Pseudogaps and Emergence of Coherence in Two-Dimensional Electron Liquids in SrTiO 3

PRL 117, 046402 (2016) week ending 22 JULY 2016 PHYSICAL REVIEW LETTERS Pseudogaps and Emergence of Coherence in Two-Dimensional Electron Liquids in SrTiO 3 Patrick B. Marshall, Evgeny Mikheev, Santosh Raghavan, and Susanne Stemmer * Materials Department, University of California, Santa Barbara, California 93106-5050, USA (Received 21 November 2015; revised manuscript received 9 June 2016; published 22 July 2016) Using tunneling spectroscopy, we show that pseudogaps emerge in strongly correlated, two-dimensional electron liquids in SrTiO 3 quantum wells that are tuned near a quantum critical point. Coherence peaks emerge at low temperatures in quantum wells embedded in antiferromagnetic SmTiO 3 that remain itinerant to the lowest thickness. Quantum wells embedded in ferrimagnetic GdTiO 3 that become ferromagnetic at low temperatures show no indication of quasiparticle coherence. They undergo a symmetry-lowering metal-to-insulator transition at the lowest thicknesses that coincides with a vanishing single-particle density of states (DOS) around the Fermi level. Both types of quantum wells show a power-law depletion of the DOS at high energies. The results show that the different pseudogap behaviors are closely correlated with the type of magnetism in the proximity of the quantum wells and thus provide insights into the microscopic mechanisms. DOI: 10.1103/PhysRevLett.117.046402 Pseudogaps are a reduction of the single-particle spectral weight around the Fermi level and are a hallmark of strongly correlated systems that are near quantum critical points or unusual types of order. They have been observed in high-temperature superconductors [1–7], heavy-fermion compounds [8], charge density wave systems [9,10], rare- earth nickelates [11], and even cold atom systems [12]. While pseudogaps in many correlated materials are still not fully understood [3–5,13], they provide unique information about electron correlation physics. Tunneling and photo- emission measurements of pseudogaps probe the degree to which the low-energy excitations of an interacting electron liquid differ from those of a Fermi gas. Features above the gap contain information about quantum phase fluctuations and the emergence of coherence. Conversely, systematic manipulation of critical behavior and dimensionality can yield new insights into which critical fluctuations give rise to pseudogaps and how new ordered states emerge. Additionally, disorder can play a strong role in correlated electron systems and can produce observable anomalies in tunneling, such as zero-bias anomalies in the metallic phase [14] and Coulomb gaps deep in the insulating state [15–17]. Disentangling the effects of disorder, electron-electron, and electron-lattice interactions, and understanding their effects on low-energy excitations, is critical to advancing the understanding of correlated materials. Here, we study these questions in a strongly correlated low-dimensional electron system, namely, two-dimensional electron liquids (2DELs) in narrow SrTiO 3 quantum wells, which are confined between insulating RTiO 3 barriers (R ¼ Sm or Gd); see Fig. 1(a). The 2DELs in these quantum wells offer relative simplicity and tunability, while at the same time exhibiting the phenomena that have become hallmarks of strongly correlated systems, in particular, magnetism [18], metal-insulator transitions [19], non-Fermi liquid behavior [20,21], and transport FIG. 1. (a) Schematic of the tunnel device structure. The thickness of the SrTiO 3 quantum well is specified in terms of the number of SrO layers it contains—the example shown here contains two SrO layers, or one unit cell of SrTiO 3 . (b) Phase diagram of the electronic and magnetic states in GdTiO 3 =SrTiO 3 =GdTiO 3 (top) and SmTiO 3 =SrTiO 3 =SmTiO 3 (bottom) quantum wells as a function of the SrTiO 3 well thickness, summarizing the results from both prior works [18–21,23] as well as this study [insulator (Ins.); density wave (DW)]. © 2016 American Physical Society