Session F52: Topological Superconductivity: Symmetry Breaking and Spin-Orbit Coupling

Live

The emergence of Majorana fermions is a salient feature of topological superconductors. Whereas the emergent Majorana fermions are often discussed as possible qubits of topological quantum computers, they also provide important information to identify paring symmetry of underlying unconventional superconductors. We develop here a theory of electric and magnetic responses of Majorana fermions in superconductors and clarify the relation between the electromagnetic responses and Cooper pair symmetry [1,2]. We point out that Majorana fermions belong to short representations of particle-hole or chiral symmetries, which is a group theoretical manifestation of their self-antiparticle nature. We reveal magnetic octupole responses of Majorana fermions that characterize spin 3/2 superconductors or non-symmorphic superconductors. We also apply our theory to spin 3/2 half-Heusler superconductors and other unconventional superconductors.
[1] S. Kobayashi, A. Yamakage, Y. Tanaka, M. Sato, Phys. Rev. Lett. 123, 097002 (2019).
[2] S. Kobayashi, Y. Yamazaki, A. Yamakage, M. Sato, in preparation.   

Live

Magnetic flux quantization is one of the defining characteristics of a superconductor. We report the observation of half-integer magnetic flux quantization in mesoscopic rings of superconducting β-Bi₂Pd thin films [1]. The half-quantum fluxoid (HQF) manifests itself as a phase shift in the quantum oscillations of the superconducting critical temperature. The superconducting ring energetically prefers half flux quanta with fractional quantum numbers of 1/2, 3/2, 5/2, etc., instead of usual integer numbers of 0, 1, 2, etc. This result is consistent with β-Bi₂Pd having a spin-triplet pairing symmetry, which may be expected from β-Bi₂Pd as a topological supercondcutor [2,3]. Our findings usher in a new paradigm for identifying spin-triplet pairing, and new venues for studying topological superconductivity.


[1] Y. Li et al., Science 366, 238-241 (2019).
[2] M. Sakano, et al., Nature Communications 6, 8595 (2015).
[3] K. Iwaya, et al., Nature Communications 8, 976 (2017).   

Live

Recently, nematic superconductivity, exhibiting spontaneous rotational symmetry breaking in bulk superconducting quantities, has been discovered in A_xBi₂Se₃ (A = Cu, Sr, Nb) [1]. In an analogy to the nematic liquid crystals accompanying high controllability of the order-parameter directions, similar controllability can be expected for nematic superconductivity. Indeed, we succeeded in controlling nematic superconductivity in Sr_xBi₂Se₃ via external uniaxial strain [2]. By applying uniaxial strain in situ along the a axis, we reversibly controlled the superconducting nematic domain structure, from the multi-domain state under zero strain into a nearly single-domain state under 1% uniaxial compression. This is the first achievement of domain engineering using nematic superconductors.
[1] For a recent review, see S. Yonezawa, Condens. Matter 4, 2 (2019).
[2] I. Kostylev, S. Yonezawa et al., Nature Commun. 11, 4152 (2020).   

Live

Experimentally realizable chiral topological superconductors are actively pursued since they are expected to host Majorana quasiparticles. Here we develop an effective tight-binding description of Pb₃Bi/Ge(111), a candidate system for realizing chiral p-wave topological superconductor [Nat. Phys. 15, 796 (2019)]. The model is demonstrated to be able to capture the two central characters of the electronic bands found in first-principle calculations, namely, the giant Rashba spin-orbit coupling and type-II van Hove singularity. By introducing local superconducting pairing and perpendicular Zeeman field, we show the system can transform into a chiral topological superconducting phase with Chern number C=2. The nontrivial topology is further confirmed by edge state calculations and manifested as two pairs of chiral Majorana edge modes propagating along the same direction. We also discuss the experimental conditions for observing such a topological state by taking account of realistic material parameters, including the Landé g-factor, upper critical magnetic field, and real-space length scale of the Majorana edge modes. This study provides a guide for realizing and detecting Majorana quasiparticles in the Pb₃Bi/Ge(111) system.   

Live

Spin-triplet superconductors, rare and challenging to identify, play central roles in Majorana fermions and quantum computing. It has been proposed that superconductors with broken inversion symmetry may host spin-triplet Cooper pairs. Unique features of half-quantum fluxoid in flux quantization is one of the few methods that can identify spin-triplet superconductors [1]. We fabricated thin films of non-centrosymmetric α-BiPd by sputtering and patterned them into sub-µm-sized rings. Measurements of the Little-Parks oscillations in magnetoresistance show half-quantum fluxoid (n + ½)Φ_o, a key signature of spin-triplet pairing, where flux quantum Φ_o = hc/2e and n is an integer. Our extensive measurements support an admixture of pairing states of spin-singlet and spin-triplet Cooper pairs in α-BiPd [2].

