FERROMAGNETIC TOPOLOGICAL INSULATORS (SPECTRE)
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Researchers
Dr. Inhee Lee, Dr. Chung Koo Kim, Dr. Jinho Lee


Introduction

Over last years, topological insulators (TI) have been of tremendous interest to condensed matter physicists and material engineers because of its novel quantum state in which helical surface state contains the spin locked to momentum k and its backscattering is prohibited. This unusual surface state has been identified from the 3D TI compounds such as Bi2Se3, Bi2Te3, and Sb2Te3, especially by angle-resolved photoemission spectroscopy (ARPES). In particular, the Dirac point of surface state is topologically protected from the gap formation due to time-reversal symmetry. However, this gapless nature can be broken in the ferromagnetic TI which is often achievable by magnetic doping. Once the surface state gap is opened and chemical potential μ is located within both surface-state and bulk gaps, new exotic physics are predicted, including quantum anomalous Hall effect (QAHE) with σxy=±e2/2h, charge induced magnetic monopole, magneto-optical Kerr and Faraday rotations, topological surface state magneto-electric effects, and axionic-like electrodynamics. Actually, in recent transport measurements of Crx(BiySb1-y)2-xTe3 thin films, QAHE with σxy=±e2/2h was detected at extremely low temperature (<1K). However, except that, none of other predictions has been observed. Regarding these issues, it is very important to visualize the spatial distribution of magnetic dopants and Dirac mass gap as well as to investigate their spatial correlations.

[Cr dopant atom locations at the TI surface] A. Topographic image T(r) of Cr0.08(Bi0.1Sb0.9)1.92Te3 surface in a 47 x 47 nm2 field of view (FOV). Inset : zoomed-in red dashed-box area. Both images were measured at 10pA/-200mV. A single Cr dopant atom exists substituted at the Bi/Sb site at the symmetry point of every dark triangle in T(r). B. Schematic of the crystal structure of Crx(BiySb1-y)2-xTe3. Each substitutional Cr atom is located at a Bi/Sb site at the symmetry point of a triangle of surface Te atoms.


Instrument : variable-temperature Spectroscopic Imaging STM (SI-STM)

    BNL1_control room

SI-STM in acoustic room (front)

 

SI-STM in acoustic room (top)

  Control room

Our SI-STM cryostat (dewar plus integrated vibration isolation structure) is placed in an acoustically isolated chamber. The floor in the acoustic room consisting of several hundred tons of concrete is disconnected from the rest of the building in order to prevent any undesirable vibrational noise from affecting the measurement. Most electronic instruments are installed in a separate control room removing any possible noise sources from the electronics. Sample exchange and cleaving are performed in cryogenic ultra high vacuum with temperature near 10 K. SI-STM operation temperature ranges 4.2~70K. In the near future, this system will be upgraded to house an 11 T superconducting magnet and 4He fridge.


Recent Research Achievements

Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic TI Crx(BiySb1-y)2-xTe3.

[1] Identification of Dirac-mass gap by means of quasi-particle interference (QPI) imaging


Differential conductance map g(r,E) (left) and associated K(q,E) (right). The FOV size of g(r,E) is 90x90 nm2. Click this link to download the movie for full energy-dependence of both g(r,E) and K(q,E).

QPI is a powerful technique to analyze the band structure of surface states. Dispersion of surface states of Cr0.08(Bi0.1Sb0.9)1.92Te3 is observed in the spectral density K(q,E), Fourier transform of K(r,E) = <I(E)>g(r,E)/I(r,E) in which the undesirable setup effect is alleviated ( g(r,E) : differential conductance, I(r,E) : tunneling current, <I(E)> : spatially averaged current at energy E). Our surface-state QPI dispersion at E<EF is coincident with ARPES data measured from the same samples. Most of all, the evolution of QPI signatures of surface states reveal the clear presence of Dirac-mass gap. Within the Dirac-mass gap, K(q,E) is totally suppressed around q~0. This gap region is also demonstrated independently from the suppression of g(r,E)~0.

