Evidence for Pre-formed Pairs in an Oxide Superconductor
Authors: Guanglei Cheng, Michelle Tomczyk, Jeremy Levy
Department of Physics and Astronomy, University of Pittsburgh, USA.
Pittsburgh Quantum Institute, Pittsburgh, Pennsylvania, USA.
Link to Levy Research Group >>
Strontium titanate (SrTiO3 or simply STO) is the first and best-known superconducting semiconductor. Its many fascinating properties, especially superconductivity, motivated Georg Bednorz and Alex Müller to search for high-temperature (high-Tc) superconductors in perovskite oxides . STO shares many features related to the cuprate high-Tc superconductors, including a dome-shaped phase diagram and a pseudogap phase . However, STO has much lower temperature and carrier density than the high-Tc compounds. A longstanding question surrounds the nature of the pseudogap state: ‘To pair or not to pair?’ – Does the existence of a pseudogap indicate electron pairing in the absence of superconductivity?
In 1969, long before high-Tc superconductivity was discovered, D.M. Eagles predicted  that electrons could remain paired outside of the superconducting state in STO. Eagles predicted that electrons can form a dilute gas so that the size of pairs is very small compared to the inter-electron distance. Namely, electrons pair in real space and the superconductivity is a result of Bose-Einstein condensation (BEC), contrasting the weak pairing in momentum space described by Bardeen-Schrieffer-Cooper (BCS) theory, which is highly successful in explaining conventional superconductors. Eagles was the first to propose the concept of BEC-BCS crossover, which was later independently developed by Nobel laureate Anthony Leggett  and experimentally realized in an ultracold atomic gas . The discovery of BEC-type superconductivity in solid state systems has been challenging.
The LaAlO3/SrTiO3 (LAO/STO) interface  has attracted numerous interests in the last decade. It hosts a two-dimensional conducting interface that possesses a wealth of strongly correlated phenomena including superconductivity, magnetism, metal-insulator transition (MIT) and spin-orbit interaction . A few years ago, we developed a lithography technique that allows us to ‘write’ and ‘erase’ nanostructures at the LAO/STO interface by using a sharp conductive atomic force microscope (c-AFM) tip, thus effectively programming all the novel properties at the nanoscale [8,9]. The writing mechanism relies critically on the MIT, in which the interface becomes conducting above the critical 3 unit cell (uc) LAO thickness. While the 3uc LAO/STO interface is insulating, it is switchable by a voltage-biased c-AFM tip. Under the c-AFM tip, a series of nanoscale devices have been made available. The resulting nanowires are only a few nanometers wide, exhibit anomalously high mobility  and show potential for the development of new types of nanoelectronics.
To investigate electron pairing, we use a superconducting single-electron transistor (Figure 1a). The device consists of a main superconducting nanowire channel intersected with voltage leads. Two tunnel potential barriers are engineered through c-AFM ‘cutting’ procedures so that a nanoscale island is defined. Due to the nanoscale confinement, the energy levels inside the island are quantized, and carrier transport is only possible when the chemical levels of external electrodes (source and drain) are aligned with an island energy level, which is dependent on the side gate voltages.
Figure 1: (click on the figure to view with higher resolution) Device schematic and transport characteristics. (a), Device schematic written by c-AFM lithography. The nanowires are typically 5 nm wide, and the length between 2 barriers is 1 μm. (b) and (c) Differential conductance dependent on the source-drain bias and side gate voltages at B=0 T (b) and B=4 T (c). The number of diamonds is doubled in (c). Color scales are 0-80 µS. (d) Magnetic field dependence of the conductance peaks. The bifurcation of conductance peaks above Bp suggest electron pairing without superconductivity. Color scale: 0-40 µS.
