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Alex Gurevich

Publications and source records attributed to Alex Gurevich.

At least 19 recordsLinked to original sources

Superheating Field of Extreme Type-II Superconductors Calculated from the Eliashberg Theory

We calculate the superheating field $H_s$ of a type-II superconductor with a large Ginzburg-Landau parameter from the isotropic Eliashberg theory. It is shown that the temperature dependencies of $H_s(T)$ can be obtained from a thermodynamic approach for different scattering parameters $p=\hbar/2\pi\tau_Nk_BT_c$ in a wide range of the nonmagnetic impurity scattering times $\tau_N$ ranging from the clean $(p\ll 1)$ to the dirty $(p\gg 1)$ limits. Specific calculations were done for Nb and Nb$_3$Sn using their electron-phonon spectral functions extracted from tunneling measurements. We show that the ratio $H_s(T,p)/H_c(T)$ calculated from the Eliashberg theory exceeds that of the weak coupling BCS model, where $H_c$ is the thermodynamic magnetic field. We also show that, even though nonmagnetic impurities are pairbreakers in the current-carrying state, $H_s(0,p)$ for Nb$_3$Sn at $T=0$ has a maximum at $p\approx 0.2$ at which the ratio $H_s/H_c$ is about $6\%$ higher than that in the BCS clean limit.

cond-mat.supr-con

Tuning current flow in superconducting thin film strips by control wires. Applications to single photon detectors and diodes

It is shown that integration of a thin film superconducting strip with current-carrying control wires enables one to engineer a profile of supercurrent density $J(x)$ with no current crowding at the edges of a strip wider than the magnetic Pearl length $\Lambda$. Moreover, $J(x)$ in a strip can be tuned by control wires to produce an inverted $J(x)$ profile with dips at the edges to mitigate current crowding at lithographic defects and block premature penetration of vortices. These conclusions are corroborated by calculations of $J(x)$ in a thin strip coupled inductively with side control wires or in bilayer strip structures by solving the London and Ginzburg Landau equations in the thin film Pearl limit. Thermally-activated penetration of vortices from the edges and unbinding of vortex-antivortex pairs in inverted $J(x)$ profiles are evaluated. It is shown that these structures can be used to develop single-photon strip detectors much wider than $\Lambda$. Such detectors can be tuned {\it in situ} by varying current in control wires to reach the ultimate photon sensitivity limited by unbinding of vortex-antivortex pairs. The structures considered here exhibit a non-reciprocal current response and behave as superconducting diodes. They can also be used to study the physics of vortex matter in thin films not masked by penetration of vortices from the edges.

cond-mat.supr-con

Reaching the intrinsic performance limits of superconducting nanowire single-photon detectors up to 0.1 mm wide

Superconducting nanowire single-photon detectors (SNSPDs) combine high detection efficiency, low noise, and excellent timing resolution, making them a leading platform for photon-counting applications. However, despite decades of materials and fabrication research, detector performance has never been shown to match theoretical performance expectations. Here, we demonstrate for the first time in situ tuning of a detector from its typical, suboptimal operation, to a regime limited only by material quality, allowing the device to reach its intrinsic performance limit. Our approach is based on current-biased superconducting "rails" placed on either side of the detector that redistribute current across its width to achieve its peak performance. This technique reduces the dark count rate by ten orders of magnitude. Further, we show operation at this intrinsic performance limit for devices up to 0.1 mm wide, and also demonstrate near-unity internal detection efficiency (IDE) at a wavelength of 4um for a 20um-wide detector--a factor of 20 wider than the current state of the art. This work enables future detectors to overcome the Pearl limit for device width, paving the way for arbitrarily large detectors.

cond-mat.supr-con

Superradiant emission stimulated by vortex-antivortex pair production in layered superconductors