[Measuring Dirac-mass gap from both tunneling spectrum and QPI] A-P. Quasiparticle interference of TI surface states is visualized as a function of energy using the spectral-density K(q,E), the Fourier transform of K(r,E)=<I(E)>g(r,E)/I(r,E). Here we see directly the disappearance of the surface-state QPI in an energy window between 130 meV and 200 meV. The white number in the top right corner represents the measured energy in unit of meV. Q. Measured dispersions in quasiparticle interference of the TI surface states is plotted using K(qx=0, qy, E), the E-q line cut along Γ-K. Here the evolution of scattering interference signature of surface states to reach q=0 at ~130 meV, followed by their disappearance, and the reappearance at and dispersion away from q=0 near E ~200 meV, is manifest. The Dirac gap magnitude Δ is half the energy range between the two q=0 tips of the surface-state bands, as indicated by fine grey lines. R. spatially averaged tunneling conductance, simultaneously measured with Q showing that conductance becomes indistinguishable from zero within the same energy window as in Q. Again, this indicates that the Dirac gap magnitude Δ is half the energy range between points at which conductance disappears/reappears, as indicated by black arrows.

[2] Visualization of Dirac mass gap

Dirac-mass gap at an array of locations r of FOV can be characterized by two parameters, gap width 2Δ and gap center ED, from the sequence of spectra g(r,E). Our gap map consisting of Δ(r) and ED(r) constructed from the atomically flat surface of Cr0.08(Bi0.1Sb0.9)1.92Te3 shows strongly disordered surface-state gap structures. This consequence is expected to be due to randomly distributed Cr dopants, however, it is unknown how the arrangement of Cr dopants influences on the development of heterogeneous ferromagnetic structures, and furthermore, how it is connected to the formation of gap structures.

[Dirac-mass gapmap] A. Measured average conductance spectra, each representing the average of all spectra with the same value of Δ in C. Each curve is offset vertically for clarity and the zero of conductance is shown by a fine horizontal line. The value 2Δ in each spectrum is the energy span between the pairs of arrows. B. Histogram of the Δ(r) measured in C. C. Dirac-mass gapmap Δ(r) [or Dirac-mass map Δ(r)]. D. Fourier transform of the Dirac-mass gapmap Δ(r). E. Dirac-mass gapmap Δ(r) measured in 360 x 360 nm2 FOV much larger than the map in C. Inset : the histogram of Δ(r). F. Map of estimated ungapped Dirac-point energy (gap center) ED(r). Inset : correlation between gap center ED and Cr dopant density n.

[3] Interplay of Cr dopant and Dirac-mass gap

The effect of Cr dopants distribution on Dirac mass gap disorder can be examined by spatial correlation of Dirac-mass gap Δ(r) and Cr density n(r). Here n(r) includes the spatial fluctuation of Cr dopant rather than Delta-point like placement. In our analysis, Δ(r) and n(r) shows a straightforward quasi-linear relationship, i.e., Δ(r)∝n(r). From the slope of this relationship between Δ(r) and n(r), we find a universal dopant-surface state interaction energy scale J*=145 meV∙nm2 for Cr0.08(Bi0.1Sb0.9)1.92Te3.

[Atomic-scale measurements of interaction strength of surface states with magnetic dopant atoms] Dirac-mass gap map Δ(r) with Gaussian smoothing length 0.55 nm, overlaid with Cr locations (red triangles). Cr atoms are observed to be positioned with high probability in the larger gap areas (yellow), but rarely in the smaller gap areas (blue). Red and black circles on the right bottom corner indicate correlation radii 0.82 nm and 0.55 nm associated with n(r) and Δ(r), respectively. Inset : Each data point represents the average value of Dirac mass gap over all of the regions having the same value of Cr density n. The resulting slope of best linear fit yields J*=145 meV∙nm2. This is to our knowledge the first atomic-scale measurement of the interaction strength of surface states with magnetic dopant atoms in a ferromagnetic TI. The uncertainty represented by two dashed lines is not statistical but comes from the systematic uncertainty in magnitude of Sz, which we take to be 20%.

Collaborators
Genda Gu - Brookhaven National Laboratory
John Tranquada - Brookhaven National Laboratory
Simon Billinge - Brookhaven National Laboratory & Columbia University

 

TOPOLOGICAL QUANTUM MATTER

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Researchers
Dr. Jinho Lee, Dr. Tien-Ming Chuang, Dr. 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 aputative 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 Bi2Sr2CaCu2O8+δ, Bi2Sr2Ca2Cu3O10+δ, YBa2Cu3O6+δ, Th2Ba2CuO6+δ, and Pr2-xCexCuO4. Sample exchange to 4K takes ~4 hours and to 250mK ~8 hours.


Recent Research Achievements
Heavy d-Electron Quasiparticle Interference and Real-space Electronic Structure of Sr3Ru2O7
(More information available at Nature Physics 5, 800)

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 dxz and dyz 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 dxz and dyz 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 qi 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 qi(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 qi(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 qi 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