T)$, converted from the penetration depth $\lambda(T)$, is best fitted by an anisotropic two-band BCS model. We argue that such a complex order parameter is attributed to the admixture of spin-singlet and spin-triplet pairing states as a result of antisymmetric spin-orbit coupling in BiPd.

Magneto-Electric Effect in Three-Dimensional Coupled Zigzag Chains

Stimulated by recent studies of quantum phases with broken local inversion symmetry, we study the magnetoelectric effect in locally noncentrosymmetric metals. We consider three-dimensional (3D) coupled zigzag chains and demonstrate that the antiferromagnetic moment is induced by the electric current through a staggered antisymmetric spin-orbit coupling. This current-induced magnetism is much larger than that in globally noncentrosymmetric metals. We provide an intuitive understanding of the current-induced antiferromagnetic moment by showing the inverse magnetoelectric effect, that is, the ferroic p-wave charge nematic order accompanied by the asymmetric band structure in the antiferromagnetic state. We also examine conduction electrons coupled to localized spins via Kondo exchange coupling and demonstrate a significant enhancement of the magnetoelectric effect. A possible experimental observation of the magnetoelectric effect in metals is discussed, with focus on LnM_2Al_10 compounds, such as NdRu_Al_10 and TbRu_2Al_10.

Spin Susceptibility in Non-Centrosymmetric Superconductors with Topological Transition of Fermi Surfaces

The non-centrosymmetric superconductors Li2Pd3B and Li2Pt3B show different superconducting properties despite having the same crystal symmetry. Motivated by experimental results, we investigate the spin susceptibility of non-centrosymmetric superconductors accompanied by the topological transition of Fermi surfaces due to antisymmetric spin-orbit coupling, which is indicated by the first-principles band structure calculation for Li2Pt3B. We study three types of topological transition, namely, (A) the disappearance of the Fermi surface, (B) crossing the Dirac point, and (C) crossing the saddle point van-Hove singularity. The spin susceptibility in the superconducting state is increased by the topological transitions (A) and (C), while it is decreased by (B). We discuss the unusual magnetic properties observed in Li2Pt3B on the basis of these results.

Multi-Orbital Superconductivity in SrTiO3/LaAlO3Interface and SrTiO3Surface

We investigate the superconductivity in two-dimensional electron systems formed in SrTiO3 nanostructures. Our the- oretical analysis is based on the three-orbital model, which takes into account t2g orbitals of Ti ions. Because of the interfacial breaking of mirror symmetry, a Rashba-type antisymmetric spin-orbit coupling arises from the cooperation of intersite and interorbital hybridyzation and atomic LS coupling. This model shows a characteristic spin texture and carrier density dependence of Rashba spin-orbit coupling through the orbital degree of freedom. Superconductivity is mainly caused by heavy quasiparticles consisting of dyz and dzx orbitals at high carrier densities. We find that the Rashba spin-orbit coupling stabilizes a quasi-one-dimensional superconducting phase caused by one of the dyz or dzx orbitals at high magnetic fields along interfaces. This quasi-one-dimensional superconducting phase is protected against para- magnetic depairing effects by the Rashba spin-orbit coupling and realizes a large upper critical field Hc2 beyond the Pauli-Clogston-Chandrasekhar limit. This finding is consistent with an extraordinarily large upper critical field observed in SrTiO3 /LaAlO3 interfaces and its carrier density dependence. The possible coexistence of superconductivity and fer- romagnetism in SrTiO3 /LaAlO3 interfaces may also be attributed to this quasi-one-dimensional superconducting phase.

Superconductivity without Local Inversion Symmetry; Multi-layer Systems

While multi-layer systems can possess global inversion centers, they can have regions with locally broken inversion symmetry. This can modify the superconducting properties of such a system. Here we analyze two dimensional multi-layer systems yielding spatially modulated antisymmetric spin-orbit coupling (ASOC) and discuss superconductivity with mixed parity order parameters. In particular, the influence of ASOC on the spin susceptibility is investigated at zero temperature. For weak inter-layer coupling we find an enhanced spin susceptibility induced by ASOC, which hints the potential importance of this aspect for superconducting phase in specially structured superlattices.

Fermi Surface Properties and Antisymmetric Spin–Orbit Coupling in Noncentrosymmetric CeCoSi3

We report de Haas–van Alphen (dHvA) effect measurement of the intermediate-valence compound CeCoSi 3 whose crystal structure lacks space-inversion symmetry. Some dHvA frequencies of CeCoSi 3 qualitatively correspond to those of CeRhSi 3 which is a heavy-fermion antiferromagnet exhibiting pressure-induced superconductivity. We observed multiply splitting dHvA frequencies and attributed them to the magnetic breakdown between two separated Fermi surfaces due to the antisymmetric spin–orbit coupling (ASOC). Strikingly, the cyclotron effective masses of the separated Fermi surfaces are largely different, indicating that the mass enhancement depends on the spin direction. The evaluated ASOC energy of CeCoSi 3 is less than that of LaCoGe 3 , which is probably characteristic of a heavy-fermion band with an itinerant f -electron.

