Field-Induced SIT in Disordered 2D Electron systems: The case of amorphous Indium-Oxide thin films

TL;DR

This paper tackles the field-induced superconductor-insulator transition (SIT) in disordered 2D electron systems with strong spin-orbit scattering, challenging the necessity of boson-vortex duality. It develops a time-dependent Ginzburg-Landau (TDGL) framework for Cooper-pair fluctuations (CPFs) and shows that CPFs form real-space mesoscopic puddles that localize under increasing parallel magnetic field, while a dynamical equilibrium with residual fermions governs transport. A phenomenological quantum tunneling and pair-breaking mechanism is introduced, linking CPF localization to thermally activated fermionic quasi-particle transport and yielding a parity between AL-like bosonic paraconductivity and FQP activation, which reproduces the observed high-field negative magnetoresistance and a crossing of isotherms at a quantum critical field near the MR peak. Quantitative fits to amorphous Indium-Oxide thin-film data yield realistic parameters (e.g., ε_SO ≈ 5 meV, T_Q ≈ 0.1–0.15 K) and demonstrate that SIT behavior can emerge without invoking boson-vortex duality, offering a unified framework applicable to related disordered superconductors and oxide interfaces. The work highlights the critical role of spin-orbit coupling in suppressing Zeeman-limited pair-breaking and clarifies the interplay between localized CPF bosons and fermionic transport in 2D SIT phenomena.

Abstract

The phenomenon of field-induced superconductor to insulator transition (SIT) in disordered 2D electron systems has been a subject of controversy since its discovery in the early 1990s. Here we present a phenomenological quantitative theory of this phenomenon which is not based exclusively on the boson-vortex duality used commonly in the field. Within a new low-temperature framework of the time-dependent Ginzburg-Landau (TDGL) functional approach to superconducting fluctuations we propose and develop a scenario in which bosons of Cooper-pair fluctuations (CPFs) condense and localize in real-space mesoscopic puddles under increasing magnetic field due to diminishing stiffness of the fluctuation modes at low temperatures in a broad range of momentum space. Quantum tunneled CPFs relieving the condensed mesoscopic puddles, which consequently pair break into fermionic quasi-particle excitations, dominate the thermally activated inter-puddles transport. The spatially shrinking puddles of CPFs, embedded in expanding normal-state regions, upon further increasing field, suppress the quasi-particle excitation gap and so lead to high-field negative magneto-resistance (MR). Application to amorphous Indium-Oxide thin films shows good quantitative agreement with experimental sheet resistance data. In particular, in agreement with the experiment at low temperatures (i.e. well below the quantum tunneling pair breaking "temperature"), the sheet resistance isotherms are predicted to show a single crossing point at a quantum critical field not far below the MR peak.

Figures (5)

• Figure 1: Characteristic mean-field and thermal fluctuations aspects of the 2D electron system under study. Note the low temperatures mean-field critical field $H_{c}\left( 0\right) \sim 10$ T, in comparison with Fig.3, where the effect of the quantum fluctuations discussed in Sec.V strongly suppresses it toward $\sim 6$ T. For both (a) and (b) $\varepsilon _{SO}=5.6$ meV, and: $T_{c0}=0.8$ K. The additional parameters used in the calculation of $T_{sat}(H)$ are: $E_{F}=50$ meV, $\hbar / \tau _{OR}=10$ meV, and the dimensionless cutoff parameter: $x_{c0}\equiv \hbar Dq_{c}^{2}/4 \pi k_{B}T_{c0}=0.01$
• Figure 2: Upper panels: The tunneling-pair-breaking modified rduced stifness $\Theta \left( H;T_{Q}\right)$ (Eq. \ref{['Theta']}) at two temperatures calculated for various $T_{Q}$ values. Lower panels: The corresponding tunneling-pair-breaking modified interaction parameter $\Lambda \left( H;T_{Q}\right)$ (Eq. \ref{['Lambda']}) at the same two temperatures and for the same $T_{Q}$ values as in the upper panels.
• Figure 3: Illustration of the first stage of the fitting process described in the text at two representative temperatures; $T=32$ mK (a) and $T=195$ mK (b). Upper-left panel in both (a) and (b): The calculated field-dependent sheet resistance, plotted (solid line) together with the corresponding experimental sheet resistance data (dotes). Upper-right panel: The calculated paraconductivity (thin blue solid line) and the FQP conductivity (thick blue solid line), plotted together with the corresponding experimentally measured sheet conductance data (dotes) as functions of the field. Also shown in each upper-right panel is the corresponding effective (normal-state) Drude conductivity $\sigma _{n}^{Drude}\left( H\right)$ as influenced by the CPFs density shown in each lower-left panel. Lower panels: The corresponding calculated normalized CPFs density $\widetilde{n}_{CPF}^{U}\left( H;\widetilde{ \varepsilon }_{H}^{U}\right)$ (left panel) and the "bare" (red) and "dressed" (blue) critical shift parameters; $\varepsilon _{H}^{U}$ and $\widetilde{ \varepsilon }_{H}^{U}$, respectively (right panel).
• Figure 4: The FQP conductivity ingredients used in the first stage of the fitting process, plotted as fuctions of temperature.
• Figure 5: The sheet resistance isotherms calculated at a series of increasing temperatures; $T=32,60,79,114,195$ mK (their maxima are decreasing respectively with increasing $T$), plotted together with the corresponding experimentally measured data (full circles). Insets: Zoom into the crossing regions of the isotherms showing their dramatic convergence into a single crossing point by moving from (b) to (a) upon narrowing the distribution of the quantum tunneling-pair breaking "temperature" $T_{Q}$ over temperature $T$. The other parameters used for both (a) and (b) are: $\ T_{c0}=0.8$ K, $E_{F}=50$ meV, $\hbar / \tau _{OR}=10$ meV, and: $x_{c0}\equiv \hbar Dq_{c}^{2}/4 \pi k_{B}T_{c0}=0.01$