Researchers
Dr. Jinho Lee, Dr. Alfred "Miao" Wang, Dr. Tien-Ming Chuang, Milan P. Allan, Yang Xie

Introduction
The quantum mechanical problem of correlated electron in solids is one of the great,unsolved mysteries faced by modern physics.Transition metal oxides provide an ideal environment to study this problem.

We study the bilayer perovskite Sr₃Ru₂O₇, which exhibits some diverse physical phenomena: it is an itinerant metamagnet with several metamagnetic transitions, it can be tuned towards a putative quantum critical point in an external magnetic field, and in ultrapure samples, an electronic nematic forms in a small region of the phase diagram around this putative quantum critical point. Much insight about these phenomena in Sr₃Ru₂O₇ come from a wealth of high-quality thermodynamic experiments, but little is known about the microscopic origin of criticality and nematicity. Spectroscopic imaging scanning tunneling microscopy (SI-STM) is potentially an ideal technique for studying such systems because simultaneous studies of r-space and k-space electronic structure can be performed, at magnetic fields covering the nematic phase.

We were able to obtain a high-resolution k-space mapping of the electronic structure using angle-resolved photoemission spectroscopy (ARPES) and SI-STM. We find a complex bandstructure with well-defined quasiparticles and Fermi velocities up to an order of magnitude lower than in single layer Sr₃RuO₄. Furthermore, SI-STM reveals fast changing subatomic structures, not inconsistent with the symmetries of the relevant d-orbitals.

Fruitful collaboration with the Mackenzie Group (thermodynamic measurements, crystal growth), the Baumberger Group (ARPES), and the Kim and Lawler groups (theory), as well as with the members of the complex materials IRG of the Cornell Center for Material research are ongoing.

Instrument : Sub-Kelvin 9-Tesla Spectroscopic Imaging STM (SI-STM) This system consists of a home-built 250mK ³He refrigerator with ultra low vibration ⁴He-pot surrounded by a persistent American Magnetics magnet. It is suspended in a very low boil rate dewar from a massive low vibration cryostat. The cryostat is housed inside an acoustic shield room, itself supported on a 25 ton inertial block on vibration isolators. Again, this assembly is installed in an underground acoustic / vibration isolation vault. The pump set is remote and highly vibration isolated and the control room is remote. The STM head is at the center of the magnet suspended below the refrigerator. We use this system to study Bi₂Sr₂CaCu₂O_8+δ, Bi₂Sr₂Ca₂Cu₃O_10+δ, YBa₂Cu₃O_6+δ, Th₂Ba₂CuO_6+δ, and Pr_2-xCe_xCuO₄. Sample exchange to 4K takes ~4 hours and to 250mK ~8 hours.

Results
Heavy d-Electron Quasiparticle Interference and Real-space Electronic Structure of Sr₃Ru₂O₇
(More information available at Nature Physics Online.)

Topography and subunit-cell electronic structure imaging in Sr₃Ru₂O₇
a. Topographic image of the SrO cleaved Sr₃Ru₂O₇ surface, taken at -100mV and 10GΩ. The top inset shows a schematic view from above along the c-axis showing the sequential 6.8° rotations of the RuO₆ octahedra which double the unit cell. The Ti dopant site is shown in black and two types of octahedra are labeled α and β. On the topographic image, dark and light spots stem from Ti impurities located at the Ru sites on the higher and lower Ru-O sheet of the top bilayer respectively. The white Ti sites appear in two different orientations, corresponding to the different RuO octahedra orientations (inset). Data for figure b were taken far from any Ti dopant atom. b The top left-hand panel shows the locations of Ru atoms and their d_xz and d_yz orbitals in red. Yellow and blue circles mark the positions of Sr, and O atoms, respectively. Each subsequent panel shows g(r,E) maps resolving sub-unit-cell spatial features in the same field of view. While some g(r,E) show high intensity mainly at the positions of the Sr atoms (-9, 0 meV), others clearly resolve sub-unit-cell features with the symmetry and location of the d_xz and d_yz orbitals (-13, +9, +13 meV).

Fourier Transform STS of Sr₃Ru₂O₇
a-f A sequence of g(r,E) maps taken at -100mV, 1GΩ in the same 28nm-square field of view. Each Ti scatterer exhibits energy-dispersive QPI fringes around it.
g-l The corresponding two dimensional Fourier transform image g(q,E) revealing heavy delectron QPI directly. The dark area near (0,0) is where spectral weight has been reduced to allow for clearer viewing of the g(q,E) contrast and the images are octet-symmetrized. A complex and fast-dispersing set of wavevectors q_i is seen in these g(q,E). Remarkably, this q-space complexity and dispersion can be explained by scattering between states in only one very simple band of Sr₃Ru₂O₇.

Quasiparticle Interference in the α₂ band of Sr₃Ru₂O₇
a. The LDA band structure in the first Brillouin zone with the α₂ band at the G-point emphasized by colorization. b. The α₂ band in the extended zone scheme of the unreconstructed system at Ebias = -9 meV. Within a single sheet there are two primary scattering vectors q₁ and q₂ as shown. The full set of inequivalent scattering vectors q_i(i=1,¡¦10) involving only the α₂ band are shown as colored arrows (see c). By using E(k) for this. c. The autocorrelation of A(k,E) derived from the band shown in b. This process picks out the regions of high joint-density-of-states(JDOS) which should dominate the quasiparticle scattering process. The full set of inequivalent scattering vectors q_i(i=1,¡¦10) which should exist for scattering interference only in the α₂ band are determined from these regions of high JDOS and are shows using the set of colored arrows (also in b). d. By overlaying as open circles the tip positions of these same q_i on g(q,E=-9 meV) we see that all inequivalent maxima can be accounted for with highly overdetermined internal consistency by α₂ band scattering interference. e. Measured dispersions of q₁ and q₂ from data in figure b . They agree well with the model α₂ band and thus with the directly measured dispersion of the α₂ band from ARPES.

Collaborators
Andrew P. Mackenzie - Correlated Electron Systems Group, University of St. Andrews
Felix Baumberger - ARPES Group, University of St. Andrews
Eun-Ah Kim - Cornell University
Michael Lawler - Cornell University
David A. Muller - Cornell University
Kyle Shen - Cornell University
Craig J. Fennie - Cornell University