We report numerical simulations of coupled sine-Gordon and heat diffusion equations describing dynamic states stimulated by a trapped vortex driven by dc current in a stack of up to $N=321$ Josephson junctions. It is shown that the Cherenkov wake behind the vortex shuttle trapped in the stack can trigger proliferation of counter-propagating vortices and antivortices which get synchronized and form large-amplitude standing electromagnetic waves. This happens if the dc current density $J$ exceeds a threshold value $J_s$ which can be well below the Josephson interlayer critical current density $J_c$ for underdamped junctions. The cavity modes stimulated by the vortex-antivortex pair production cause peaks in the radiated power $P_N(J)$ with a nearly monochromatic spectrum at discrete values of $J$ corresponding to the zero-field Fiske resonances. The power $P_N(J)$ was evaluated for small rectangular stacks in the magneto-dipole approximation and for large stacks in a single mode state. For small stacks, the highest peak in $P_N(J)$ increases rapidly, $P_N\propto N^6$, with the number of junctions at $N\leq 81$ and gradually slows down to $P_N\propto N^2$ at $161\leq N\leq 321$. For stacks larger than the radiated wavelength, we obtained $P_N\propto N^5$ at $N\lesssim 200-300$ and $P_N\propto N^2$ at larger $N$. For stacks with up to $321$ junctions and representative parameters of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, we observed moderate overheating and no hotspots. The vortex-antivortex pair production can amplify THz radiation from Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ mesas for which trapping Josephson vortices could be used to stimulate THz emission at subcritical currents and optimize the radiation output.

cond-mat.supr-con

Tuning microwave losses in superconducting resonators

Performance of superconducting resonators, particularly cavities for particle accelerators and micro cavities and thin film resonators for quantum computations and photon detectors has been improved substantially by recent materials treatments and technological advances. As a result, the niobium cavities have reached the quality factors $Q\sim 10^{11}$ at 1-2 GHz and 1.5 K and the breakdown radio-frequency (rf) fields $H$ close to the dc superheating field of the Meissner state. These advances raise the question whether the state-of-the-art cavities are close to the fundamental limits, what these limits actually are, and to what extent the $Q$ and $H$ limits can be pushed by the materials nano structuring and impurity management. These issues are also relevant to many applications using high-Q thin film resonators, including single-photon detectors and quantum circuits. This topical review outlines basic physical mechanisms of the rf nonlinear surface impedance controlled by quasiparticles, dielectric losses and trapped vortices, as well as the dynamic field limit of the Meissner state. Sections cover ways of engineering an optimum quasiparticle density of states and superfluid density to reduce rf losses and kinetic inductance by pairbreaking mechanisms related to magnetic impurities, rf currents, and proximity-coupled metallic layers at the surface. A section focuses on mechanisms of residual surface resistance which dominates rf losses at ultra low temperatures. Microwave losses of trapped vortices and their reduction by optimizing the concentration of impurities and pinning potential are also discussed.

cond-mat.supr-con

Challenges and opportunities of srf theory for next generation particle accelerators

We suggest a program to establish theoretical performance limits of srf cavities using modern theories of nonequilibrium superconductivity under a strong electromagnetic field. These theories will be used to calculate the main parameter of merit of srf cavities: the quality factor Q and its dependencies on the field amplitude, temperature and frequency, which would allow us to understand how far the srf cavity performance could be pushed from the current state of the art. Given that the quality factor is determined by multiple mechanisms operating on very different length scales, we will address the interconnected problems of a nonlinear surface resistance, rf losses of vortices trapped in the cavity, the effect of materials defects and surface topography, and the opportunities to boost the srf performance by surface nano-structuring, impurity management and multilayers. We suggest the following directions of theoretical srf research to address the goals of boosting the performance of the next generation particle accelerators: 1. Establishing the Q limit, mechanisms of nonlinear surface resistance and the residual resistance in a nonequilibrium superconductor under a strong RF field. 2. Establishing the srf breakdown field limit, dynamic superheating field and its dependencies on frequency, temperature and concentration of impurities. 3. Losses due to trapped vortices and extreme dynamics of ultrafast vortices driven by strong rf Meissner currents in srf cavities. 4. Optimization of srf performance due to surface nanostructuring of the cavity surface, multilayers and impurity management.

physics.acc-ph

Dynamic pair-breaking current, critical superfluid velocity and nonlinear electromagnetic response of nonequilibrium superconductors

