In superconducting thin films, engineered lattice of antidots (holes) act as an array of columnar pinning sites for the vortices and thus lead to vortex matching phenomena at commensurate fields guided by the lattice spacing. The strength and nature of vortex pinning is determined by the geometrical characteristics of the antidot lattice (such as the lattice spacing $a_0$, antidot diameter $d$, lattice symmetry, orientation, etc) along with the characteristic length scales of the superconducting thin films, viz., the coherence length ($ξ$) and the penetration depth ($λ$). There are at least two competing scenarios: (i) multiple vortices sit on each of the antidots at a higher matching period, and, (ii) there is nucleation of vortices at the interstitial sites at higher matching periods. Furthermore it is also possible for the nucleated interstitial vortices to reorder under suitable conditions. We present our experimental results on NbN antidot arrays in the light of the above scenarios.
We investigate anisotropy in the vortex pinning in thin superconducting films with a square array of rectangular submicron holes ("antidots"). The size of the antidots is chosen in such a way that it corresponds to a saturation number n_s=1, i.e. each antidot can trap at most one flux quantum. Therefore, interstitial vortices, appearing when the magnetic field exceeds the first matching field, are "caged" at the interstitial positions by the repulsion from the saturated antidots. We observe an overall higher critical current Ic(H) when it is measured parallel to the long side of the antidots t…
Shapiro voltage steps at voltages V_n=nV_0 (n integer) have been observed in the voltage-current characteristics of a superconducting film with a square lattice of perforating microholes (antidots)in the presence of radiofrequent radiation. These equidistant steps appear at the second matching field H_2 when the flow of the interstitial vortex lattice in the periodic potential created by the antidots and the vortices trapped by them, is in phase with the applied rf frequency. Therefore, the observation of Shapiro steps clearly reveals the presence of mobile intersitial vortices in superconduct…
We present a detailed study of the transport properties of a superconducting Pb/Cu microdot with a 2x2 antidot cluster. The superconducting-normal (S/N) phase boundary, critical currents and current-voltage characteristics of this structure have been measured. The S/N phase boundary as a function of field B (T_c(B)) reveals an oscillatory structure caused by the limited number of possible vortex configurations which can be realized in these small clusters of pinning centres (antidots). We have analyzed the stability of these configurations and discussed the possible dissipation mechanisms usin…
We examine a building block for logic devices in which the positions of superconducting vortices in coupled elongated antidots provide the elementary logic states of 0 and 1. We show analytically and through simulation the maximum operating frequency of a pair of antidots as a function of antidot spacing and elongation. At finite temperatures, a signal can propagate through a series of identically shaped antidots with correctly chosen spacing, with an exponential distribution of switching times for the signal to move over by one antidot.
Triangular arrays of Ni nanotriangles embedded in superconducting Nb films exhibit unexpected dynamical vortex effects. Collective pinning with a vortex lattice configuration different from the expected fundamental triangular "Abrikosov state" is found. The vortex motion which prevails against the triangular periodic potential is produced by channelling effects between triangles. Interstitial vortices coexisting with pinned vortices in this asymmetric potential, lead to ratchet reversal, i.e. a DC output voltage which changes sign with the amplitude of an applied alternating drive current. In …
Novel behavior of the critical current density $j_{c}$ of a regularly perforated superconducting film is found, as a function of applied magnetic field $H$. Previously pronounced peaks of $j_{c}$ at matching fields were always found to decrease with increasing $H$. Here we found a {\it reversal of this behavior} for particular geometrical parameters of the antidot lattice and/or temperature. This new phenomenon is due to a strong ``caging'' of interstitial vortices between the pinned ones. We show that this vortex-vortex interaction can be further tailored by an appropriate choice of the super…
We analyze the vortex dynamics in superconducting thin films with a periodic array of pinning centers. In particular, we study the effect of anisotropy for a Kagomé pinning network when longitudinal and transverse transport currents are applied. By solving the equations of motion for the vortex array numerically at zero temperature we find different phases for the vortex dynamics depending on the pinning and driving force. An unusual sequence of peaks along and perpendicular to the main hexagonal lattice axes is observed for the differential resistance reflecting the anisotropy of the transpor…
We have studied the dynamic response of Pb thin films with a square array of antidots by means of ac susceptibility chi(T,H) measurements. At low enough ac drive amplitudes h, vortices moving inside the pinning potential give rise to a frequency- and h-independent response together with a scarce dissipation. For higher amplitudes, the average distance travelled by vortices surpasses the pinning range and a critical state develops. We found that the boundary h*(H,T) between these regimes smoothly decreases as T increases whereas a step-like behavior is observed as a function of field. We demons…
We show that by nano-patterning a superconductor (NbSe2 single crystal) with an array of blind holes produces significant magnetic field sweep rate dependent metastable magnetization response. Our results are explained on the basis of a unique collective action of the blind holes pins which creates a barrier against vortex redistribution inside the sample. We propose that this barrier leads to a phase separation creating distinct population of vortices viz., those pinned on blind holes and those confined in the interstitials between the holes.
