Pair-breaking quantum phase transition in superconducting nanowires

Abstract

Quantum phase transitions (QPT) between distinct ground states of matter are widespread phenomena [1][2][3][4][5] , yet there are only a few experimentally accessible systems 6,7 where the microscopic mechanism of the transition can be tested and understood. These cases are unique and form the experimentally established foundation for our understanding of quantum critical phenomena. Here we report that a magnetic-fielddriven QPT in superconducting nanowires-a prototypical one-dimensional system (d= 1)-can be fully explained by the critical theory 8,9 of pair-breaking transitions characterized by a correlation length exponent v≈1 and dynamic critical exponent z≈ 2. We find that in the quantum critical regime, the electrical conductivity is in agreement with a theoretically predicted scaling function and, moreover, that the theory quantitatively describes the dependence of conductivity on the critical temperature, field magnitude and orientation, nanowire crosssectional area, and microscopic parameters of the nanowire material. At the critical field, the conductivity follows a T Quantum phase transitions occur in many systems, including magnetic materials 1 , superconductors [13][14][15] , cold atomic gases 3 and also atomic nuclei 4 and stars 5. Similar to the thermal fluctuations in classical temperature-driven phase transitions, strong quantum fluctuations near the critical point of a QPT lead to the emergence of universal long-range behaviour, which can be common in very diverse systems. However, for a complete description of a QPT one must also identify and quantitatively incorporate into a theory specific microscopic processes which drive a system across the critical point and induce the fluctuations. Examples where such complete theories can be experimentally tested are scarce and include the two-channel Kondo effect in quantum dots 7 and Luttinger liquid behaviour in materials composed of weakly coupled one-dimensional (1D) spin-chains 6 . Superconducting systems present special interest in the context of QPTs because the fluctuations near the critical point can lead to the formation of unconventional superconducting phases (most notably this is one of the scenarios for high-temperature superconductivity in the cuprates 16 ). They also present a challenge-despite many years of efforts and overall success of phenomenological finite-size scaling analyses 2,13,14,17 , the microscopic mechanism of QPTs in 2d superconductors is still debated. In contrast, the physics of a QPT becomes much more transparent in 1D superconductors.Here we show that essentially all long-range and microscopic characteristics of a QPT driven in superconducting nanowires by a magnetic field can be described by a pair-breaking critical theory.A 1D superconductor can be defined as a wire with diameter smaller than π 2 1/2 ξ(0), where ξ(0) is the zero-temperature Ginzburg-Landau coherence length 18 . This condition ensures that vortices do not form within the wire and that the superconducting order parameter is approximately constant at a...

Deficiency of the scaling collapse as an indicator of a superconductor-insulator quantum phase transition

“…Recently, we have found that another 1d system, namely superconducting nanowires, undergoes a QPT when driven by a magnetic field, B . 30 We have also found that the transition can be completely described by the pair-breaking critical theory with only one adjustable parameter, C , in the scaling formula 31…”

“…In this equation, D is the diffusion coefficient, c B critical field, and F a non-universal constant computed from the parameters of nanowires such as cross-sectional area and critical temperature. 30 The scaling function 1σ…”

“…1a, we show the resistance versus temperature dependence for nanowire E (we use the same notations as in Ref. [30]) in a parallel magnetic field. The nanowire is made from amorphous Mo 78 Ge 22 alloy; it has length 3 L = µm, width 13 w = nm, thickness 6 t = nm, and 1.5 c T = K. As Fig.…”

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“…Superconducting fluctuations (SFs) lead to several interesting quantum phenomena such as superconductor-insulator quantum transition (SIT) 1,2 , quantum criticality 3 , phase slip (PS) effects 4–7 , etc. These quantum phenomena are mainly controlled by sample properties like geometry and dimensions, crystallinity, disorder and inhomogeneity and also by external parameters like electro-magnetic field, driving current, temperature etc.…”

Monte Carlo simulations of a disordered superconductor-metal quantum phase transition

“…Recently, a pair-breaking superconductor-metal quantum phase transition has been observed in amorphous Mo-Ge nanowires [60]. In these wires, the disorder turns out to be rather weak and plays no role in the measured temperature range.…”