As silicon is the basis of conventional electronics, so strontium titanate (SrTiO(3)) is the foundation of the emerging field of oxide electronics. SrTiO(3) is the preferred template for the creation of exotic, two-dimensional (2D) phases of electron matter at oxide interfaces that have metal-insulator transitions, superconductivity or large negative magnetoresistance. However, the physical nature of the electronic structure underlying these 2D electron gases (2DEGs), which is crucial to understanding their remarkable properties, remains elusive. Here we show, using angle-resolved photoemission spectroscopy, that there is a highly metallic universal 2DEG at the vacuum-cleaved surface of SrTiO(3) (including the non-doped insulating material) independently of bulk carrier densities over more than seven decades. This 2DEG is confined within a region of about five unit cells and has a sheet carrier density of ∼0.33 electrons per square lattice parameter. The electronic structure consists of multiple subbands of heavy and light electrons. The similarity of this 2DEG to those reported in SrTiO(3)-based heterostructures and field-effect transistors suggests that different forms of electron confinement at the surface of SrTiO(3) lead to essentially the same 2DEG. Our discovery provides a model system for the study of the electronic structure of 2DEGs in SrTiO(3)-based devices and a novel means of generating 2DEGs at the surfaces of transition-metal oxides.

Spin-orbit coupling has been conjectured to play a key role in the low-energy electronic structure of Sr 2 RuO 4 . By using circularly polarized light combined with spin-and angle-resolved photoemission spectroscopy, we directly measure the value of the effective spin-orbit coupling to be 130 AE 30 meV. This is even larger than theoretically predicted and comparable to the energy splitting of the d xy and d xz;yz orbitals around the Fermi surface, resulting in a strongly momentum-dependent entanglement of spin and orbital character in the electronic wavefunction. As demonstrated by the spin expectation value h ⃗ s k · ⃗ s −k i calculated for a pair of electrons with zero total momentum, the classification of the Cooper pairs in terms of pure singlets or triplets fundamentally breaks down, necessitating a description of the unconventional superconducting state of Sr 2 RuO 4 in terms of these newly found spin-orbital entangled eigenstates. DOI: 10.1103/PhysRevLett.112.127002 PACS numbers: 74.25.Jb, 74.20.Rp, 74.70.Pq, 79.60.-i After a flurry of experimental activity [1-5], Sr 2 RuO 4 has become a hallmark candidate for spin-triplet chiral p-wave superconductivity, the electronic analogue of superfluid 3 He [6][7][8]. However, despite the apparent existence of such a pairing, some later experiments [9-11] do not fully support this conclusion, as they cannot be explained within a theoretical model using spin-triplet superconductivity alone [12]. A resolution might come from the inclusion of spin-orbit (SO) coupling, which has been conjectured to play a key role in the normal-state electronic structure [13] and may be important when describing superconductivity as well. By mixing the canonical spin eigenstates, the relativistic SO interaction might play a fundamental role beyond simply lifting the degeneracy of competing pairing states [13][14][15][16][17].Thus far, the experimental study of SO coupling's effects on the electronic structure of Sr 2 RuO 4 has been limited to the comparison of band calculations against angle-resolved photoemission spectroscopy (ARPES) [13,[18][19][20][21] -no success has been obtained in observing experimentally either the strength of SO coupling or its implications for the mixing between spin and orbital descriptions. Here we probe this directly by performing spin-resolved ARPES [22], with circularly polarized light: by using the angular momentum inherent in each photon-along with electricdipole selection rules [23]-to generate spin-polarized photoemission from the SO mixed states. Combined with a novel spin-and orbitally-resolved ab initio based tightbinding (TB) modeling of the electronic structure [24], these results demonstrate the presence of a nontrivial spinorbital entanglement over much of the Fermi surface, i.e., with no simple way of factoring the band states into the spatial and spin sectors. Most importantly, the analysis of the corresponding Cooper pair spin eigenstates establishes the need for a description of the unconventional superconductivity of Sr 2 RuO 4 beyond...