Phase slips are topological fluctuation events that carry the superconducting order-parameter field between distinct current carrying states 1 . Owing to these phase slips low-dimensional superconductors acquire electrical resistance 2 . In quasi-one-dimensional nanowires it is well known that at higher temperatures phase slips occur via the process of thermal barrier-crossing by the orderparameter field. At low temperatures, the general expectation is that phase slips should proceed via quantum tunnelling events, which are known as quantum phase slips (QPS). However, resistive measurements have produced evidence both pro 3-6 and con [7][8][9] and hence the precise requirements for the observation of QPS are yet to be established firmly. Here we report strong evidence for individual quantum tunnelling events undergone by the superconducting order-parameter field in homogeneous nanowires. We accomplish this via measurements of the distribution of switching currents-the high-bias currents at which superconductivity gives way to resistive behaviour-whose width exhibits a rather counter-intuitive, monotonic increase with decreasing temperature. We outline a Quantum phenomena involving systems far larger than individual atoms are one of the most exciting fields of modern physics. Initiated by Leggett more than twentyfive years ago 14,15 , the field has seen widespread development, important realizations being furnished, e. g., by macroscopic quantum tunnelling (MQT) of the phase in Josephson junctions, and of the magnetization in magnetic nanoparticles [16][17][18][19] . More recently, the breakthrough recognition of the potential advantages of quantum-based computational methods has initiated the search for viable implementations of qubits 20 , several of which are rooted in MQT in superconducting systems. In particular, it has been recently proposed that superconducting nanowires (SCNWs) could provide a valuable setting for realizing qubits 12 . In this case, the essential behaviour needed of SCNWs that they undergo QPS, i.e., topological quantum fluctuations of the superconducting order-parameter field via which tunnelling occurs between currentcarrying states. It has also been proposed that QPS in nanowires could allow one to build a current standard, and thus could play a useful role in aspects of metrology 13 .Additionally, QPS are believed to provide the pivotal processes underpinning the 3 superconductor-insulator transition observed in nanowires 21-25, Observations of QPS have been reported previously on wires having high normal resistance (i.e., R N > R Q , where R Q = h/4e 2 ≈ 6,450 Ω) via low-bias resistance (R) vs. temperature (T) measurements 3,4 . Yet, low-bias measurements on short wires with normal resistance R N < R Q have been unable to reveal QPS 7,8 . Also, it has been suggested that some results ascribed to QPS could in fact have originated in inhomogeneity of the nanowires.Thus, no consensus exists about the conditions under which QPS occur, and qualitatively new evidence for QPS remains highl...

Large sensitive-area NbN nanowire superconducting single-photon detectors fabricated on single-crystal MgO substrates Appl. Phys. Lett. 92, 061116 (2008); 10.1063/1.2870099Effect of heating rates on superconducting properties of pure MgB 2 , carbon nanotube-and nano-SiC-doped in situ MgB 2 ∕ Fe wires Continuous Nb wires, 7-15 nm in diameter, have been fabricated by sputter-coating single fluorinated carbon nanotubes. Transmission electron microscopy revealed that the wires are polycrystalline, having grain sizes of about 5 nm. The critical current of wires thicker than ϳ12 nm is very high (10 7 A/cm 2 ) and comparable to the expected depairing current. The resistance versus temperature curves measured down to 0.3 K are well described by the Langer-Ambegaokar-McCumber-Halperin theory of thermally activated phase slips. Quantum phase slips are suppressed.

