Discovery of a strain-stabilised smectic electronic order in LiFeAs

Design and performance of an ultrahigh vacuum spectroscopic-imaging scanning tunneling microscope with a hybrid vibration isolation system

A spectroscopic imaging-scanning tunneling microscope (SI-STM) allows for the atomic scale visualization of the surface electronic and magnetic structure of novel quantum materials with a high energy resolution. To achieve the optimal performance, a low vibration facility is required. Here, we describe the design and performance of an ultrahigh vacuum STM system supported by a hybrid vibration isolation system that consists of a pneumatic passive and a piezoelectric active vibration isolation stage. We present the detailed vibrational noise analysis of the hybrid vibration isolation system, which shows that the vibration level can be suppressed below 10-8 m/sec/√Hz for most frequencies up to 100 Hz. Combined with a rigid STM design, vibrational noise can be successfully removed from the tunneling current. We demonstrate the performance of our STM system by taking high resolution spectroscopic maps and topographic images on several quantum materials. Our results establish a new strategy to achieve an effective vibration isolation system for high-resolution STM and other scanning probe microscopies to investigate the nanoscale quantum phenomena.

Toward large-scale, ordered and tunable Majorana-zero-modes lattice on iron-based superconductors

Majorana excitations are the quasiparticle analog of Majorana fermions in solid materials. Typical examples are the Majorana zero modes (MZMs) and the dispersing Majorana modes. When probed by scanning tunneling spectroscopy, the former manifest as a pronounced conductance peak locating precisely at zero-energy, while the latter behaves as constant or slowly varying density of states. The MZMs obey non-abelian statistics and are believed to be building blocks for topological quantum computing, which is highly immune to the environmental noise. Existing MZM platforms include hybrid structures such as topological insulator, semiconducting nanowire or 1D atomic chains on top of a conventional superconductor, and single materials such as the iron-based superconductors (IBSs) and 4Hb-TaS2. Very recently, ordered and tunable MZM lattice has also been realized in IBS LiFeAs, providing a scalable and applicable platform for future topological quantum computation. In this review, we present an overview of the recent local probe studies on MZMs. Classified by the material platforms, we start with the MZMs in the iron-chalcogenide superconductors where FeTe0.55Se0.45and (Li0.84Fe0.16)OHFeSe will be discussed. We then review the Majorana research in the iron-pnictide superconductors as well as other platforms beyond the IBSs. We further review recent works on ordered and tunable MZM lattice, showing that strain is a feasible tool to tune the topological superconductivity. Finally, we give our summary and perspective on future Majorana research.

Electronic stripe patterns near the fermi level of tetragonal Fe(Se,S)

FeSe1-xSx remains one of the most enigmatic systems of Fe-based superconductors. While much is known about the orthorhombic parent compound, FeSe, the tetragonal samples, FeSe1-xSx with x > 0.17, remain relatively unexplored. Here, we provide an in-depth investigation of the electronic states of tetragonal FeSe0.81S0.19, using scanning tunneling microscopy and spectroscopy (STM/S) measurements, supported by angle-resolved photoemission spectroscopy (ARPES) and theoretical modeling. We analyze modulations of the local density of states (LDOS) near and away from Fe vacancy defects separately and identify quasiparticle interference (QPI) signals originating from multiple regions of the Brillouin zone, including the bands at the zone corners. We also observe that QPI signals coexist with a much stronger LDOS modulation for states near the Fermi level whose period is independent of energy. Our measurements further reveal that this strong pattern appears in the STS measurements as short range stripe patterns that are locally two-fold symmetric. Since these stripe patterns coexist with four-fold symmetric QPI around Fe-vacancies, the origin of their local two-fold symmetry must be distinct from that of nematic states in orthorhombic samples. We explore several aspects related to the stripes, such as the role of S and Fe-vacancy defects, and whether they can be explained by QPI. We consider the possibility that the observed stripe patterns may represent incipient charge order correlations, similar to those observed in the cuprates.