Characteristic feature of dynamical susceptibility in noncentrosymmetric system

The static spin susceptibility ναβ(q) of spin components Sα and Sβ is examined in the non-centrosymmetric system with the antisymmetric spin-orbit coupling (so-called Rashba coupling), where Sα is α-component of spin. Unlike in centrosymmetric case, off-diagonal spin susceptibilities do not vanish due to the Rashba coupling. The anomalous spin susceptibilities show significant momentum dependences like νxx (q) — νyy (q) ∼ qx2 – qy2 and νxy (q)+ νyx (q) ∼ qxqy Increasing the on-site Coulomb interaction, not only usual spin susceptibility but also anomalous spin susceptibilies are enhanced, especially, around the magnetic instability. As the direct prove to observe the anomalous spin susceptibility, a polarized neutron scattering experiment is proposed.

Possible two-gap behavior in noncentrosymmetric superconductorMg10Ir19B16: A penetration depth study

We report measurements of the magnetic penetration depth $\ensuremath{\lambda}(T)$ of ${\text{Mg}}_{10}{\text{Ir}}_{19}{\text{B}}_{16}$ down to 50 mK $(l0.01{T}_{c})$. We observe a sample-independent small second drop around 0.8 K and an overall low-temperature response that indicate a possible two-gap superconductivity in ${\text{Mg}}_{10}{\text{Ir}}_{19}{\text{B}}_{16}$. A two-isotropic-gap model can account for the present penetration depth data. However, the lack of inversion symmetry in this compound with the heavy transition element Ir may lead to a large antisymmetric spin-orbit coupling that splits the spin bands and mixes spin-singlet and spin-triplet states. A model based on the two spin-split bands, with nodeless anisotropic gaps and dominant spin-triplet components, can also explain the present results. The data rule out an isotropic spin-singlet gap structure, as suggested by specific-heat measurements.

Conventional s-Wave Superconductivity in Noncentrosymmetric Ir2Ga9: 71Ga-NQR Evidence

Superconductivity without spatial inversion symmetry has begun to attract much attention since the discovery of the superconductor CePt3Si. 1) It is presumed that the absence of spatial inversion symmetry causes an admixture between even and odd parities of superconducting pairing due to antisymmetric spin–orbit coupling (ASOC). However, there has been no clear evidence of the admixture thus far, and hence the spatial noncentrosymmetric effect on superconductivity remains experimentally controversial. Recently, ASOC has also been discussed in transition-metal superconductors. In this system, we can consider ASOC without strongly correlated electron systems, which would be appropriate for tracing the effect of ASOC. Interestingly, in Li2Pt3B, it was reported that unconventional superconductivity with a line node and a spin-triplet pairing state emerge, which are ascribed to ASOC. These reports suggest that ASOC can induce a novel superconducting state even though there is no strong electron correlation. The intermetallic binary Ir2Ga9 does not possess spatial inversion symmetry and becomes superconducting below Tc 1⁄4 2:2K. Specific heat and resistivity measurements showed that the compound is a weak-coupling BCS superconductor with an isotropic gap, and located near the boundary between type-I and type-II superconductivities with an upper critical field Hc2 150Oe. In this letter, we report on the characteristics of superconductivity in noncentrosymmetric Ir2Ga9 probed by Ga-nuclear-quadrupole-resonance (NQR) measurement at a zero field (H 1⁄4 0). The spatial noncentrosymmetric effect on the superconducting state is discussed. A single crystal of Ir2Ga9 was grown by the Ga flux method. Powder X-ray diffraction indicated that the compound forms in the primitive monoclinic Rh2Ga9 type structure. The sample of Ir2Ga9 was crushed into coarse powder for NQR measurement to allow the penetration of the rf field. The NQR measurement was performed by the conventional spin-echo method in the temperature (T) range of 1–280K. T1 was measured at f 26:45MHz, which was the 1 Qð 1=2 $ 3=2Þ transition of Ga (I 1⁄4 3=2), as shown in Fig. 1. The NQR spectrum ensures the quality of the sample, because the full width at half maximum (FWHM) is as small as 54 kHz, as shown in Fig. 1. The NQR signal of the isotope Ga (I 1⁄4 3=2) was confirmed at f 42:08MHz, which was consistent with the ratio 69Q=Q 1:59 (Q is the quadrupole moment) because NQR frequency is proportional to Q. Figure 2 shows 1=T1T as a function of T in the temperature range of 1 T 280K along with the ac-susceptibility measured using an in-situ NQR coil. In the normal state above Tc, a T1T 1⁄4 const. relation is valid up to T 50K, which is usually seen in conventional metals. Above T 50K, although 1=T1T gradually deviates from the constant, it is probably ascribed to the local structural distortion of the crystal because NQR frequency also shifts in the same T range, as seen in the inset of Fig. 2. This structural change may bring about an increase in the density of states at the Fermi level, leading to an increase of the 1=T1T constant value in the high T region. It is important to investigate the precise crystal structure of Ir2Ga9 at a low T where the superconductivity emerges. In the superconducting state, NQR intensity is largely suppressed below Tc 1⁄4 2:2K, as shown in the inset of Fig. 1. This is consistent with the previous reports that 26.2 26.3 26.4 26.5 26.6 26.7 26.8 N Q R in te ns ity ( ar b. u ni t)

