Suppression of the Berezinskii-Kosterlitz-Thouless and quantum phase transitions in two-dimensional superconductors by finite-size effects

Abstract

We perform a detailed finite-size scaling analysis of the sheet resistance in Bi-films and the LaAlO3/SrTiO3 interface in the presence and absence of a magnetic field applied perpendicular to the system. Our main aim is to explore the occurrence of Berezinskii-Kosterlitz-Thouless (BKT) and quantum phase transition behavior in the presence of limited size, stemming from the finite extent of the homogeneous domains or the magnetic field. Moreover we explore the implications thereof. Above an extrapolated BKT transition temperature, modulated by the thickness d, gate voltage Vg or magnetic field H, we identify a temperature range where BKT behavior occurs. Its range is controlled by the relevant limiting lengths,which are set by the extent of the homogeneous domains or the magnetic field. The extrapolated BKT transition lines Tc (d, Vg, H) uncover compatibility with the occurrence of a quantum phase transition where Tc (dc, Vgc, Hc) = 0. However, an essential implication of the respective limiting length is that the extrapolated phase transition lines Tc (d, Vg, H) are unattainable. Consequently, given a finite limiting length, BKT and quantum phase transitions do not occur. Nevertheless, BKT and quantum critical behavior is observable, controlled by the extent of the relevant limiting length. Additional results and implications include: the magnetic field induced finite size effect generates a flattening out of the sheet resistance in the T → 0 limit, while in zero field it exhibits a characteristic temperature dependence and vanishes at T = 0 only. The former prediction is confirmed in both, the Bi-films and the LaAlO3/SrTiO3 interface, as well as in previous studies. The latter is consistent with the LaAlO3/SrTiO3 interface data, while the Bi-films exhibit a flattening out.

Substrate mediated nitridation of niobium into superconducting Nb2N thin films for phase slip study

“…Besides, we have observed the PSLs for all the samples indicating significant contributions from phase fluctuations to the resistive states. Similarly, due to the nanoscale dimension of the grains, FSE can play the substantial role in the resistive tailing and the residual resistance 42,48 and also to the deviation of the BKT fit from the experimental data 17,38,42 . When the quantized energy level spacing due to FSE in quasi 0D nanoscale grains becomes comparable to the superconducting energy gap, residual resistance appear due to the decreased density of states at the Fermi level, Coulomb repulsion and suppression of Josephson coupling between the grains 35 .…”

Comprehensive phase diagram of two-dimensional space charge doped Bi2Sr2CaCu2O8+x

“…Such a transition is difficult to observe experimentally because of competing phenomena such as disorder 27 and finite-size effects 49 , which broaden the superconducting transition for T  <  T KT . These factors induce spatial inhomogeneities of the superconducting condensate on the mesoscopic scale 50 affecting critical temperatures and the superconducting gap 51 .…”

“…However, in all devices Δ T / T c decreases strongly with doping until the optimal doping is attained and then remains almost unchanged. This can be ascribed to a change in the inhomogeneity landscape 49, 52 , which in turn increases the characteristic dimension of homogeneous superconducting domains and the spatial coherence of the superconducting state. Electronic correlations are also reduced as carrier density and coherence increase.

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Metallic ground state in an ion-gated two-dimensional superconductor

“…3 up to 1.3 T, indicating that the quantum-creep model holds for a wide range. It should be noted that (i) finite-size effects (42) or (ii) the model of random Josephson junction arrays that originate from surface roughness (for example, amorphous Bi thin films) (31) or inhomogeneous carrier accumulation, both of which can cause the flattening of the resistance with a finite value, can be excluded because of the following reasons: (i) a BKT transition, and a zero resistance state (below ~0.05 W) are observed (see Fig. 1D); and (ii) the channel surface preserved atomically flat morphology with an average mean square roughness of ~0.068 nm, which is less than 4% of d sc , even after all the measurements (fig.…”