Pair density wave state in a monolayer high-Tc iron-based superconductor

The pair density wave (PDW) is an extraordinary superconducting state in which Cooper pairs carry non-zero momentum^1,2. Evidence for the existence of intrinsic PDW order in high-temperature (high-T_c) cuprate superconductors^3,4 and kagome superconductors⁵ has emerged recently. However, the PDW order in iron-based high-T_c superconductors has not been observed experimentally. Here, using scanning tunnelling microscopy and spectroscopy, we report the discovery of the PDW state in monolayer iron-based high-T_c Fe(Te,Se) films grown on SrTiO₃(001) substrates. The PDW state with a period of λ ≈ 3.6a_Fe (a_Fe is the distance between neighbouring Fe atoms) is observed at the domain walls by the spatial electronic modulations of the local density of states, the superconducting gap and the π-phase shift boundaries of the PDW around the vortices of the intertwined charge density wave order. The discovery of the PDW state in the monolayer Fe(Te,Se) film provides a low-dimensional platform to study the interplay between the correlated electronic states and unconventional Cooper pairing in high-T_c superconductors.

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

Majorana zero modes (MZMs) obey non-Abelian statistics and are considered building blocks for constructing topological qubits^1,2. Iron-based superconductors with topological bandstructures have emerged as promising hosting materials, because 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 tunnelling microscopy/spectroscopy. 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 that more than 90 per cent of the vortices are topological and possess the characteristics of isolated MZMs at the vortex centre, forming an ordered MZM lattice with the density and the geometry tunable by an external magnetic field. Notably, with decreasing the spacing of neighbouring vortices, the MZMs start to couple with each other. Our findings provide a pathway towards tunable and ordered MZM lattices as a platform for future topological quantum computation.

Two distinct superconducting states controlled by orientations of local wrinkles in LiFeAs

For iron-based superconductors, the phase diagrams under pressure or strain exhibit emergent phenomena between unconventional superconductivity and other electronic orders, varying in different systems. As a stoichiometric superconductor, LiFeAs has no structure phase transitions or entangled electronic states, which manifests an ideal platform to explore the pressure or strain effect on unconventional superconductivity. Here, we observe two types of superconducting states controlled by orientations of local wrinkles on the surface of LiFeAs. Using scanning tunneling microscopy/spectroscopy, we find type-I wrinkles enlarge the superconducting gaps and enhance the transition temperature, whereas type-II wrinkles significantly suppress the superconducting gaps. The vortices on wrinkles show a C₂ symmetry, indicating the strain effects on the wrinkles. By statistics, we find that the two types of wrinkles are categorized by their orientations. Our results demonstrate that the local strain effect with different directions can tune the superconducting order parameter of LiFeAs very differently, suggesting that the band shifting induced by directional pressure may play an important role in iron-based superconductivity.

The evolution of superconductivity in LiFeAs with respect to pressure or strain remains elusive. Here, the authors observe different response of superconducting states due to different orientations of local wrinkles on the surface of LiFeAs.

Majorana zero modes in impurity-assisted vortex of LiFeAs superconductor

The iron-based superconductor is emerging as a promising platform for Majorana zero mode, which can be used to implement topological quantum computation. One of the most significant advances of this platform is the appearance of large vortex level spacing that strongly protects Majorana zero mode from other low-lying quasiparticles. Despite the advantages in the context of physics research, the inhomogeneity of various aspects hampers the practical construction of topological qubits in the compounds studied so far. Here we show that the stoichiometric superconductor LiFeAs is a good candidate to overcome this obstacle. By using scanning tunneling microscopy, we discover that the Majorana zero modes, which are absent on the natural clean surface, can appear in vortices influenced by native impurities. Our detailed analysis reveals a new mechanism for the emergence of those Majorana zero modes, i.e. native tuning of bulk Dirac fermions. The discovery of Majorana zero modes in this homogeneous material, with a promise of tunability, offers an ideal material platform for manipulating and braiding Majorana zero modes, pushing one step forward towards topological quantum computation.