We report numerical calculations of a dynamic pairbreaking current density $J_d$ and a critical superfluid velocity $v_d$ in a nonequilibrium superconductor carrying a uniform, large-amplitude ac current density $J(t)=J_a\sin\Omega t$ with $\Omega$ well below the gap frequency $\Omega\ll \Delta_0/\hbar$. The dependencies $J_d(\Omega,T)$ and $v_d(\Omega,T)$ near the critical temperature $T_c$ were calculated from either the full time-dependent nonequilibrium equations for a dirty s-wave superconductor and the time-dependent Ginzburg-Landau (TDGL) equations for a gapped superconductor, taking into account the GL relaxation time of the order parameter $\tau_{GL}$ and the inelastic electron-phonon relaxation time of quasiparticles $\tau_E$. We show that both approaches give similar frequency dependencies of $J_d(\Omega)$ and $v_d(\Omega)$ which gradually increase from their static pairbreaking GL values $J_c$ and $v_c$ at $\Omega\tau_E\ll 1$ to $\sqrt{2}J_c$ and $\sqrt{2}v_c$ at $\Omega\tau_E\gg 1$. Here $J_d$, $v_d$ and a dynamic superheating field at which the Meissner state becomes unstable were calculated in two different regimes of a fixed ac current and a fixed ac superfluid velocity induced by the applied ac magnetic field $H=H_a\sin\Omega t$ in a thin superconducting filament or a type-II superconductor with a large GL parameter. We also calculated a nonlinear electromagnetic response of a nonequilibrium superconducting state, particularly a dynamic kinetic inductance and a dissipative quasiparticle conductivity, taking into account the oscillatory dynamics of superconducting condensate and the kinetics of quasiparticles driven by a strong ac current. It is shown that an ac current density produces multiple harmonics of the electric field, the amplitudes of the higher-order harmonics diminishing as $\tau_E$ increases.

cond-mat.supr-con

Superconductivity in La$_2$Ni$_2$In

We report here the properties of single crystals of La$_2$Ni$_2$In. Electrical resistivity and specific heat measurements concur with the results of Density Functional Theory (DFT) calculations, finding that La$_{2}$Ni$_{2}$In is a weakly correlated metal, where the Ni magnetism is almost completely quenched, leaving only a weak Stoner enhancement of the density of states. Superconductivity is observed at temperatures below 0.9$\,$K. A detailed analysis of the field and temperature dependencies of the resistivity, magnetic susceptibility, and specific heat at the lowest temperatures reveals that La$_2$Ni$_2$In is a dirty type-II superconductor with likely s-wave gap symmetry. Nanoclusters of ferromagnetic inclusions significantly affect the subgap states resulting in a non-exponential temperature dependence of the specific heat $C(T)$ at $T\ll T_\text{c}$.

cond-mat.supr-con

Field-dependent nonlinear surface resistance and its optimization by surface nano-structuring in superconductors

We propose a theory of nonlinear surface resistance of a dirty superconductor in a strong radio-frequency (RF) field, taking into account magnetic and nonmagnetic impurities, finite quasiparticle lifetimes, and a thin proximity-coupled normal layer characteristic of the oxide surface of many materials. The Usadel equations were solved to obtain the quasiparticle density of states (DOS) and the low-frequency surface resistance $R_s$ as functions of the RF field amplitude $H_0$. It is shown that the interplay of the broadening of the DOS peaks and a decrease of a quasiparticle gap caused by the RF currents produces a minimum in $R_s(H_0)$ and an extended rise of the quality factor $Q(H_0)$ with the RF field. Paramagnetic impurities shift the minimum in $R_s(H_0)$ to lower fields and can reduce $R_s(H_0)$ in a wide range of $H_0$. Subgap states in the DOS can give rise to a residual surface resistance while reducing $R_s$ at higher temperatures. A proximity-coupled normal layer at the surface can shift the minimum in $R_s(H_0)$ to either low and high fields and can reduce $R_s$ below that of an ideal surface. The theory shows that the behavior of $R_s(H_0)$ changes as the temperature and the RF frequency are increased, and the field dependence of $Q(H_0)$ can be very sensitive to the materials processing. Our results suggest that the nonlinear RF losses can be minimized by tuning pairbreaking effects at the surface using impurity management or surface nanostructuring.

cond-mat.supr-con

Instability of flux flow and production of vortex-antivortex pairs by current-driven Josephson vortices in layered superconductors

