Evidence of quantum phase slip effect in titanium nanowires

Abstract

Electron transport properties of titanium nanowires were experimentally studied. Below the effective diameter 50 nm all samples demonstrated a pronounced broadening of the R(T ) dependencies, which cannot be accounted for thermal flcutuations. An extensive microscopic and elemental analysis indicates the absence of structural or/and geometrical imperfection capable to broaden the the R(T ) transition to such an extent. We associate the effect with quantum flucutuations of the order parameter.PACS numbers: 74.25.F-, 74.78.-w Since the early years of experimental studies in superconductivity it has been noticed that the supercondcunting transition R(T ) has always a finite width. Very often the broadening can be accounted for sample inhomogeneity. However, soon it became clear that, at least in low dimensional samples, the transition width remains finite even with the refined material purity and improved fabrication. The effect has been attributed to fluctuations typically more pronounced in objects with reduced dimensionality. The finite resistance R(T ) ∼ exp (−F 0 /k B T ) at a temperature T below the critical temperature T c of a quasi-one-dimensional superconducting channel with cross section σ has been explained by the thermal fluctuations of the order paprameter: the so called thermal activation of phase slips (TAPS), 1 , 2 . Here the condensation energy F 0 ∼ B 2 c ξσ of the smallest statistically independent volume ξσ, where ξ is the supercondcuting coherence length and B c is the critical magnetic field, competes with the thermal energy k B T . The effect manifests itself only sufficiently close to the critical temperature, and in extreemly homogeneous samples with micrometer-size diameter (e.g. pure whiskers) leads to the experimentally observable width of the R(T ) transition of about few mK 3 , 4 , 5 . In less homogeneous objects (e.g. lithographically fabricated nanowires) separation of the impact of the thermal fluctuations from the trivial inhomogeneity-determined R(T ) broadening is rather problematic 6 . Nevertheless with development of nanotechnology 7 it became clear that in extreemly narrow superconducting wires, with diameters ∼10 nm, the shape of the R(T ) transition by no means can be explained by sample inhomogeneity or/and thermal fluctuations 8 . The effect has been attributed to quantum fluctuations, also called -quantum phase slips (QPS) -and has been observed in a rather limited number of experiments studying the transport properties of ultra-narrow nanowires made of various superconducting materials: amorphous M oGe 9 , 10

The Quantum Phase Slip Phenomenon in Superconducting Nanowires with High-Impedance Environment

“…The I-V characteristics of Ti QPS nanowires with lowimpedance probes, have been studied earlier [7,20]. In those experiments sufficiently thick samples with  1/2 >45 nm demonstrated conventional I-V dependencies with well-defined critical current.…”

“…3, should exponentially depend on cross section of the nanowire The observation correlates well with our findings: no traces of Coulomb effects were observed in samples with effective diameter   nm. Note that nanowires with similar 'large' dimensions contacted with low impedance probes have revealed no traces of QPS effects: rather sharp R(T) dependencies, well defined critical current and zero resistive state [7,20].…”

“…Hence, it is quite realistic to fabricate and study quasi-one dimensional (1D) superconducting systems [1]. It has been demonstrated that in such objects quantum fluctuations of the phase of the complex order parameter e i can suppress zero resistivity at temperatures well below the critical point T<<T c [2][3][4][5][6][7] and dramatically modify the current-phase relation and the magnitude of persistent currents in narrow superconducting nanorings [8,9].…”

NbSi nanowire quantum phase-slip circuits: dc supercurrent blockade, microwave measurements, and thermal analysis

“…[14][15][16] QPS in InO x has been demonstrated via spectroscopic measurements of E S in a QPS qubit, 2 while alternative evidence for QPS (in fact, for the dual effect of coherent tunneling of single Cooper pairs) has been observed in NbSi nanowires via quantum interference in a device dual to the SQUID consisting of two QPSJs joined by a superconducting island. 15 Preliminary signs of QPS 17,18 and of dual Shapiro steps 19 have been observed in a Ti nanowire, but only traces of steps are observed.…”

Nonlinear current-voltage characteristics due to quantum tunneling of phase slips in superconducting Nb nanowire networks

“…For further information on both the normal-state and morphological properties of our samples the reader can refer to Ref. 19, where the central issue of their homogeneity, which can in principle be responsible of the observed excess of dissipation, [16,22] has been largely discussed. …”