Superconductivity and Magnetism in Non-centrosymmetric System: Application to CePt3Si

Superconductivity and magnetism in the non-centrosymmetric heavy fermion compound CePt 3 Si and related materials are theoretically investigated. On the basis of the random phase approximation (RPA) analysis of the extended Hubbard model, we describe the helical spin fluctuation induced by the Rashba-type anti-symmetric spin–orbit coupling and identify two stable superconducting phases with either the dominant p -wave ( s + P -wave) symmetry or the d -wave ( p + D + f -wave) symmetry. The effect of the coexistent antiferromagnetic order is investigated in both states. The superconducting order parameter, quasiparticle density of state, NMR 1/ T 1 T , specific heat, anisotropy of H c2 , and possible multiple phase transitions are discussed in detail. A comparison with experimental results indicates that the s + P -wave superconducting state is likely realized in CePt 3 Si.

Electronic Structure of Noncentrosymmetric Superconductor Li2(PdxPt1-x)3B Studied by Photoemission Spectroscopy

We have performed x-ray photoemission spectroscopy on the system of noncentrosymmetric superconductor, Li 2 (Pd x Pt 1- x ) 3 B. For Li 2 Pt 3 B, we found two major peaks with two other weak components, and the band calculations were in agreement with the observation. The assignment of valence band features using the calculated partial density of states determined that Pt 5 d and B 2 p contribute to the density of states at the Fermi level. The effect of antisymmetric spin–orbit coupling on the band structure might have been probed, and the analysis on the effect of Pt incorporation into the system indicates the smooth evolution of electronic structures. We presented the measurements of core levels (Pd 3 d , Pt 4 f , and B 1 s ) and discussed the chemical bonding states and electronic structures from them.

Using Josephson junctions to determine the pairing state of superconductors without crystal inversion symmetry

Theoretical studies of a planar tunnel junction between two superconductors with antisymmetric spin-orbit coupling are presented. The half-space Green's function for such a superconductor is determined. This is then used to derive expressions for the dissipative current and the Josephson current of the junction. Numerical results are presented in the case of the Rashba spin-orbit coupling, relevant to the much studied compound $\mathrm{Ce}{\mathrm{Pt}}_{3}\mathrm{Si}$. Current-voltage diagrams, differential conductance and the critical Josephson current are presented for different crystallographic orientations and different weights of singlet and triplet components of the pairing state. The main conclusion is that Josephson junctions with different crystallographic orientations may provide a direct connection between unconventional pairing in superconductors of this kind and the absence of inversion symmetry in the crystal.

Heavy Fermion Superconductivity and Antiferromagnetic Ordering in CePt3Si without Inversion Symmetry

Heavy fermion superconductivity in absence of inversion symmetry of the crystal structure is basically controlled by a Rashba-like antisymmetric spin orbit coupling which splits the Fermi surface and removes the spin degeneracy of electrons. The Fermi surface splitting originates a mixing of spin-singlet and spin-triplet states in the superconducting condensate. Such constraints are responsible for various uncommon features of the superconducting ground state and are discussed here in view of CePt 3 Si, the first heavy fermion superconductor missing a centre of symmetry. We recall and discuss normal and superconducting properties of CePt 3 Si and relate them to recently developed phenomenological theories.

Fulde–Ferrell–Larkin–Ovchinnikov state due to antisymmetric spin–orbit coupling in the noncentrosymmetric superconductor CePt3Si

When the inversion symmetry is broken, the spin–orbit coupling reduces the superconducting transition temperature of some types of spin triplet superconductivity, which is similar to the case that magnetic field weakens the spin singlet superconductivity due to Zeeman splitting. It is well known that Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state of spin singlet superconductivity is realized near the Pauli limit (or Chandrasekhar–Clogston limit). In the FFLO state the amplitude of the order parameter is not uniform in space. In this paper, we study the FFLO state of the spin triplet superconductivity due to the spin–orbit coupling with no external magnetic field. Although the FFLO state is not realized in the simple model with spherical Fermi surface, it will be stabilized if the nesting condition of the Fermi surface is favorable for the FFLO state. We discuss the possibility of FFLO state in CePt3Si in the absence of external magnetic field.