We report numerical simulations of the nonlinear dynamics of Josephson vortices driven by strong dc currents in layered superconductors. Dynamic equations for interlayer phase differences in a stack of coupled superconducting layers were solved to calculate a drag coefficient $\eta(J)$ of the vortex as a function of the perpendicular dc current density $J$. It is shown that Cherenkov radiation produced by a moving vortex causes significant radiation drag increasing $\eta(v)$ at high vortex velocities $v$ and striking instabilities of driven Josephson vortices moving faster than a terminal velocity $v_c$. The steady-state flux flow breaks down at $v>v_c$ as the vortex starts producing a cascade of expanding vortex-antivortex pairs evolving into either planar macrovortex structures or branching flux patterns propagating both along and across the layers. The pair production triggered by a rapidly moving vortex is most pronounced in a stack of underdamped planar junctions where it can occur at $J>J_s$ well below the interlayer Josephson critical current density. Both $v_c$ and $J_s$ were calculated as functions of the quasiparticle damping parameter, and the dc magnetic field applied parallel to the layers. The effects of vortex interaction on the Cherenkov instability of moving vortex chains and lattices in annular stacks of Josephson junctions were considered. It is shown that a vortex driven by a current density $J>J_s$ in a multilayer of finite length excites self-sustained large-amplitude standing waves of magnetic flux, resulting in temporal oscillations of the total magnetic moment. We evaluated a contribution of this effect to the power $W$ radiated by the sample and showed that $W$ increases strongly as the number of layers increases.

cond-mat.supr-con

Flux expulsion in niobium superconducting radio-frequency cavities of different purity and essential contributions to the flux sensitivity

Magnetic flux trapped during the cooldown of superconducting radio-frequency cavities through the transition temperature due to incomplete Meissner state is known to be a significant source of radio-frequency losses. The sensitivity of flux trapping depends on the distribution and the type of defects and impurities which pin vortices, as well as the cooldown dynamics when the cavity transitions from a normal to superconducting state. Here we present the results of measurements of the flux trapping sensitivity on 1.3 GHz elliptical cavities made from large-grain niobium with different purity for different cooldown dynamics and surface treatments. The results show that lower purity material results in a higher fraction of trapped flux and that the trapped flux sensitivity parameter $S$ is significantly affected by surface treatments but without much change in the mean free path $l$. We discuss our results within an overview of published data on the dependencies of $S(l,f)$ on $l$ and frequency $f$ using theoretical models of rf losses of elastic vortex lines driven by weak rf currents in the cases of sparse strong pinning defects and collective pinning by many weak defects. Our analysis shows how multiscale pinning mechanisms in cavities can result in a maximum in $S(l)$ similar to that observed by the FNAL and Cornell groups and how pinning characteristics can be extracted from the experimental data. Here the main contribution to $S$ come from weak pinning regions at the cavity surface, where dissipative oscillations along trapped vortices perpendicular to the surface propagate into the bulk well beyond the layer of rf screening current.

cond-mat.supr-con

Tuning vortex fluctuations and the resistive transition in superconducting films with a thin overlayer

It is shown that the temperature of the resistive transition $T_r$ of a superconducting film can be increased by a thin superconducting or normal overlayer. For instance, deposition of a highly conductive thin overlayer onto a dirty superconducting film can give rise to an "anti-proximity effect" which manifests itself in an initial increase of $T_r(d_2)$ with the overlayer thickness $d_2$ followed by a decrease of $T_r(d_2)$ at larger $d_2$. Such a nonmonotonic thickness dependence of $T_r(d_2)$ results from the interplay of the increase of a net superfluid density mitigating phase fluctuations and the suppression of the critical temperature $T_c$ due to the conventional proximity effect. This behavior of $T_r(d_2)$ is obtained by solving the Usadel equations to calculate the temperature of the Berezinskii-Kosterletz-Thouless transition, and the temperature of the resistive transition due to thermally-activated hopping of single vortices in dirty bilayers. The theory incorporates relevant materials parameters such as thicknesses and conductivities of the layers, interface contact resistance between them and the subgap quasiparticle states which affect both phase fluctuations and the proximity effect suppression of $T_c$. The transition temperature $T_r$ can be optimized by tuning the overlayer parameters, which can significantly weaken vortex fluctuations and nearly restore the mean-field critical temperature. The calculated behavior of $T_r(d_2)$ may explain the nonmonotonic dependence of $T_r(d_2)$ observed on (Ag, Au, Mg, Zn)-coated Bi films, Ag-coated Ga and Pb films or NbN and NbTiN films on AlN buffer layers. These results suggest that bilayers can be used as model systems for systematic investigations of optimization of fluctuations in superconductors.

cond-mat.supr-con

Surface impedance and optimum surface resistance of a superconductor with imperfect surface