Theoretical proposals for spin ice analogs based on nanostructured superconductors have suggested larger flexibility for probing the effects of fluctuations and disorder than in the magnetic systems. In this work, we unveil the particularities of a vortex ice system by direct observation of the vortex distribution in a kagome lattice of paired antidots using scanning Hall probe microscopy. The theoretically suggested vortex ice distribution, lacking long range order, is observed at half matching field (H_{1}/2). Moreover, the vortex ice state formed by the pinned vortices is still preserved at…
The influence of a periodic landscape of pinning sites on the vortex dynamics in Pb thin films is explored by ac-susceptibility measurements. For different amplitudes h of the ac-drive, the ac-susceptibility x=x'+ix'' exhibits a complex field dependence associated with different dynamic regimes. At very low ac-drives where both, multiquanta vortices trapped by the antidots and interstitial vortices oscillate inside the pinning potential (intra-valley motion), a small kink in x'(H) together with a very low dissipation is observed. At intermediate ac-excitations such that vortices in the antidot…
We explore the dynamic response of vortex lines in a Pb thin film with a periodic array of antidots by means of ac-susceptibility measurements. For low drive field amplitudes, within the Campbell regime, vortex motion is of intra-valley type and the penetration depth is related to the curvature of the pinning potential well, $α$. For dc-fields below the first matching field $H_1$, $α$ reaches its highest value associated with a Mott Insulator-like phase where vortex lines are strongly localized at the pinning sites. For $H_1<H_{dc}<H_2$, the response is mainly due to the interstitial vortices …
Studies with mesoscopic superconducting materials have made significant advances on the last decades. One of the applications of such systems is in devices for single photon and single electron detectors. However, depending on the geometry of these systems, crowding current effects take place and, as a consequence, the total critical current could decrease which facilitates the penetration of vortices. This effect could also be responsible for a variety of penetration morphologies of flux avalanches in macroscopic samples. Thus, in this work we used the time-dependent Ginzburg-Landau theory to…
Moving vortex matter, driven by transport currents independent of time, in which vortices and anti-vortices coexist is investigated theoretically in thin superconducting films with nanostructured defects. A simple London model is proposed for the vortex dynamics in films with periodic arrays of nanomagnets or cylindrical holes (antidots). Common to these films is that vortex anti-vortex pairs may be created in the vicinity of the defects by relatively small transport currents, because it adds to the current generated by the defects - the nanomagnets screening current, or the antidots backflow …
The vortex ratchet effect has been studied in Al films patterned with square arrays of submicron antidots. We have investigated the transport properties of two sets of samples: (i) asymmetrical antidots where vortices are driven by an unbiased ac current, and (ii) symmetrical antidots where in addition to the ac drive a dc bias was used. For each sample, the rectified (dc) voltage is measured as a function of drive amplitude and frequency, magnetic field, and temperature. As unambiguously shown by our data, the voltage rectification in the asymmetric antidots is induced by the intrinsic asymme…
We have measured the in-plane anisotropy of the vortex mobility in a thin Pb film with a square array of antidots. The Lorentz force, acting on the vortices, was rotated by adding two perpendicular currents and keeping the amplitude of the net current constant. One set of voltage probes was used to detect the vortex motion. We show that the pinning landscape provided by the square antidot lattice influences the vortex motion in two different ways. First, the modulus of the vortex velocity becomes angular dependent with a lower mobility along the diagonals of the pinning array. Second, the vort…
Using the non-linear Ginzburg-Landau (GL) theory, we obtain the possible vortex configurations in superconducting thin films containing a square lattice of antidots. The equilibrium structural phase diagram is constructed which gives the different ground-state vortex configurations as function of the size and periodicity of the antidots for a given effective GL parameter $κ^{*}$. Giant-vortex states, combination of giant- and multi-vortex states, as well as symmetry imposed vortex-antivortex states are found to be the ground state for particular geometrical parameters of the sample. The antido…
We experimentally investigate the magnetic field $B$ dependence of the critical current I_c and the transition temperature T_c, i.e. the I_c(B)-T_c(B) phase boundary, of superconducting niobium thin films patterned with periodic and quasiperiodic antidot arrays on the submicron scale. For this purpose we monitor current-voltage characteristics at different values of B and T. We investigate samples with antidots positioned at the vertices of two different tilings with quasiperiodic symmetry, namely the Shield Tiling and the Tuebingen Triangle Tiling. For reference we investigate a sample with a…