Despite the discovery of Majorana zero modes (MZM) in iron-based superconductors, sample inhomogeneity may destroy MZMs during braiding. Here, authors observe MZM in impurity-assisted vortices due to tuning of the bulk Dirac fermions in a homogeneous superconductor LiFeAs.

Strain-Stabilized (π, π) Order at the Surface of Fe1+xTe

A key property of many quantum materials is that their ground state depends sensitively on small changes of an external tuning parameter, e.g., doping, magnetic field, or pressure, creating opportunities for potential technological applications. Here, we explore tuning of the ground state of the nonsuperconducting parent compound, Fe_1+xTe, of the iron chalcogenides by uniaxial strain. Iron telluride exhibits a peculiar (π, 0) antiferromagnetic order unlike the (π, π) order observed in the Fe-pnictide superconductors. The (π, 0) order is accompanied by a significant monoclinic distortion. We explore tuning of the ground state by uniaxial strain combined with low-temperature scanning tunneling microscopy. We demonstrate that, indeed under strain, the surface of Fe_1.1Te undergoes a transition to a (π, π)-charge-ordered state. Comparison with transport experiments on uniaxially strained samples shows that this is a surface phase, demonstrating the opportunities afforded by 2D correlated phases stabilized near surfaces and interfaces.

Incommensurate smectic phase in close proximity to the high-Tc superconductor FeSe/SrTiO3

Superconductivity is significantly enhanced in monolayer FeSe grown on SrTiO₃, but not for multilayer films, in which large strength of nematicity develops. However, the link between the high-transition temperature superconductivity in monolayer and the correlation related nematicity in multilayer FeSe films is not well understood. Here, we use low-temperature scanning tunneling microscopy to study few-layer FeSe thin films grown by molecular beam epitaxy. We observe an incommensurate long-range smectic phase, which solely appears in bilayer FeSe films. The smectic order still locally exists and gradually fades away with increasing film thickness, while it suddenly vanishes in monolayer FeSe, indicative of an abrupt smectic phase transition. Surface alkali-metal doping can suppress the smectic phase and induce high-T_c superconductivity in bilayer FeSe. Our observations provide evidence that the monolayer FeSe is in close proximity to the smectic phase, and its superconductivity is likely enhanced by this electronic instability as well.

The relation between enhanced superconductivity in monolayer FeSe grown on SrTiO₃ and the large nematicity in multilayer FeSe on SrTiO₃ remains not well understood. Here, the authors observe a long-range smectic phase in bilayer FeSe films but vanishes in monolayer FeSe, providing a new instability to help enhance the superconductivity.

Possible Charge Density Wave and Enhancement of Thermoelectric Properties at Mild-Temperature Range in n-Type CuI-Doped Bi2Te2.1Se0.9 Compounds

Bi₂Te₃-based compounds have long been studied as thermoelectric materials in cooling applications near room temperature. Here, we investigated the thermoelectric properties of CuI-doped Bi₂Te_2.1Se_0.9 compounds. The Cu/I codoping induces the lattice distortion partially in the matrix. We report that the charge density wave caused by the local lattice distortion affects the electrical and thermal transport properties. From the high-temperature specific heat, we found a first-order phase transitions near 490 and 575 K for CuI-doped compounds (CuI)_xBi₂Te_2.1Se_0.9 (x = 0.3 and 0.6%), respectively. It is not a structural phase transition, confirming from the high-temperature X-ray diffraction. The temperature-dependent electrical resistivity shows a typical behavior of charge density wave transition, which is consistent with the temperature-dependent Seebeck coefficient and thermal conductivity. The transmission electron microscopy and electron diffraction show a local lattice distortion, driven by the charge density wave transition. The charge density wave formation in the Bi₂Te₃-based compounds are exceptional because of the possibility of coexistence of charge density wave and topological surface states. From the Kubo formula and Boltzmann transport calculations, the formation of charge density wave enhances the power factor. The lattice modulation and charge density wave decrease lattice thermal conductivity, resulting in the enhancement of thermoelectric performance simultaneously in CuI-doped samples. Consequently, an enhancement of thermoelectric performance ZT over 1.0 is achieved at 448 K in the (CuI)_0.003Bi₂Te_2.1Se_0.9 sample. The enhancement of ZT at high temperature gives rise to a superior average ZT_avg (1.0) value than those of previously reported ones.