We calculate a low-frequency surface impedance of a dirty, s-wave superconductor with an imperfect surface incorporating either a thin layer with a reduced pairing constant or a thin, proximity-coupled normal layer. Such structures model realistic surfaces of superconducting materials which can contain oxide layers, absorbed impurities or nonstoichiometric composition. We solved the Usadel equations self-consistently and obtained spatial distributions of the order parameter and the quasiparticle density of states which then were used to calculate a low-frequency surface resistance $R_s(T)$ and the magnetic penetration depth $λ(T)$ as functions of temperature in the limit of local London electrodynamics. It is shown that the imperfect surface in a single-band s-wave superconductor results in a non-exponential temperature dependence of $Z(T)$ at $T\ll T_c$ which can mimic the behavior of multiband or d-wave superconductors. The imperfect surface and the broadening of the gap peaks in the quasiparticle density of states $N(ε)$ in the bulk give rise to a weakly temperature-dependent residual surface resistance. We show that the surface resistance can be optimized and even reduced below its value for an ideal surface by engineering $N(ε)$ at the surface using pairbreaking mechanisms, particularly, by incorporating a small density of magnetic impurities or by tuning the thickness and conductivity of the normal layer and its contact resistance. The results of this work address the limit of $R_s$ in superconductors at $T\ll T_c$, and the ways of engineering the optimal density of states by surface nano-structuring and impurities to reduce losses in superconducting micro-resonators, thin film strip lines, and radio frequency cavities for particle accelerators.

cond-mat.supr-con

Dynamic transition of vortices into phase slips and generation of vortex-antivortex pairs in thin film Josephson junctions under dc and ac currents

We present theoretical and numerical investigations of vortices driven by strong dc and ac currents in long Josephson junctions described by a nonlinear integro-differential equation which takes into account nonlocal electrodynamics of films, vortex bremsstrahlung and Cherenkov radiation amplified by the attraction of vortices to the edges of the junction. The work focuses on the dynamics of vortices in Josephson junctions in thin films where the effects of Josephson nonlocality dominate but London screening is negligible. We obtained an exact solution for a vortex driven by an arbitrary time-dependent current in an overdamped junction where the vortex turns into a phase slip if the length of the junction is shorter than a critical length which depends on current. Our analytical and numerical results show that the dynamic behavior of vortices depends crucially on the ohmic damping parameter. In overdamped junctions vortices expand as they move faster and turn into phase slips as current increases. In underdamped junctions vortices entering from the edges produce Cherenkov radiation generating cascades of expanding vortex-antivortex pairs, which ultimately drive the entire junction into a resistive phase slip state. Simulations revealed a variety of complex dynamic states of vortices under dc and ac currents which can manifest themselves in hysteretic current-voltage characteristics with jumps and regions with negative differential resistance resulting from transitions from oscillating to ballistic propagation of vortices, their interaction with pinning centers and standing nonlinear waves in the junction.

cond-mat.supr-con

Anisotropic thermodynamic and transport properties of single crystalline CaKFe$_{4}$As$_{4}$

Single crystalline, single phase CaKFe$_{4}$As$_{4}$ has been grown out of a high temperature, quaternary melt. Temperature dependent measurements of x-ray diffraction, anisotropic electrical resistivity, elastoresistivity, thermoelectric power, Hall effect, magnetization and specific heat, combined with field dependent measurements of electrical resistivity and field and pressure dependent measurements of magnetization indicate that CaKFe$_{4}$As$_{4}$ is an ordered, stoichiometric, Fe-based superconductor with a superconducting critical temperature, $T_c$ = 35.0 $\pm$ 0.2 K. Other than superconductivity, there is no indication of any other phase transition for 1.8 K $\leq T \leq$ 300 K. All of these thermodynamic and transport data reveal striking similarities to that found for optimally- or slightly over-doped (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$, suggesting that stoichiometric CaKFe$_4$As$_4$ is intrinsically close to what is referred to as "optimal-doped" on a generalized, Fe-based superconductor, phase diagram. The anisotropic superconducting upper critical field, $H_{c\text{2}}(T)$, of CaKFe$_{4}$As$_{4}$ was determined up to 630 kOe. The anisotropy parameter $γ(T)=H_{c\text{2}}^{\perp}/H_{c\text{2}}^{\|}$, for $H$ applied perpendicular and parallel to the c-axis, decreases from $\simeq 2.5$ at $T_c$ to $\simeq 1.5$ at 25 K which can be explained by interplay of paramagnetic pairbreaking and orbital effects. The slopes of $dH_{c\text{2}}^{\|}/dT\simeq-44$ kOe/K and $dH_{c\text{2}}^{\perp}/dT \simeq-109$ kOe/K at $T_c$ yield an electron mass anisotropy of $m_{\perp}/m_{\|}\simeq 1/6$ and short Ginzburg-Landau coherence lengths $ξ_{\|}(0)\simeq 5.8 \textÅ$ and $ξ_{\perp}(0)\simeq 14.3 \textÅ$. The value of $H_{c\text{2}}^{\perp}(0)$ can be extrapolated to $\simeq 920$ kOe, well above the BCS paramagnetic limit.