In order to compare magnetic and non-magnetic pinning we have nanostructured two superconducting films with regular arrays of pinning centers: Cu (non-magnetic) dots in one case, and Py (magnetic) dots in the other. For low applied magnetic fields, when all the vortices are pinned in the artificial inclusions, magnetic dots prove to be better pinning centers, as has been generally accepted. Unexpectedly, when the magnetic field is increased and interstitial vortices appear, the results are very different: we show how the stray field generated by the magnetic dots can produce an effective reduc…
The operation of superconducting coplanar waveguide cavities, as used for circuit quantum electrodynamics and kinetic inductance detectors, in perpendicular magnetic fields normally leads to a reduction of the device performance due to energy dissipating Abrikosov vortices. We experimentally investigate the vortex induced energy losses in such Nb resonators with different spatial distributions of micropatterned pinning sites (antidots) by transmission spectroscopy measurements at 4.2 K. In comparison to resonators without antidots we find a significant reduction of vortex induced losses and th…
We examine the melting of commensurate and incommensurate vortex lattices interacting with square pinning arrays through the use of numerical simulations. For weak pinning strength in the commensurate case we observe an order-order transition from a commensurate square vortex lattice to a triangular floating solid phase as a function of temperature. This floating solid phase melts into a liquid at still higher temperature. For strong pinning there is only a single transition from the square pinned lattice to the liquid state. For strong pinning in the incommensurate case, we observe a multi-st…
We study the pinning of vortices in thin film superconductors by magnetic dots in the London approximation. A single dot is in general able to pin multiple field-induced vortices, up to a saturation number n_s, which can be much larger than one. However, the magnetic field of the dot also creates intrinsic vortices and anti-vortices, which must be accounted for. In a ferromagnetic dot array, the intrinsic anti-vortices are pinned only interstitially. Much stronger pinning effect is expected of an antiferromagnetic dot array. Possible realizations of various magnetic configurations are discusse…
We show using simulations that when interstitial vortices are present in superconductors with periodic pinning arrays, the transport in two perpendicular directions can be anisotropic. The degree of the anisotropy varies as a function of field due to the fact that the interstitial vortex lattice has distinct orderings at different matching fields. The anisotropy is most pronounced at the matching fields but persists at incommensurate fields, and it is most prominent for triangular, honeycomb, and kagome pinning arrays. Square pinning arrays can also show anisotropic transport at certain fields…
We examine Shapiro steps for vortex lattices interacting with periodic pinning arrays driven by AC and DC currents. The vortex flow occurs by the motion of the interstitial vortices through the periodic potential generated by the vortices that remain pinned at the pinning sites. Shapiro steps are observed for fields B_ϕ < B < 2.25B_ϕ with the most pronouced steps occuring for fields where the interstitial vortex lattice has a high degree of symmetry. The widths of the phase-locked current steps as a function of the magnitude of the AC driving are found to follow a Bessel function in agreement …
The dynamics of the annihilation of a vortex-antivortex pair is investigated. The pair is activated magnetically during the run of a simulated hysteresis loop on a square mesoscopic superconducting cylinder with an antidot inserted at its center. We study the nucleation of vortices and antivortices by first increasing the magnetic field, applied parallel to the axis of the sample, from zero until the first vortex is created. A further increase of the field pulls the vortex in, until it reaches the antidot. As the polarity of the field is reversed, an antivortex enters the scene, travels toward…
The pre-melting of high vortex density planes observed recently in layered superconductors in tilted magnetic field is explained theoretically. Based on the structural information of the crossing lattices of pancake and Josephson vortices the effective vortex cage potential at different lattice sites is determined numerically. Melting takes place when the thermal energy allows proliferation of vacancy-interstitial pairs. It is found that the increased density of pancake vortex stacks in the planes containing Josephson vortices, rather than their incommensurate structure, is the main cause for …
We report robust vortex matching effects in antidot arrays fabricated on thin films of NbN. The near absence of hysteresis between field sweep directions indicates a negligible residual pinning in the host thin film. Owing to the very small coherence length of NbN thin films ($ξ< 5 nm$), the observations suggests the possibility of probing physics of vortices at true nanometer length scales in suitably fabricated structures.