The effects of strong magnetic field on superconducting Nb and MoGe nanowires with diameter ∼ 10 nm have been studied. We have found that the Langer-Ambegaokar-McCumber-Halperin (LAMH) theory of thermally activated phase slips is applicable in a wide range of magnetic fields and describes well the temperature dependence of the wire resistance, over eleven orders of magnitude. The field dependence of the critical temperature, Tc, extracted from the LAMH fits is in good quantitative agreement with the theory of pair-breaking perturbations that takes into account both spin and orbital contributions. The extracted spin-orbit scattering time agrees with an estimate τso ≃ τ ( c/Ze 2 ) 4 , where τ is the elastic scattering time and Z is the atomic number.PACS numbers: 74.78. Na, 74.25.Fy, 74.25.Ha, 74.40.+k The problem of superconductivity in one-dimensional (1D) systems attracts much attentions since it involves such fundamental phenomena as macroscopic quantum tunnelling, quantum phase transitions and environmental effects [1,2,3,4,5,6,7]. It is expected that a strong magnetic field can be used to control these phenomena. Indeed, the microscopic theory predicts that a magnetic field, acting on a superconducting condensate, lifts the time reversal symmetry of the spin and orbital states of paired electrons and suppresses the critical temperature, T c [8,9]. A strong enough field destroys superconductivity. The magnetic field pair-breaking effects were studied in depth in two and zero-dimensional systems, i.e. thin films [10] and nanograins [11]. However, an experimental verification of the pair breaking effects in 1D superconductors is long overdue.A distinct feature of 1D superconductors is the absence of the phase coherence. Due to fluctuations the amplitude of the order parameter has a finite probability to reach zero at some point along the wire, allowing the phase of the order parameter to slip by 2π [12]. The theory of thermally activated phase slips (TAPS) was developed by Langer, Ambegaokar, McCumber and Halperin (LAMH). However the effect of the magnetic field on the phase slippage process is not established. It is also unknown whether the magnetic field can change the relative contributions of quantum and thermally activated phase slips in thin wires [3,4].In this Letter we study the effects of the magnetic field on the phase slippage rate and the critical temperature of thin wires. It is found that the LAMH provides a good description for 1D superconductors in magnetic fields up to 11 T. The dependence of the critical temperature on the magnetic field, T c (B) agrees well with the theory of pair-breaking perturbations that takes into account both spin and orbital contributions [8,9]. This is our main result. No significant contribution of quantum phase slips has been detected in the studied samples.The samples were made by sputter-coating of suspended fluorinated carbon nanotubes with Nb or Mo 79 Ge 21 . Transport measurements were performed in a He-3 cryostat, as described previously [2,4,5]. The magnet...

We study the effect of an applied magnetic field on sub-10nm wide MoGe and Nb superconducting wires. We find that magnetic fields can enhance the critical supercurrent at low temperatures, and does so more strongly for narrower wires. We conjecture that magnetic moments are present, but their pair-breaking effect, active at lower magnetic fields, is suppressed by higher fields. The corresponding microscopic theory, which we have developed, quantitatively explains all experimental observations, and suggests that magnetic moments have formed on the wire surfaces.

PACS. 74.78.Na -Mesoscopic and nanoscale systems. PACS. 73.23.Hk -Coulomb blockade; single-electron tunneling.Abstract. -Quasi-one-dimensional superconductors or nanowires exhibit a transition into a nonsuperconducting regime, as their diameter shrinks. We present measurements on ultrashort nanowires (∼40-190 nm long) in the vicinity of this quantum transition. Properties of all wires in the superconducting phase, even those close to the transition, can be explained in terms of thermally activated phase slips. The behavior of nanowires in the nonsuperconducting phase agrees with the theories of the Coulomb blockade of coherent transport through mesoscopic normal metal conductors. Thus it is concluded that the quantum transition occurs between two phases: a "true superconducting phase" and an "insulating phase". No intermediate, "metallic" phase was found.Under certain conditions, usually associated with a critical resistance per square [1,2], critical total resistance [3][4][5][6], or a characteristic diameter [7,8], a wire made of a superconducting metal looses its superconductivity and acquires two signatures of insulating behavior: i) The resistance increasing with cooling and ii) a zero-bias resistance peak [3,4]. There are many models that capture certain features of the SIT in 1D wires. Some rely on the "fermionic" mechanism, in which disorder combined with electron-electron repulsion suppresses the critical temperature, T c , to zero [9]. In other, "bosonic", models the order parameter remains nonzero in the "insulating" phase while the coherence is destroyed by proliferating quantum phase slips (QPS) [10][11][12][13][14][15]. Existing theoretical models frequently predict a quantum superconductor-insulator transition (SIT) in thin wires [11,13,16,17], driven, in many cases, by the interaction of the fluctuating phase with the Caldeira-Leggett environment [18]. Conditions that make QPS experimentally observable and the relation of the QPS to the SIT are still being actively researched [1][2][3][4][5][6][7][8][19][20][21][22].Here we present a quantitative analysis of the transport properties of ultrashort nanowires in each of the two phases -the insulating phase and the superconducting phase. We show that the insulating phase is characterized by the normal-electron transport and governed by the Coulomb blockade physics [23,24]. The wires in the superconducting phase exhibit good agreement with the Langer-Ambegaokar-McCumber-Halperin (LAMH) theory of thermally activated phase slips (TAPS) [25][26][27], without any QPS contribution. The TAPS physics is dominant, even in the vicinity of the SIT. Thus we conclude that the observed transition c EDP Sciences

