How the vortex lattice of a superconductor becomes disordered: a study by scanning tunneling spectroscopy

Tunable vortex bound states in multiband CsV3Sb5-derived kagome superconductors

Vortices and bound states offer an effective means of comprehending the electronic properties of superconductors. Recently, surface-dependent vortex core states have been observed in the newly discovered kagome superconductors CsV3Sb5. Although the spatial distribution of the sharp zero energy conductance peak appears similar to Majorana bound states arising from the superconducting Dirac surface states, its origin remains elusive. In this study, we present observations of tunable vortex bound states (VBSs) in two chemically-doped kagome superconductors Cs(V1-xTrx)3Sb5 (Tr = Ta or Ti), using low-temperature scanning tunneling microscopy/spectroscopy. The CsV3Sb5-derived kagome superconductors exhibit full-gap-pairing superconductivity accompanied by the absence of long-range charge orders, in contrast to pristine CsV3Sb5. Zero-energy conductance maps demonstrate a field-driven continuous reorientation transition of the vortex lattice, suggesting multiband superconductivity. The Ta-doped CsV3Sb5 displays the conventional cross-shaped spatial evolution of Caroli-de Gennes-Matricon bound states, while the Ti-doped CsV3Sb5 exhibits a sharp, non-split zero-bias conductance peak (ZBCP) that persists over a long distance across the vortex. The spatial evolution of the non-split ZBCP is robust against surface effects and external magnetic field but is related to the doping concentrations. Our study reveals the tunable VBSs in multiband chemically-doped CsV3Sb5 system and offers fresh insights into previously reported Y-shaped ZBCP in a non-quantum-limit condition at the surface of kagome superconductor.

Order-disorder phase transition and elastic-to-plastic vortex creep crossover in a triclinic iron pnictide superconductor (Ca[Formula: see text]La[Formula: see text])[Formula: see text](Pt[Formula: see text]As[Formula: see text])(Fe[Formula: see text]As[Formula: see text])[Formula: see text]

Vortex matter in layered high-[Formula: see text] superconductors, including iron-pnictides, undergo several thermodynamic phase transitions due to the complex interplay of pinning energy, thermal energy and elastic energy. Moreover, the presence of anisotropy makes their vortex physics even more intriguing. Here, we report a detailed vortex dynamics study, using dc magnetization measurements, in a triclinic iron-pnictide superconductor (Ca[Formula: see text]La[Formula: see text])[Formula: see text](Pt[Formula: see text]As[Formula: see text])(Fe[Formula: see text]As[Formula: see text])[Formula: see text], with a superconducting transition temperature, T[Formula: see text] [Formula: see text] 31 K. A second magnetization peak (SMP) feature is observed for magnetic field perpendicular (H[Formula: see text]c) and parallel (H[Formula: see text]ab) to the crystal plane. However, its fundamental origin is quite different in both directions. For H[Formula: see text]c, the SMP can be well explained using an elastic-to-plastic vortex creep crossover, using collective creep theory. In addition, a possible rhombic-to-square vortex lattice phase transition is also observed for fields in between the onset-field and peak-field related to the SMP. On the other hand, for H[Formula: see text]ab, a clear signature of an order-disorder vortex phase transition is observed in the isothermal M(H) measurements at T [Formula: see text] 6 K. The disordered phase exhibits the characteristics of entangled pinned vortex-liquid. We construct a comprehensive vortex phase diagram by displaying characteristic temperatures and magnetic fields for both crystal geometries in this unique superconducting compound. Our study sheds light on the intricate vortex dynamics and pinning in an iron-pnictide superconductor with triclinic symmetry.

Nematically Templated Vortex Lattices in Superconducting FeSe

New pathways to controlling the morphology of superconducting vortex lattices─and their subsequent dynamics─are required to guide and scale vortex world-lines into a computing platform. We have found that the nematic twin boundaries align superconducting vortices in the adjacent terraces due to the incommensurate potential between vortices surrounding twin boundaries and those trapped within them. With the varying density and morphology of twin boundaries, the vortex lattice assumes several distinct structural phases, including square, regular, and irregular one-dimensional lattices. Through concomitant analysis of vortex lattice models, we have inferred the characteristic energetics of the twin boundary potential and furthermore predicted the existence of geometric size effects as a function of increasing confinement by the twin boundaries. These findings extend the ideas of directed control over vortex lattices to intrinsic topological defects and their self-organized networks, which have direct implications for the future design and control of strain-based topological quantum computing architectures.