Charge ordering in high-temperature superconductors visualized by scanning tunneling microscopy

Since the discovery of stripe order in La_1.6-x Nd_0.4Sr _x CuO₄ superconductors in 1995, charge ordering in cuprate superconductors has been intensively studied by various experimental techniques. Among these studies, scanning tunneling microscope (STM) plays an irreplaceable role in determining the real space structures of charge ordering. STM imaging of different families of cuprates over a wide range of doping levels reveal similar checkerboard-like patterns, indicating that such a charge ordered state is likely a ubiquitous and intrinsic characteristic of cuprate superconductors, which may shed light on understanding the mechanism of high-temperature superconductivity. In another class of high-temperature superconductors, iron-based superconductors, STM studies reveal several charge ordered states as well, but their real-space patterns and the interplay with superconductivity are markedly different among different materials. In this paper, we present a brief review on STM studies of charge ordering in these two classes of high-temperature superconductors. Possible origins of charge ordering and its interplay with superconductivity will be discussed.

Quasi-1D Topological Nodal Vortex Line Phase in Doped Superconducting 3D Dirac Semimetals

We study vortex bound states in three-dimensional (3D) superconducting Dirac semimetals with time reversal symmetry. We find that there exist robust gapless vortex bound states propagating along the vortex line in the s-wave superconducting state. We refer to this newly found phase as the quasi-1D nodal vortex line phase. According to the Altland-Zirnbauer classification, the phase is characterized by a topological index (ν;N) at k_{z}=0 and k_{z}=π, where ν is the Z_{2} topological invariant for a 0D class-D system and N is the Z topological invariant for a 0D class-A system. Furthermore, we show that the vortex end Majorana zero mode can coexist with the quasi-1D nodal phase in certain types of Dirac semimetals. The possible experimental observations and material realization of such nodal vortex line states are discussed.

Manipulating surface magnetic order in iron telluride

Control of emergent magnetic orders in correlated electron materials promises new opportunities for applications in spintronics. For their technological exploitation, it is important to understand the role of surfaces and interfaces to other materials and their impact on the emergent magnetic orders. Here, we demonstrate for iron telluride, the nonsuperconducting parent compound of the iron chalcogenide superconductors, determination and manipulation of the surface magnetic structure by low-temperature spin-polarized scanning tunneling microscopy. Iron telluride exhibits a complex structural and magnetic phase diagram as a function of interstitial iron concentration. Several theories have been put forward to explain the different magnetic orders observed in the phase diagram, which ascribe a dominant role either to interactions mediated by itinerant electrons or to local moment interactions. Through the controlled removal of surface excess iron, we can separate the influence of the excess iron from that of the change in the lattice structure.

Exchange Interactions and Curie Temperature of Ce-Substituted SmCo5

A partial substitution such as Ce in SmCo 5 could be a brilliant way to improve the magnetic performance, because it will introduce strain in the structure and breaks the lattice symmetry in a way that enhances the contribution of the Co atoms to magnetocrystalline anisotropy. However, Ce substitutions, which are benefit to improve the magnetocrystalline anisotropy, are detrimental to enhance the Curie temperature ( T C ). With the requirements of wide operating temperature range of magnetic devices, it is important to quantitatively explore the relationship between the T C and ferromagnetic exchange energy. In this paper we show, based on mean-field approximation, artificial tensile strain in SmCo 5 induced by substitution leads to enhanced effective ferromagnetic exchange energy and T C , even though Ce atom itself reduces T C .