In a micro ring of a superconductor with a spin-triplet equal-spin pairing state, a fluxoid, a combined object of magnetic flux and circulating supercurrent, can penetrate as half-integer multiples of the flux quantum. A candidate material to investigate such half-quantum fluxoids is Sr$_\mathsf{2}$RuO$_\mathsf{4}$. We fabricated Sr$_\mathsf{2}$RuO$_\mathsf{4}$ micro rings using single crystals and measured their resistance behavior under magnetic fields controlled with a three-axes vector magnet. Proper Little-Parks oscillations in the magnetovoltage as a function of an axially applied field, associated with fluxoid quantization are clearly observed, for the first time using bulk single crystalline superconductors. We then performed magnetovoltage measurements with additional in-plane magnetic fields. By carefully analyzing both the voltages $V_+$ ($V_-$) measured at positive (negative) current, we find that, above an in-plane threshold field of about 10 mT, the magnetovoltage maxima convert to minima. We interpret this behavior as the peak splitting expected for the half-quantum fluxoid states.
We have measured the dynamics of individual magnetic fluxoids entering and leaving photolithographically patterned thin film rings of the underdoped high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, using a variable sample temperature scanning SQUID microscope. These results can be qualitatively described using a model in which the fluxoid number changes by thermally activated nucleation of a Pearl vortex in, and transport of the Pearl vortex across, the ring wall.
We have measured the dynamics of individual magnetic fluxoids entering and leaving thin film, photolithographically patterned rings of underdoped high-temperature superconductor BSCCO using a variable sample temperature scanning SQUID microscope. These measurements can be understood within a phenomenological model in which the fluxoid number changes by thermal activation of a Pearl vortex in the ring wall. We place upper limits on the "vison" binding energy in these samples from these measurements.
We have observed spontaneous fluxoid generation in thin-film rings of the amorphous superconductor Mo$_3$Si, cooled through the normal-superconducting transition, as a function of quench rate and externally applied magnetic field, using a variable sample temperature scanning SQUID microscope. Our results can be explained using a model of freezout of thermally activated fluxoids, mediated by the transport of bulk vortices across the ring walls. This mechanism is complementary to a mechanism proposed by Kibble and Zurek, which only relies on causality to produce a freezout of order parameter flu…
We present the first measurements of thermal signatures of the Little-Parks effect using a highly sensitive nanocalorimeter. Small variations of the heat capacity $C\_p$ of 2.5 millions of non interacting micrometer-sized superconducting rings threaded by a magnetic flux $Φ$ have been measured by attojoule calorimetry. This non-invasive method allows the measurement of thermodynamic properties -- and hence the probing of the energy levels -- of nanosystems without perturbing them electrically. It is observed that $C\_p$ is strongly influenced by the fluxoid quantization (Little-Parks effect) n…
In superconductors, the condensation of Cooper pairs gives rise to fluxoid quantization in discrete units of $Φ_0 = hc / 2e$. The denominator of $2e$ is the signature of electron pairing, which is evidenced by a number of macroscopic quantum phenomena, such as the Little-Parks effect and the Josephson effect, where the critical temperature or the critical current oscillates in the period of $Φ_0$. Here we report the observation of fractional Little-Parks effect in mesoscopic rings of epitaxial $β$-Bi$_2$Pd, a topological superconductor. Besides $Φ_0$, novel Little-Parks oscillation periodiciti…
Spin-triplet superfluids can support exotic objects, such as half-quantum vortices characterized by the nontrivial winding of the spin structure. We present cantilever magnetometry measurements performed on mesoscopic samples of Sr2RuO4, a spin-triplet superconductor. For micron-sized annular-shaped samples, we observe transitions between integer fluxoid states, as well as a regime characterized by "half-integer transitions," i.e., steps in the magnetization with half the height of the ones we observe between integer fluxoid states. These half-height steps are consistent with the existence of …
When a thin-film ring with supercurrent is irradiated by coherent microwave field, the field induces coherent oscillations of all the Cooper pairs involved in the supercurrent. The oscillating charged condensate will emit photons with energies determined by the difference of quantized energy levels of the superconducting ring. This effect can be observed only in the rings, the thickness of which is less than both the field skin-depth and the London penetration depth. The probability of the microwave field-induced single-photon and two-photon emission is calculated. The energy - angle distribut…
We present a scanning probe technique for measuring the dynamics of individual fluxoid transitions in multiply connected superconducting structures. In these measurements, a small magnetic particle attached to the tip of a silicon cantilever is scanned over a micron-size superconducting ring fabricated from a thin aluminum film. We find that near the superconducting transition temperature of the aluminum, the dissipation and frequency of the cantilever changes significantly at particular locations where the tip-induced magnetic flux penetrating the ring causes the two lowest-energy fluxoid sta…
It is shown that currents in thin-film superconducting rings irradiated by coherent microwave fields, can discretely decay with photons emission. These quantized jumps of the supercurrent correspond to destruction one or several magnetic flux quanta trapped in the ring. The ring thickness should be less than the skin-depth of the low-frequency field. The probability of the microwave field-induced single-photon decay of the supercurrent states in these rings is obtained. The angle distributions of the photons emitted by superconducting rings, and the current state lifetimes, depending on the ri…
The properties of single submicron high-temperature superconductor (HTS) rings are investigated. The Little-Parks effect is observed and is accompanied by an anomalous behavior of the magnetic dependence of the resistance, which we ascribe to non-uniform vorticity (superfluid angular momentum) within the ring arms. This effect is linked to the peculiar HTS-relationship between the values of the coherence length and the London penetration depth.
