Fate of Majorana Modes in CeCoIn5/YbCoIn5 Superlattices: A Test Bed for the Reduction of Topological Classification

Abstract

In this paper, we propose CeCoIn5/YbCoIn5 superlattice systems as a test bed for the reduction of topological classification in free fermions. We find that the system with quad-layer of CeCoIn5 shows a topological crystalline superconducting phase with the mirror Chern number eight at the non-interacting level. Furthermore, we demonstrate that in the presence of two-body interactions, gapless edge modes are no longer protected by the symmetry in the system with quad-layer, but are protected in the systems with bi-or tri-layer. This clearly exemplifies the reduction of topological classification from Z ⊕ Z to Z ⊕ Z8.-Introduction-After the discovery of the topological insulators (TIs) and topological superconductors (TSCs), topological properties of quantum phases have been extensively studied 1,2 . In TIs/TSCs, nontrivial topology of the wave function in the bulk predicts gapless excitations at boundary/surface of the systems, which are sources of novel transport properties. These systems are free fermion systems (i.e., they are described by a quadratic Hamiltonian), and the topology of TIs/TSCs is protected by symmetries. Examining how many topological phases exist under a given local symmetry (i.e., classification of TIs and TSCs) is an important issue and gives useful information 3-5 . On the experimental side, realization of TIs/TSCs has been a significant issue, and various numbers of TIs/TSCs have been indeed realized; a two-dimensional TI was first confirmed for a quantum well of HgTe/CdTe 6,7 , and three-dimensional TIs were reported for Bi 2 Se 3 etc. [8][9][10] . Also, a TSC was proposed for Cu x Bi 2 Se 3 11 .Understanding the effects of electron correlations, which are generally neglected in the treatment of TIs/TSCs, is one of the current important issues in this field. Theoretical proposals of TIs in strongly correlated compounds have further stimulated this issue 12-20 . Recent extensive studies have discovered the reduction of topological classification for free fermion systems. In particular, Fidkowski and Kitaev have found that for a one-dimensional TSC of class BDI, the topological classification for free fermions, Z, collapses into Z 8 in the presence of electron correlations [21][22][23] . This means that gapless edge modes can be unstable against electron interactions. The reduction of topological classification has further been extended to two-and three-dimensional systems by examining stability/instability of gapless edge modes [24][25][26][27][28][29][30][31][32][33][34][35][36] . In spite of such significant progress on the theoretical side, the reduction of topological classification has not been experimentally reported yet. Therefore, an experimental platform is indispensable for progress in this direction.In this paper, we address the following question. How can we realize an experimentally accessible test bed to observe the reduction of the classification? In order to answer this question, we analyze topological properties of superconducting phases in a superlattice system composed ...

Interacting topological insulators: a review

“…(iii) The role of interactions in the context of SPT phases is somewhat ambivalent -on the one hand they can stabilize SPT phases which do not have a free fermionic analog, a nice example is provided by parafermionic chains (Alicea and Fendley, 2016;Motruk et al, 2013); on the other hand they can destroy SPT phases, best illustrated by the reduction of the BDI symmetry class to the Z 8 classification in one spatial dimension (Fidkowski and Kitaev, 2011;Turner et al, 2011). To test this reduction experimentally was suggested both in the superlattice material CeCoIn 5 /YbCoIn 5 (Yoshida et al, 2017a) and in a cold atom system (Yoshida et al, 2017b). (iv) It is possible to construct states of matter which exhibit topological order and possess a protecting symmetry simultaneously.…”

Odd-parity multipole fluctuation and unconventional superconductivity in locally noncentrosymmetric crystal

“…These features are opposite to those expected from a group-theoretical analysis of symmorphic superconductors [80]. In the following sections, we study superconductivity in a model preserving the space group symmetry (8). The gap functions obtained from numerical calculations satisfy the symmetry constraints, which have been revealed in this section.…”

Multiple odd-parity superconducting phases in bilayer transition metal dichalcogenides

“…Another intriguing topic for the unconventional superconductivity is relation between crystalline symmetry and the pairing states [39]. Particularly, various ex- * kanasugi.shouta.62w@st.kyoto-u.ac.jp otic superconducting (SC) phenomena have been elucidated in locally noncentrosymmetric (NCS) systems [40][41][42][43][44][45][46][47][48][49], in which the inversion symmetry in a local atomic site is broken although the global inversion symmetry is preserved. Microscopically, a key aspect of locally NCS systems is the sublattice-dependent antisymmetric spin-orbit coupling (SOC), which leads to exotic superconductivity e.g., singlet-triplet mixed paring states [42], pair density wave states [44,48], complex stripe states [45], and topological superconductivity [43,46,47].…”

“…Particularly, various ex- * kanasugi.shouta.62w@st.kyoto-u.ac.jp otic superconducting (SC) phenomena have been elucidated in locally noncentrosymmetric (NCS) systems [40][41][42][43][44][45][46][47][48][49], in which the inversion symmetry in a local atomic site is broken although the global inversion symmetry is preserved. Microscopically, a key aspect of locally NCS systems is the sublattice-dependent antisymmetric spin-orbit coupling (SOC), which leads to exotic superconductivity e.g., singlet-triplet mixed paring states [42], pair density wave states [44,48], complex stripe states [45], and topological superconductivity [43,46,47]. Especially, it has been clarified that odd-parity topological superconductivity is realized by a combination of antiferromagnetic spin fluctuations and the sublattice-dependent antisymmetric SOC, namely odd-parity magnetic multipole fluctuations [49].…”