The physics of the superconducting state in two-dimensional (2D) electron systems is relevant to understanding the high-transition-temperature copper oxide superconductors and for the development of future superconductors based on interface electron systems1. But it is not yet understood how fundamental superconducting parameters, such as the spectral density of states, change when these superconducting electron systems are depleted of charge carriers. Here we use tunnel spectroscopy with planar junctions to measure the behaviour of the electronic spectral density of states as a function of carrier density, clarifying this issue experimentally. We chose the conducting LaAlO3–SrTiO3 interface2 as the 2D superconductor, because this electron system can be tuned continuously with an electric gate field3. We observed an energy gap of the order of 40 microelectronvolts in the density of states, whose shape is well described by the Bardeen–Cooper–Schrieffer superconducting gap function. In contrast to the dome-shaped dependence of the critical temperature, the gap increases with charge carrier depletion in both the underdoped region and the overdoped region. These results are analogous to the pseudogap behaviour of the high-transition-temperature copper oxide superconductors and imply that the smooth continuation of the superconducting gap into pseudogap-like behaviour could be a general property of 2D superconductivity.
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We acknowledge discussions with M. Beasley, A. P. Kampf and T. Kopp, technical support from M. Hagel, I. Hagel, M. Schmid and D. Zhang, and financial support from the German Science Foundation (TRR 80). Electron microscopy and spectroscopy was performed at the Cornell Center for Materials Research (CCMR), which is an NSF MRSEC supported by NSF grant DMR-1120296.
The authors declare no competing financial interests.
Extended data figures and tables
a, b, High-angle annular dark-field STEM image (a) and simultaneously recorded electron energy-loss spectroscopic map (b) of a Au–LaAlO3–SrTiO3 tunnel junction. The spectroscopic image maps the concentration of La in green, that of Ti in blue and that of O in red. c, Ti, O and La concentration profiles were computed by averaging the elemental map from b parallel to the interface. The LaAlO3–SrTiO3 interface shows a small amount of cation interdiffusion. No variations of the oxygen concentration across the interface are observed.
Best fits (solid lines) used to extract the temperature dependence of the superconducting gap, Δ, from the measured tunnel spectra (dots). The model used is based on a lifetime-broadened s-wave quasiparticle density of states (equation (1)) with no additional conductance contributions (G0 = 0 in equation (2)). The inset shows the obtained fit results for Δ and the quasiparticle decay-rate parameter, Γ. The solid line is the prediction of the BCS model for Tc = 0.28 K and 2Δ/kBTc = 3.3.
a–c, Temperature dependence of the gap at VG = −200 V (a), 0 V (b) and 200 V (c). Above Tgap, the spectra are independent of temperature, but a depression of the DOS at EF is still present. d, The T = 0.07 K data together with the best fits (solid lines). The spectra above Tgap were used as a background in the fitting routine.
Extended Data Figure 4 Temperature dependence of the 2DEL sheet resistance for different gate voltages.
The inset shows a sketch of the device layout.
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Richter, C., Boschker, H., Dietsche, W. et al. Interface superconductor with gap behaviour like a high-temperature superconductor. Nature 502, 528–531 (2013). https://doi.org/10.1038/nature12494
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