A conformal pinning array can be created by conformally transforming a uniform triangular pinning lattice to produces a new structure in which the six-fold ordering of the original lattice is conserved but where there is a spatial gradient in the density of pinning sites. Here we examine several aspects of vortices interacting with conformal pinning arrays and how they can be used to create a flux flow diode effect for driving vortices in different directions across the arrays. Under the application of an ac drive, a pronounced vortex ratchet effect occurs where the vortices flow in the easy d…
Using numerical simulations we study the configurations, dynamics, and melting properties of vortex lattices interacting with elliptical pinning sites at integer matching fields with as many as 27 vortices per pin. Our pinning model is based on a recently produced experimental system [G. Karapetrov et al., Phys. Rev. Lett. 95, 167002 (2005)], and the vortex configurations we obtain match well with experimental vortex images from the same system. We find that the strong pinning sites capture more than one vortex each, and that the saturation number of vortices residing in a pin increases with a…
In topological insulators doped with magnetic ions, spin-orbit coupling and ferromagnetism give rise to the quantum anomalous Hall effect. Here we show that in s-wave superconductors with strong spin-orbit coupling, magnetic impurity ions can generate topological vortices in the absence of external magnetic fields. Such vortices, dubbed quantum anomalous vortices, support robust Majorana zero-energy modes when superconductivity is induced in the topological surface states. We demonstrate that the zero-energy bound states observed in Fe(Te,Se) superconductors are possible realizations of the Ma…
A direct visualization of the flux distribution in a Pb film covering a five-fold Penrose array of Co dots is obtained by mapping the local field distribution with a scanning Hall probe microscope. We demonstrate that stable vortex configurations can be found for fields H~0.8H_1, H_1 and 1.6H_1, where H_1 corresponds to one flux quantum per pinning site. The vortex pattern at 0.8H_1 corresponds to one vacancy in one of the vertices of the thin tiles whereas at 1.6H_1 the vortex structure can be associated with one interstitial vortex inside each thick tile. Strikingly, for H=1.6H_1 interstitia…
We show that under an a.c. magnetic field excitation the vortex lattice in a superconductor with periodic array of holes can undergo a transition from a Mott-like state where each vortex is localized in a hole, to a metal-like state where the vortices get delocalized. The vortex dynamics is studied through the magnetic shielding response which is measured using a low frequency two-coil mutual inductance technique on a disordered superconducting NbN film having periodic array of holes. We observe that the shielding response of the vortex state is strongly dependent on the amplitude of the a.c. …
We show using numerical simulations that vortices in honeycomb pinning arrays can exhibit a remarkable variety of dynamical phases that are distinct from those found for triangular and square pinning arrays. In the honeycomb arrays, it is possible for the interstitial vortices to form dimer or higher n-mer states which have an additional orientational degree of freedom that can lead to the formation of vortex molecular crystals. For filling fractions where dimer states appear, a novel dynamical symmetry breaking can occur when the dimers flow in one of two possible alignment directions. This l…
Vortex-antivortex arrays that are created in a type-II superconducting film by lattices of ferromagnetic dots with perpendicular anisotropy have been investigated. The highest critical current is shifted to a nonzero value of the applied field, and current-voltage characteristics show different regimes of vortex motion even in zero-applied field due to the presence of the vortex-antivortex arrays. Creep of interstitial vortices is observed at low driving forces. This flux creep is strongly field-polarity dependent.