cond-mat.supr-con

Anisotropic magnetoresistance and upper critical fields up to 63 T in CaKFe$_4$As$_4$ single crystals

We report the temperature dependencies of the upper critical fields $H_{c\text{2}}^{\text{c}}(T)$ parallel to the c-axis and $H_{c\text{2}}^{\text{ab}}(T)$ parallel to the ab-plane of single crystalline CaKFe$_4$As$_4$ inferred from the measurements of the temperature-dependent resistance in static magnetic fields up to 14 T and magnetoresistance in pulsed fields up to 63 T. We show that the observed decrease of the anisotropy parameter $γ(T)=H_{c\text{2}}^{\text{ab}}/H_{c\text{2}}^{\text{c}}$ from $\simeq 2.5$ at $T_c$ to $\simeq 1.5$ at 25 K can be explained by interplay of paramagnetic pairbreaking and orbital effects in a multiband theory of $H_{c2}$. The slopes of $dH_{c\text{2}}^{\text{c}}/dT\simeq-4.4$ T/K and $dH_{c\text{2}}^{\text{ab}}/dT \simeq-10.9$ T/K at $T_c$ yield an electron mass anisotropy of $m_{ab}/m_c\simeq 1/6$ and short coherence lengths $ξ_c\simeq 5.8\,\textÅ$ and $ξ_{ab}\simeq 14.3\,\textÅ$. The behavior of $H_{c\text{2}}(T)$ turns out to be similar to that of the optimal doped (Ba,K)Fe$_2$As$_2$, with $H_{c\text{2}}^{\text{ab}}(0)$ extrapolating to $\simeq 92$ T, well above the BCS paramagnetic limit.

cond-mat.supr-con

Fragmentation of Fast Josephson Vortices and Breakdown of Ordered States by Moving Topological Defects

Topological defects such as vortices, dislocations or domain walls define many important effects in superconductivity, superfluidity, magnetism, liquid crystals, and plasticity of solids. Here we address the breakdown of the topologically-protected stability of such defects driven by strong external forces. We focus on Josephson vortices that appear at planar weak links of suppressed superconductivity which have attracted much attention for electronic applications, new sources of THz radiation, and low-dissipative computing. Our numerical simulations show that a rapidly moving vortex driven by a constant current becomes unstable with respect to generation of vortex-antivortex pairs caused by Cherenkov radiation. As a result, vortices and antivortices become spatially separated and accumulate continuously on the opposite sides of an expanding dissipative domain. This effect is most pronounced in thin film edge Josephson junctions at low temperatures where a single vortex can switch the whole junction into a resistive state at currents well below the Josephson critical current. Our work gives a new insight into instability of a moving topological defect which destroys global long-range order in a way that is remarkably similar to the crack propagation in solids.

cond-mat.supr-con

Thermally-activated dynamics of spontaneous perpendicular vortices tuned by parallel magnetic fields in thin superconducting films

We report magneto-transport measurements on a superconducting molybdenum-germanium (MoGe) film of thickness $d$=50 nm in parallel magnetic fields and show evidence of a transition from a Meissner state to a resistive state of spontaneous perpendicular vortices generated by thermal fluctuations above a certain temperature $T>T_v(B)$. Here $T_v$ appears to match the vortex core explosion condition $d\approx 4.4ξ(T_v)$, where $ξ$ is the coherence length. For $T>T_v$, we observed that a nonlinear current-voltage ($IV$) response (Ohmic at low currents and the power law $V\propto I^β$ at higher $I$) is exponentially dependent on $B^2$. We propose a model in which the resistive state at $T>T_v$ is due to thermally-activated hopping of spontaneous perpendicular vortices tuned by the pairbreaking effect of the parallel $B$. keywords: vortex, vortices, fluxon, flux lattice, mixed state, lower critical field

cond-mat.supr-con