[1] Li, Xu, Lee, Chu, and Chien, Science 366, 238 (2019)
[2] Xu, Li, Chien, Phys. Rev. Lett. 124, 167001 (2020)   

Live

Nodal line semimetals are novel quantum states of matter, hosting topological nodal rings in the bulk band structures. Among the nodal line semimetals, PbTaSe₂ family without the inversion symmetry in the crystal structure has been reported to be superconducting, and can be a promising platform for the study of topological superconductivity [1,2]. Here we present the superconducting properties of single crystals of PbTaSe₂ family. Our resistivity measurements under high magnetic fields reveal the unusual temperature dependence and magnitude of the upper critical field in this family, strikingly distinct from those for conventional BCS-type superconductors. Compering theoretical models, we will discuss the possible superconducting pairing symmetry realized in this family.


[1] M.N. Ali et al., Phys. Rev. B 89 020505 (2014).
[2] G. Bian et al., Nat. Commun. 7, 10556 (2016).   

Live

We theoretically study potential superconductivity in doped IV-VI semiconductors in the presence of the interaction restricted to the next nearest neighbors. We show that point-group-symmetry-breaking Cooper pairing, for example in the E_u-, the T_1u- or the T_2u-channel, appears in different regions of the phase diagram that is plotted with respect to model parameters such as effective mass anisotropy. The topological properties of these superconductors are also predicted and discussed.   

Live

The Majorana fermion is an exotic particle that is its own antiparticle. Chiral Majorana fermion can arise in a one-dimensional edge of topological materials, and especially that in a topological superconductor can be exploited in non-Abelian quantum computation. While the chiral Majorana mode (CMM) remains elusive, a promising situation is realized when superconductivity coexists with a topologically non-trivial surface state. Here, we perform fully non-empirical calculation for the CMM considering superconductivity and surface relaxation, and show that hexagonal close-packed thallium (Tl) has an ideal electronic state that harbors the CMM [1]. The k_z = 0 plane corresponds to the TCI with mirror Chern number |N_M|=2. One of the Dirac points on the (01-10) surface is located almost at the Fermi level. Tl is a textbook-like s-wave superconductor and the gap function has no significant wave-number dependence. Only one of the two Dirac points is relevant for the gap opening due to the superconducting transition, and the CMM appears at the hinge under the Zeeman field. Our calculation indicates that Tl will provide a new platform of the Majorana fermion and quantum computation.
[1] M. Hirayama, T. Nomoto, and R. Arita, submitted.   

Live

We found superconductivity in CaSb₂ with the transition onset of 1.8 K by means of electrical-resistivity, magnetic-susceptibility, and specific-heat measurements [1]. Zero resistance was observed below 1.2 K, and the superconducting volume fraction at 0 K was estimated to be 65% from specific heat. This material crystallizes in a nonsymmorphic structure and is predicted to have multiple Dirac nodal lines in the bulk electronic band structure protected by crystalline symmetry even in the presence of spin-orbit coupling. In this presentation, we will briefly introduce the band structure of CaSb₂ and then show experimental results evidencing its bulk superconductivity.
[1] A. Ikeda et al., Phys. Rev. Mater. 4, 041801(R) (2020).   

Live

The advent of superlattices in recent years has made possible the realization of two-dimensional lattices with large magnetic fluxes per unit cell when in the presence of an external magnetic field. The interplay of lattice effects and magnetic field creates a scenario of multiple Fermi surfaces related by magnetic translation symmetry. I will discuss the onset of time-reversal symmetry breaking superconductivity in such systems, and demonstrate the existence of mean-field superconductors characterized by multi-component triplet order parameters, which are greatly constrained by the action of the magnetic translation group. An outstanding property of these large flux superconductors is that Cooper pairs have finite momentum, and bulk state is characterized by higher Chern numbers, signaling the presence of many chiral Majorana edge modes. I will discuss their bulk properties as well as multi-stage phase transitions that change the bulk topology and the nature of the chiral edge Majorana fermions.   

On Demand

Two-dimensional topological superconductors host topologically protected edge states guaranteed by the bulk-boundary correspondence. However, the associated edge currents are not quantized as the superconducting state breaks the electron’s U(1) symmetry. Indeed, here we show how the spin and charge edge currents can change continuously even when going through a topological phase transition.
Specifically, we investigate for a two-dimensional superconductor with Rashba spin-orbit coupling (broken mirror symmetry) and an out-of-plane Zeeman field (broken time-reversal symmetry) how the superconducting order parameter adapts under these consecutive symmetry reductions. We then examine the emerging edge currents in a strip geometry in the different topological phases of this system, namely the trivial, the helical (class DIII), and the chiral (class D) phase.
Using both a Ginzburg-Landau and a microscopic approach, we find edge currents irrespective of the topology of the system and the associated edge states. Our study underscores how edge currents in topological superconductors derive mostly from the symmetry of the system.