Ordered and tunable Majorana-zero-mode lattice in naturally strained LiFeAs

Abstract

Majorana zero modes (MZMs) obey non-Abelian statistics and are considered building blocks for constructing topological qubits 1,2 . Iron-based superconductors with topological band structures have emerged as promising hosting materials, since isolated candidate MZMs in the quantum limit have been observed inside the topological vortex cores 3-9 . However, these materials suffer from issues related to alloying-induced disorder, uncontrolled vortex lattices 10-13 and a low yield of topological vortices 5-8 . Here, we report the formation of an ordered and tunable MZM lattice in naturally-strained stoichiometric LiFeAs by scanning tunneling microscopy/spectroscopy (STM/S). We observe biaxial charge density wave (CDW) stripes along the Fe-Fe and As-As directions in the strained regions. The vortices are pinned on the CDW stripes in the As-As direction and form an ordered lattice. We detect more than 90 percent of the vortices to be topological and possess the characteristics of isolated MZMs at the vortex center, forming an ordered MZM lattice with the density and the geometry tunable by an external magnetic field. Remarkably, with decreasing the spacing of neighboring vortices, the MZMs start to couple with each other. Our findings provide a new pathway towards tunable and ordered MZM lattices as a platform for future topological quantum computation.The long quest for Majorana excitations [14][15][16][17][18][19] has been fueled by recent experimental progress in material platforms where the localized MZM has been observed 16,[20][21][22][23] . Among these platforms, ironbased superconductors are considered promising for the observation of clean and robust MZMs 3-5 . FeTe0.55Se0.45 was the first iron-based superconductor found to possess topological surface states (TSS) 24,25 . The largeratio, where Δ is the superconducting (SC) energy gap and 𝐸 𝐹 is the Fermi energy, allows the observation of an isolated MZM in the center of a topological vortex 4 , which exhibits nearly quantized plateaus in differential conductance 9 . Later on, stoichiometric iron pnictides were investigated and the existence of MZMs has been verified in CaKFe4As4 (ref. 8 ) and LiFeAs (ref. 6 ). Very recently, 1D dispersing Majorana modes and MZMs have been observed in the layered 2D superconductors with topological band structures [26][27][28] . However, these platforms suffer from alloyinginduced disorder, uncontrolled vortex lattice and a low yield of topological vortices, hindering their potential applications.We start with LiFeAs crystal due to its homogeneous bulk electronic structure, well-defined cleaving surface and rich topological band structures 29 . LiFeAs belongs to the tetragonal crystal system, with lattice constants a=b=3.8 Å and c=6.3 Å (Fig. 1a). The As-As atomic direction defines the high-

Two-dimensional superconductors with intrinsic p-wave pairing or nontrivial band topology

“…We have attempted to outline three of the tuning knobs in acquiring one or both of the essential ingredients of TSC, including strain, gating, and ferroelectricity. In particular, strain has been demonstrated very recently as an effective means to regulate the spatial distribution and mutual interaction of a MZM lattice [64]. Furthermore, we optimistically expect that the reversible and nonvolatile ferroelectric tunability will play a major role in gaining precise control and manipulation of MZMs.…”

“…Beyond FeSe-based superconductors, impurity-assisted vortex states in LiFeAs have also been shown to exhibit MZMs [294], attesting the nontrivial nature of the superconducting systems. Furthermore, as a compelling example for the strain-based tunability, a very recent study reported that the surface strain can alter the charge density waves (CDWs) appearing on the surfaces of the LiFeAs, and such CDWs can in turn regulate the special distribution of the vertex lattice that harbors the MZMs [64]. More coverages on this line of advances can be found in a separate review within this volume [295].…”

“…This real-space proximity scheme has been generalized to heterostructure comprised of a 2D or 1D semiconductor with spin-orbit coupling proximity coupled to spin-singlet superconductors [44][45][46][47][48][49][50]. For reciprocal-space proximity or band proximity effect-induced TSC, typical examples are doped 3D topological insulators [51][52][53][54] and iron-based superconductors [55][56][57][58][59][60][61][62][63][64], where superconductivity arising from the bulk bands is proximity coupled to the topological surface states, mimicking effective 2D chiral p-wave superconductors. Intrinsic TSC means that superconductivity and nontrivial topology arise from the same electronic states of the same material [12,37,39].…”

Majorana lattice gauge theory: symmetry breaking, topological order and intertwined orders all in one

“…Recently, the Majorana-zero-mode lattice has been realized in a tunable way 53 , which provides a natural platform to implement interacting Majorana fermion model composed of local interactions only. A theoretically interacting question is the doping effect, that is doping on γ or χ Majorana fermions to study the effect on AFM order or quantum spin liquid, which may provide clues to high-T c cuprates.…”

Strong Majorana evidence of a vortex from scanning tunneling microscopy with a dissipative environment

“…Zero-bias conductance peak (ZBCP) has also been reported as a Majorana feature in spectroscopic measurements of vortex states via the standard scanning tunneling microscopy (STM) technique [23][24][25][26][27][28][30][31][32][33][34][35][36][37]. More inspiringly, a recent progress [53] shows that topological vortexes can form into an ordered lattice through the introduction of a biaxial charge density wave. This technical advance can potentially reduce the difficulty of Majorana manipulation: the next stage in the realization of topological quantum computation.…”