We establish the superconductor-insulator phase diagram for quasi-one-dimensional wires by measuring a large set of MoGe nanowires. This diagram is roughly consistent with the Chakravarty-Schmid-Bulgadaev phase boundary, namely, with the critical resistance being equal to RQ=h/4e2. Deviations from this boundary for a small fraction of the samples prompt us to suggest an alternative phase diagram, which matches the data exactly. Transport properties of wires in the superconducting phase are dominated by phase slips, whereas insulating nanowires exhibit a weak Coulomb blockade behavior.

We study the effect of morphology on the low temperature behavior of superconducting nanowires of length ≈100 nm. A well-defined superconductor-insulator transition (SIT) is observed only in homogenous wires, in which case the transition occurs when the normal resistance is close to h/4e 2 . Inhomogeneous wires, on the other hand, exhibit a mixed behavior, such that signatures of the superconducting and insulating regimes can be observed in the same sample. The resistance versus temperature curves of inhomogeneous wires show multiple steps, each corresponding to a weak link constriction (WLC) present in the wire. Similarly, each WLC generates a differential resistance peak when the bias current reaches the critical current of the WLC. Due to the presence of WLCs an inhomogeneous wire splits into a sequence of weakly interacting segments where each segment can act as a superconductor or as an insulator. Thus the entire wire then shows a mixed behavior.PACS numbers: 74.48. Na, 74.81.Fa, 74.40.+k Evidence for a superconductor-insulator quantum phase transition (SIT) in one-dimensional (1D) wires has been found in a number of experiments. 1,2 Yet, other studies have demonstrated a crossover, as opposed to an SIT, in thin wires where superconductivity disappears gradually, as diameter is reduced, presumably due to an increasing number of quantum phase slips (QPS). 3,4,5 Thus the existence and possible origins of superconductor-insulator transitions in 1D remain important open problems. In particular it is not known how the SIT depends on the morphology of nanowires.In two-dimensional system, for example, the crucial role of morphology (i.e. granularity) on the SIT is well known. 6,7,8 For uniform films, as the film thickness is reduced, a reduction of the critical temperature is observed while the superconducting transition remains sharp. The SIT occurs when the square resistance of the film reaches a critical value close to the quantum resistance R Q =h/4e 2 =6.5 kΩ. 9 In nonhomogeneous (granular) films, on the other hand, a reduction of the film thickness results in a crossover between superconducting and insulating regimes, with very broad resistive transitions in the thinnest superconducting samples. 6,10,11 Our goal here is to determine the morphological requirements for 1D nanowires under which an SIT can occur.In this Communication, we present a comparative study of homogeneous and inhomogeneous nanotubetemplated wires and find a qualitatively different behavior at low temperatures. Homogeneous samples (of length ≈100 nm) show an SIT which occurs when the wire's normal resistance is close to R Q , confirming previous results where different nanotubes were utilized as substrates. 2 Inhomogeneous wires, on the other hand, exhibit a mixed behavior displaying properties of superconductors and insulators at once. Such samples frequently show multiple steps in the resistive transitions but no resistive tails typical of QPS. 3,4,5 We propose a model which regards the inhomogeneous wire as a sequence of weak link c...

The properties of one-dimensional superconducting wires depend on physical processes with different characteristic lengths. To identify the process dominant in the critical regime we have studied the transport properties of very narrow (9-20 nm) MoGe wires fabricated by advanced electron-beam lithography in a wide range of lengths, 1-25  μm. We observed that the wires undergo a superconductor-insulator transition (SIT) that is controlled by cross sectional area of a wire and possibly also by the width-to-thickness ratio. The mean-field critical temperature decreases exponentially with the inverse of the wire cross section. We observed that a qualitatively similar superconductor-insulator transition can be induced by an external magnetic field. Our results are not consistent with any currently known theory of the SIT. Some long superconducting MoGe nanowires can be identified as localized superconductors; namely, in these wires the one-electron localization length is much smaller than the length of a wire.