Second magnetization peak, anomalous field penetration, and Josephson vortices in KCa[Formula: see text]Fe[Formula: see text]As[Formula: see text]F[Formula: see text] bilayer pnictide superconductor

We performed magnetization measurements in a single crystal of the anisotropic bilayer pnictide superconductor KCa[Formula: see text]Fe[Formula: see text]As[Formula: see text]F[Formula: see text], with [Formula: see text] [Formula: see text] 34 K, for [Formula: see text] [Formula: see text] [Formula: see text]-axis and [Formula: see text] [Formula: see text] [Formula: see text]-planes. A second magnetization peak (SMP) was observed in the isothermal M(H) curves measured below 16 K for [Formula: see text] [Formula: see text] [Formula: see text]-planes. A peak in the temperature variation of the critical current density, [Formula: see text](T), at 16 K, strongly suggests the emergence of Josephson vortices at lower temperatures, which leads to the SMP in the sample. In addition, it is noticed that the appearance of Josephson vortices below 16 K renders easy magnetic flux penetration. A detailed vortex dynamics study suggests that the SMP can be explained in terms of elastic pinning to plastic pinning crossover. Furthermore, contrary to the common understanding, the temperature variation of the first peak field, [Formula: see text], below and above 16 K, behaves non-monotonically. A highly disordered vortex phase, governed by plastic pinning, has been observed between 17 and 23 K, within a field region around an extremely large first peak field. Pinning force scaling suggests that the point defects are the dominant source of pinning for H [Formula: see text] [Formula: see text]-planes, whereas, for H [Formula: see text] [Formula: see text]-axis, point defects in addition to surface defects are at play. Such disorder contributes to the pinning due to the variation in charge carrier mean free path, [Formula: see text] -pinning. Moreover, the large [Formula: see text] observed in our study is consistent with the literature, which advocates this material for high magnetic field applications.

Dynamic manipulation of three-color light reflection in a defective atomic lattice

We extend a recent theoretical work [Phys. Rev. A101, 053856 (2020)10.1103/PhysRevA.101.053856] by replacing disorders characterized by varied atomic densities with defects characterized by vacant lattice cells to evaluate again three-color reflection in a one-dimensional optical lattice filled with cold ⁸⁷Rb atoms. This is based on the consideration that trapped atoms may escape from some lattice cells and effects of vacant cells on light propagation are of major importance from both fundamental and applied research viewpoints. We consider two types of defective atomic lattices where vacant cells are randomly or continuously distributed among filled cells. Numerical results show that the wider reflection band in a large detuning region of negligible off-resonance absorption is quite sensitive to, while the narrower reflection bands in two near-resonant regions of electromagnetically induced transparency are rather robust against, the number of random vacant cells. In contrast, all three reflection bands exhibit strong robustness against the number of continuous vacant cells. Note, however, that both narrower reflection bands may become widened and exhibit a blue shift when continuous vacant cells appear in the front of our atomic lattice due to the joint contributions of Bragg scattering and quantum interference.

Second magnetization peak, rhombic-to-square Bragg vortex glass transition, and intersecting magnetic hysteresis curves in overdoped BaFe2(As1-xPx)2 single crystals