Indeed, bias spectroscopy reveals  a series of conductance diamonds (Fig. 1b), reminiscent of so-called ‘Coulomb diamonds’ in conventional blockade physics. In the latter case, each sequential Coulomb diamond corresponds to the stability of one additional electron, and applying an external magnetic field merely changes the size of diamonds due to Zeeman Effect. Remarkably, when we increase the magnetic field, the diamonds initially remain insensitive to field, then bifurcate above a critical magnetic field Bp~2 T (Fig. 1b,c). Such behavior is clearly revealed when we track the magnetic field dependence of the zero-bias conductance peaks. We find that all of the peaks bifurcate above a ‘pairing field’ Bp (Fig. 1d), suggesting transport is dominated by electron pairs rather than single electrons below Bp. Electron pairing persists far above the critical temperature (Tc~0.3 K) and for magnetic fields far above the upper critical field (Hc2~0.2 T) for superconductivity in bulk STO.
The observed electron pairing without superconductivity is difficult to explain using BCS theory. Pair fluctuations in disordered BCS superconductor films may give signatures of pairing above Tc which is greatly suppressed by disorder. However, the corresponding pairing temperature will not exceed Tc in the clean limit. Here the pairing temperature we have observed is around several kelvin, one order of magnitude higher than the Tc in the bulk. These experimental signatures are captured by a phenomenological model that favors BEC pairing, consistent with D. M. Eagles’s theory proposed 46 years back.
 J. Georg Bednorz and K. Alex Müller, "Perovskite-type oxides - the new approach to High Tc superconductivity", Nobel Lecture (1987).
 C. Richter, H. Boschker, W. Dietsche, E. Fillis-Tsirakis, R. Jany, F. Loder, L. F. Kourkoutis, D. A. Muller, J. R. Kirtley, C. W. Schneider, J. Mannhart, "Interface superconductor with gap behaviour like a high-temperature superconductor", Nature, 502, 528 (2013). Abstract.
 D.M. Eagles, "Possible pairing without superconductivity at low carrier concentrations in bulk and thin-film superconducting semiconductors", Physical Review, 186, 456 (1969). Abstract.
 Anthony J. Leggett, "A theoretical description of the new phases of liquid 3He", Reviews of Modern Physics, 47, 331 (1975). Abstract.
 M. W. Zwierlein, J.R. Abo-Shaeer, A. Schirotzek, C.H. Schunck, W. Ketterle, "Vortices and superfluidity in a strongly interacting Fermi gas", Nature, 435, 1047 (2005). Abstract.
 A. Ohtomo, H.Y. Hwang, "A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface", Nature, 427, 423 (2004). Abstract.
 Joseph A. Sulpizio, Shahal Ilani, Patrick Irvin, Jeremy Levy, "Nanoscale Phenomena in Oxide Heterostructures", Annual Review of Materials Research, 44, 117 (2014). Abstract.
 C. Cen, S. Thiel, G. Hammerl, C. W. Schneider, K. E. Andersen, C. S. Hellberg, J. Mannhart, and J. Levy, "Nanoscale control of an interfacial metal-insulator transition at room temperature", Nature Materials, 7, 298 (2008). Abstract.
 Cheng Cen, Stefan Thiel, Jochen Mannhart, Jeremy Levy, "Oxide nanoelectronics on demand", Science, 323, 1026 (2009). Abstract.
 Patrick Irvin, Joshua P. Veazey, Guanglei Cheng, Shicheng Lu, Chung-Wung Bark, Sangwoo Ryu, Chang-Beom Eom, Jeremy Levy, "Anomalous High Mobility in LaAlO3/SrTiO3 Nanowires", Nano Letters, 13, 364 (2013). Abstract.
 Guanglei Cheng, Michelle Tomczyk, Shicheng Lu, Joshua P. Veazey, Mengchen Huang, Patrick Irvin, Sangwoo Ryu, Hyungwoo Lee, Chang-Beom Eom, C. Stephen Hellberg, Jeremy Levy, "Electron pairing without superconductivity", Nature 521, 196 (2015). Abstract.