A conformal transformation of a uniform triangular pinning array produces a structure called a conformal crystal which preserves the six-fold ordering of the original lattice but contains a gradient in the pinning density. Here we use numerical simulations to show that vortices in type-II superconductors driven with an ac drive over gradient pinning arrays produce the most pronounced ratchet effect over a wide range of parameters for a conformal array, while square gradient or random gradient arrays with equivalent pinning densities give reduced ratchet effects. In the conformal array, the lar…
FeSeTe has recently emerged as a leading candidate material for the two-dimensional topological superconductivity (TSC). Two reasons for the excitement are the high $T_c$ of the system and the fact that the Majorana zero modes (MZMs) inside the vortex cores live on the exposed surface rather than at the interface of a heterostructure as in the proximitized topological insulators. However, the recent scanning tunneling spectroscopy data have shown that, contrary to the theoretical expectation, the MZM does not exist inside every vortex core. Hence there are ``full'' vortices with MZMs and ``emp…
The critical current and melting temperature of a vortex system are analyzed. Calculations are made for a two dimensional film at finite temperature with two kinds of periodic pinning: hexagonal and Kagomé. A transport current parallel and perpendicular to the main axis of the pinning arrays is applied and molecular dynamics simulations are used to calculate the vortex velocities to obtain the critical currents. The structure factor and displacements of vortices at zero transport current are used to obtain the melting temperature for both pinning arrays. The critical currents are higher for th…
We study the transport of vortices excited by an ac current in an Al film with an array of nanoengineered asymmetric antidots. The vortex response to the ac current is investigated by detailed measurements of the voltage output as a function of ac current amplitude, magnetic field and temperature. The measurements revealed pronounced voltage rectification effects which are mainly characterized by the two critical depinning forces of the asymmetric potential. The shape of the net dc voltage as a function of the excitation amplitude indicates that our vortex ratchet behaves in a way very differe…
Using numerical simulations, we investigate vortex configurations and pinning in superconductors with honeycomb and kagome pinning arrays. We find that a variety of novel vortex crystal states can be stabilized at integer and fractional matching field densities. The honeycomb and kagome pinning arrays produce considerably more pronounced commensuration peaks in the critical depinning force than triangular pinning arrays, and also cause additional peaks at noninteger matching fields where a portion of the vortices are located in the large interstitial regions of the pinning lattices. For the ho…
We show that a remarkable variety of dynamical phenomena, including switching, polarization, symmetry locking, and dynamically induced pinning, can occur for vortices in type-II superconductors in the presence of a honeycomb pinning array and an ac or combined ac and dc drive. These effects occur at the second matching field where there are two vortices per pinning site, and arise due to the formation of vortex dimer states in the interstitial regions of the honeycomb array. The orientation of the pinned and moving vortex dimers can be controlled externally by the application of a drive. We te…
Using large-scale simulations on parallel processors, we analyze in detail the dynamical behavior of superconducting vortices undergoing avalanches. In particular, we quantify the effect of the pinning landscape on the macroscopic properties of vortex avalanches and vortex plastic flow. These dynamical instabilities are triggered when the external magnetic field is increased slightly, and are thus driven by a flux gradient rather than by thermal effects. The flux profiles, composed of rigid flux lines that interact with 100 or more vortices, are maintained in the Bean critical state and do not…
We analyze transverse phase locking for vortex motion in a superconductor with a longitudinal DC drive and a transverse AC drive. For both square and triangular arrays we observe a variety of fractional phase locking steps in the velocity versus DC drive which correspond to stable vortex orbits. The locking steps are more pronounced for the triangular arrays which is due to the fact that the vortex motion has a periodic transverse velocity component even for zero transverse AC drive. All the steps increase monotonically in width with AC amplitude. We confirm that the width of some fractional s…