The second magnetization peak (SMP) in the fourfold symmetric superconducting single crystals (such as iron pnictides and tetragonal cuprates) has been attributed to the rhombic-to-square transition (RST) of the quasi-ordered vortex solid (the Bragg vortex glass, BVG). This represents an alternative to the pinning-induced BVG disordering as the actual SMP mechanism. The analysis of the magnetic response of BaFe2(As1-xPx)2 specimens presented here shows that the SMP is not generated by the RST. However, the latter can affect the pinning-dependent SMP onset field if this is close to the (intrinsic) RST line, through the occurrence of a "shoulder" on the magnetic hysteresis curves m(H), and a maximum in the temperature variation of the DC critical current density. These features disappear in AC conditions, where the vortex system is dynamically ordered in the RST domain, emphasizing the essential role of vortex dislocations for an efficient accommodation of the vortex system to the pinning landscape and the SMP development. The m(H) shoulder is associated with a precipitous pinning-induced proliferation of dislocations at the RST, where the BVG elastic "squash" modulus softens. The DC magnetization relaxation indicates that the pinning-induced vortex system disordering continues above the RST domain, as the basic SMP mechanism.

Collective flux pinning in hexatic vortex fluid in a-MoGe thin film

We investigate the magnetic field variation of the thermally activated flux flow resistivity, ρ _TAFF and flux flow critical current density, J _c, in a weakly pinned thin film of the amorphous superconductor a-MoGe, where vortices are in a fluid state over a large range of magnetic fields. We show that both quantities can be understood within the framework of collective pinning theory. In particular, our results demonstrate that a 'peak effect' can arise at the order-disorder transition of the vortex lattice even when both the ordered and disordered states are vortex fluids, such as the boundary between a hexatic vortex fluid and an isotropic vortex liquid.

Melting of the Vortex Lattice through Intermediate Hexatic Fluid in an a-MoGe Thin Film

The hexatic fluid refers to a phase in between a solid and a liquid that has short-range positional order but quasi-long-range orientational order. In the celebrated theory of Berezinskii, Kosterlitz, and Thouless and subsequently refined by Halperin, Nelson, and Young, it was predicted that a two-dimensional hexagonal solid can melt in two steps: first, through a transformation from a solid to a hexatic fluid, which retains quasi-long-range orientational order; and then from a hexatic fluid to an isotropic liquid. In this Letter, using a combination of real space imaging and transport measurements, we show that the two-dimensional vortex lattice in an a-MoGe thin film follows this sequence of melting as the magnetic field is increased. Identifying the signatures of various transitions on the bulk transport properties of the superconductor, we construct a vortex phase diagram for a two-dimensional superconductor.

Negative velocity fluctuations and non-equilibrium fluctuation relation for a driven high critical current vortex state

Under the influence of a constant drive the moving vortex state in 2H-NbS2 superconductor exhibits a negative differential resistance (NDR) transition from a steady flow to an immobile state. This state possesses a high depinning current threshold ([Formula: see text]) with unconventional depinning characteristics. At currents well above [Formula: see text], the moving vortex state exhibits a multimodal velocity distribution which is characteristic of vortex flow instabilities in the NDR regime. However at lower currents which are just above [Formula: see text], the velocity distribution is non-Gaussian with a tail extending to significant negative velocity values. These unusual negative velocity events correspond to vortices drifting opposite to the driving force direction. We show that this distribution obeys the Gallavotti-Cohen Non-Equilibrium Fluctuation Relation (GC-NEFR). Just above [Formula: see text], we also find a high vortex density fluctuating driven state not obeying the conventional GC-NEFR. The GC-NEFR analysis provides a measure of an effective energy scale (E eff ) associated with the driven vortex state. The E eff corresponds to the average energy dissipated by the fluctuating vortex state above [Formula: see text]. We propose the high E eff value corresponds to the onset of high energy dynamic instabilities in this driven vortex state just above [Formula: see text].

Enhancement of superconducting critical current density by Fe impurity substitution in NbSe2 single crystals and the vortex pinning mechanism

Magnetization measurements have been used to determine the effect of magnetic impurities (Fe) on the Larkin-Ovchinnikov (LO) 3D collective pinning model in NbSe₂ single crystals. Upon increasing the concentration of Fe impurities, the superconducting critical current density enhances appreciably compared to pure NbSe₂ reflecting the fact that the addition of magnetic impurities assists in improving the practical applicability of NbSe₂. The random pinning potential that is introduced by the Fe impurities also shows a considerable change in the interaction between the vortices and the core region, resulting in a competitive nature of single vortex, small bundle and large bundle pinning regimes in the H-T phase diagram. The intrinsic disorder in pure NbSe₂ single crystals shows δT_c flux pinning; however, the extrinsic disorder created by Fe atoms in NbSe₂ shows δl flux pinning. Furthermore, the field dependence of the pinning force on both NbSe₂ and Fe-incorporated NbSe₂ represents the existence of point pinning and the surface pinning mechanism with a broadening of the f_p curves in the Fe-incorporated single crystals.