Superconducting current instability in thin rings, irradiated by a coherent microwave electromagnetic field, is studied. On the regular circular motion of the Cooper pairs in the supercurrent states the field imposes coherent oscillations of the condensate as a whole. The oscillating condensate should emit photons with the energies determined mainly by the discrete values of the superconducting ring energy. For the first time the probability of the supercurrent decay accompanied by the two- photon emission, is derived. The ring thickness is less than both the field skin-depth and the London pe…
The intense search for topological superconductivity is inspired by the prospect that it hosts Majorana quasiparticles. We explore in this work the optimal design for producing topological superconductivity by combining a quantum Hall state with an ordinary superconductor. To this end, we consider a microscopic model for a topologically trivial two-dimensional p-wave superconductor exposed to a magnetic field, and find that the interplay of superconductivity and Landau level physics yields a rich phase diagram of states as a function of $μ/t$ and $Δ/t$, where $μ$, $t$ and $Δ$ are the chemical …
A critical power dissipation resulting from an oscillating magnetic field, Hp cos wt, can produce a magnetic breakdown field, H <Hc, the critical field of the superconductor. The analysis shows, for example, why the breakdown field of a superconducting microwave cavity can be well below Hc in some cases, and indicates what the functional dependence of the cavity Q may be for values of Hp near H . The effective resistivity of a single isolated oscillating fluxoid, as well as that of a stationary normal region, is also derived for both type I and type Il superconductors.
We investigate the nucleation of superconductivity in a uniform perpendicular magnetic field H in aluminum microsquares containing a few (2 and 4) submicron holes (antidots). The normal/superconducting phase boundary T_c(H) of these structures shows a quite different behavior in low and high fields. In the low magnetic field regime fluxoid quantization around each antidot leads to oscillations in T_c(H), expected from the specific sample geometry, and reminiscent of the network behavior. In high magnetic fields, the T_c(H) boundaries of the perforated and a reference non-perforated microsquare…
The experimental investigation of the $I_c(B)$--$T_c(B)$ phase boundary of superconducting niobium films with large area quasihexagonal hole arrays is reported. The hole arrays were patterned with microsphere photolithography. We investigate the perforated niobium films by means of electrical directed current transport measurements close to the transition temperature $T_c$ in perpendicularly applied magnetic fields. We find pronounced modulations of the critcal current with applied magnetic field, which we interpret as a consequence of commensurable states between the Abrikosov vortex lattice …
As a function of the magnetic flux threading the object, the Little-Parks oscillation in the critical temperature of a large-radius, thin-walled superconducting ring or hollow cylinder has a period given by $h/2e$, due to the binding of electrons into Cooper pairs. On the other hand, the single-electron Aharonov-Bohm oscillation in the resistance or persistent current for a clean (i.e. ballistic) normal-state system having the same topological structure has a period given by $h/e$. A basic question is whether the Little-Parks oscillation changes its character, as the radius of the superconduct…
It has been shown [1] that many seemingly contradictory experimental findings concerning the superconducting state in Sr$_2$RuO$_4$ can be accounted for as resulting from the existence of an assumed tetra-critical point at near ambient pressure at which $d_{x^2-y^2}$ and $g_{xy(x^2-y^2)}$ superconducting states are degenerate. We perform both a Landau-Ginzburg and a microscopic mean-field analysis of the effect of spatially varying strain on such a state. In the presence of finite $xy$ shear strain, the superconducting state consists of two possible symmetry-related time-reversal symmetry (TRS…
We report results of our low-temperature magneto electric transport measurements on micron-sized short cylinders of odd-parity, spin-triplet superconductor Sr$_2$RuO$_4$ with the cylinder axis along the $c$ axis. The in-plane magnetic field and measurement current dependent magnetoresistance oscillations were found to feature an amplitude much larger than that expected from the conventional Little-Parks effect, suggesting that the magnetoresistance oscillations originate from vortex crossing. The free-energy barrier that controls the vortex crossing was modulated by the magnetic flux enclosed …