Phenomenological theory of the s-wave state in superconductors without an inversion center

In materials without an inversion center of symmetry the spin degeneracy of the conducting band is lifted by an antisymmetric spin orbit coupling (ASOC). Under such circumstances, spin and parity cannot be separately used to classify the Cooper pairing states. Consequently, the superconducting order parameter is generally a mixture of spin singlet and triplet pairing states. In this paper we investigate the structure of the order parameter and its response to disorder for the most symmetric pairing state (A1). Using the example of the heavy Fermion superconductor CePt3Si, we determine characteristic properties of the superconducting instability. Depending on the type of the pairing interaction, the gap function is characterized by the presence of line nodes. We show that this line nodes move in general upon temperature. Such nodes would be essential to explain recent low-temperature data of thermodynamic quantities such as the NMR-T1 -1, London penetration depth, and heat conductance. Moreover, we study the effect of (non-magnetic) impurity on the superconducting state.

Nonuniform Spin Triplet Superconductivity due to Antisymmetric Spin–Orbit-Coupling in Noncentrosymmetric Superconductor CePt3Si

We show that the nonuniform state [Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state] of the spin triplet superconductivity in noncentrosymmetric systems is stabilized by antisymmetric spin–orbit coupling even if the magnetic field is absent. The transition temperature of the spin triplet superconductivity is reduced by the antisymmetric spin–orbit coupling in general. This pair breaking effect is shown to be similar to the Pauli pair breaking effect due to magnetic field for the spin singlet superconductivity, in which FFLO state is stabilized near the Pauli limit (or Chandrasekhar–Clogston limit) of external magnetic field. Since there are gapless excitations in nonuniform superconducting state, some physical quantities such as specific heat and penetration depth should obey different temperature-dependences from those in the uniform superconductivity. We discuss the possibility of the realization of nonuniform state in CePt 3 Si.

S-Wave Spin-Triplet Order in Superconductors without Inversion Symmetry:Li2Pd3BandLi2Pt3B

We investigate the order parameter of noncentrosymmetric superconductors Li2Pd3B and Li2Pt3B via the behavior of the penetration depth lambda(T). The low-temperature penetration depth shows BCS-like behavior in Li2Pd3B, while in Li2Pt3B it follows a linear temperature dependence. We propose that broken inversion symmetry and the accompanying antisymmetric spin-orbit coupling, which admix spin-singlet and spin-triplet pairing, are responsible for this behavior. The triplet contribution is weak in Li2Pd3B, leading to a wholly open but anisotropic gap. The significantly larger spin-orbit coupling in Li2Pt3B allows the spin-triplet component to be larger in Li2Pt3B, producing line nodes in the energy gap as evidenced by the linear temperature dependence of lambda(T). The experimental data are in quantitative agreement with theory.

Characterization of the ‘s-wave’ state in parity-violating superconductors

The lack of an inversion center in a crystal lattice is reflected in the presence of an antisymmetric spin–orbit coupling which leads to a splitting of the bands into two non-degenerate bands with different spin structure. If the corresponding energy scale exceeds the superconducting gap, a new structure of the multi-band pairing states appears, characterized by the generating point group. We study here the superconducting state belonging to the trivial representation A 1, in the context of the heavy Fermion superconductor CePt 3Si [E. Bauer, et al., Phys. Rev. Lett. 92 (2004) 027003], which turns out to be best described by a mixture of an ‘s-wave’ and a ‘p-wave’ pairs. We show that the topology of the nodes in the superconducting quasi-particles spectrum is in this case dictated by the pairing potential and by the distribution of the density of state in the non-degenerate bands. These nodes are not symmetry protected and also depend on the purity of the material as we will demonstrate.

Spin susceptibility in superconductors without inversion symmetry

In materials without spatial inversion symmetry, the spin degeneracy of the conduction electrons can be lifted by an antisymmetric spin–orbit coupling. We discuss the influence of this spin–orbit coupling on the spin susceptibility of such superconductors, with a particular emphasis on the recently discovered heavy Fermion superconductor CePt3Si. We find that, for this compound (with tetragonal crystal symmetry) irrespective of the pairing symmetry, the stable superconducting phases would give a very weak change of the spin susceptibility for fields along the c-axis and an intermediate reduction for fields in the basal plane. We also comment on the consequences for the paramagnetic limiting in this material.