Universal lower limit on vortex creep in superconductors

Superconductors are excellent testbeds for studying vortices, topological excitations that also appear in superfluids, liquid crystals and Bose-Einstein condensates. Vortex motion can be disruptive; it can cause phase transitions, glitches in pulsars, and losses in superconducting microwave circuits, and it limits the current-carrying capacity of superconductors. Understanding vortex dynamics is fundamentally and technologically important, and the competition between thermal energy and energy barriers defined by material disorder is not completely understood. Specifically, early measurements of thermally activated vortex motion (creep) in iron-based superconductors unveiled fast rates (S) comparable to measurements of YBa ₂Cu₃O_7-δ (refs ,,,,,). This was puzzling because S is thought to somehow correlate with the Ginzburg number (Gi), and Gi is significantly lower in most iron-based superconductors than in YBa ₂Cu₃O_7-δ. Here, we report very slow creep in BaFe ₂(As_0.67P_0.33)₂ films, and propose the existence of a universal minimum realizable S ∼ Gi^1/2(T/T_c) (T_c is the superconducting transition temperature) that has been achieved in our films and few other materials, and is violated by none. This limitation provides new clues about designing materials with slow creep and the interplay between material parameters and vortex dynamics.

Composite Topological Excitations in Ferromagnet-Superconductor Heterostructures

We investigate the formation of a new type of composite topological excitation-the Skyrmion-vortex pair (SVP)-in hybrid systems consisting of coupled ferromagnetic and superconducting layers. Spin-orbit interaction in the superconductor mediates a magnetoelectric coupling between the vortex and the Skyrmion, with a sign (attractive or repulsive) that depends on the topological indices of the constituents. We determine the conditions under which a bound SVP is formed and characterize the range and depth of the effective binding potential through analytical estimates and numerical simulations. Furthermore, we develop a semiclassical description of the coupled Skyrmion-vortex dynamics and discuss how SVPs can be controlled by applied spin currents.

Quasi-Long-Range Order and Vortex Lattice in the Three-State Potts Model

We show that the order-disorder phase transition in the three-state Potts ferromagnet on a square lattice is driven by a coupled proliferation of domain walls and vortices. Raising the vortex core energy above a threshold value decouples the proliferation and splits the transition into two. The phase between the two transitions exhibits an emergent U(1) symmetry and quasi-long-range order. Lowering the core energy below a threshold value also splits the order-disorder transition but the system forms a vortex lattice in the intermediate phase.

Filming the formation and fluctuation of skyrmion domains by cryo-Lorentz transmission electron microscopy

Magnetic skyrmions are promising candidates as information carriers in logic or storage devices thanks to their robustness, guaranteed by the topological protection, and their nanometric size. Currently, little is known about the influence of parameters such as disorder, defects, or external stimuli on the long-range spatial distribution and temporal evolution of the skyrmion lattice. Here, using a large (7.3 × 7.3 μm(2)) single-crystal nanoslice (150 nm thick) of Cu2OSeO3, we image up to 70,000 skyrmions by means of cryo-Lorentz transmission electron microscopy as a function of the applied magnetic field. The emergence of the skyrmion lattice from the helimagnetic phase is monitored, revealing the existence of a glassy skyrmion phase at the phase transition field, where patches of an octagonally distorted skyrmion lattice are also discovered. In the skyrmion phase, dislocations are shown to cause the emergence and switching between domains with different lattice orientations, and the temporal fluctuation of these domains is filmed. These results demonstrate the importance of direct-space and real-time imaging of skyrmion domains for addressing both their long-range topology and stability.