Spectroscopic Imaging STM: Atomic-Scale Visualization of Electronic Structure and Symmetry in Underdoped Cuprates

Kim

Proc. Natl. Acad. Sci. U.S.A.

et al. 2015

Self Cite

233

To achieve and use the most exotic electronic phenomena predicted for the surface states of 3D topological insulators (TIs), it is necessary to open a "Dirac-mass gap" in their spectrum by breaking timereversal symmetry. Use of magnetic dopant atoms to generate a ferromagnetic state is the most widely applied approach. However, it is unknown how the spatial arrangements of the magnetic dopant atoms influence the Dirac-mass gap at the atomic scale or, conversely, whether the ferromagnetic interactions between dopant atoms are influenced by the topological surface states. Here we image the locations of the magnetic (Cr) dopant atoms in the ferromagnetic TI Cr 0.08 (Bi 0.1 Sb 0.9 ) 1.92 Te 3 . Simultaneous visualization of the Dirac-mass gap Δ(r) reveals its intense disorder, which we demonstrate is directly related to fluctuations in n(r), the Cr atom areal density in the termination layer. We find the relationship of surface-state Fermi wavevectors to the anisotropic structure of Δ(r) not inconsistent with predictions for surface ferromagnetism mediated by those states. Moreover, despite the intense Dirac-mass disorder, the anticipated relationship Δ(r) ∝ n(r) is confirmed throughout and exhibits an electron-dopant interaction energy J* = 145 meV·nm 2 . These observations reveal how magnetic dopant atoms actually generate the TI mass gap locally and that, to achieve the novel physics expected of time-reversal symmetry breaking TI materials, control of the resulting Dirac-mass gap disorder will be essential.ferromagnetic topological insulator | Dirac-mass gapmap | Dirac-mass disorder | magnetic dopant atoms T hat the surface states of 3D topological insulators (TIs) exhibit a "massless" Dirac spectrum EðkÞ = Zvk · σ with spinmomentum locking and protected by time-reversal symmetry is now firmly established. Opening a gap in this spectrum is key to the realization of several extraordinary new types of electronic phenomena. The prevalent approach to opening this "Dirac-mass gap" is to dope the materials with magnetic atoms (1-6). A plethora of new physics is then predicted, including σ xy = ±e 2 =h quantum anomalous Hall effects (QAHE) (7, 8), topological surface-state magneto-electric effects (9-12), related magneto-optical Kerr and Faraday rotations (10, 13, 14), axionic-like electrodynamics (15, 16), and even E-field induced magnetic monopoles (17,18). As yet, none of these phenomena except the QAHE (19-22) have been detected, and the QAHE itself is poorly understood because σ xy = ±e 2 =h is observed only at temperatures far below 1 K.Interactions between the TI surface electrons and the magnetic dopant atoms at random surface locations r i can be represented theoretically by a Hamiltonian of the type H DA = −J p P S i · sδðr − r i Þ. Here S i (s) is the spin of each dopant (surfacestate carrier) measured in units of Z, and J p is their exchangeinteraction energy scale. In the simple case of a homogenous ferromagnetic state with magnetization parallel to the surface normal z, the Hamiltonian becomes H = −J p n 0...

Section: Experimental Methodsmentioning

confidence: 99%

Imaging Dirac-mass disorder from magnetic dopant atoms in the ferromagnetic topological insulator Cr _x (Bi _0.1 Sb _0.9 ) _2-x Te ₃

Kim

Proc. Natl. Acad. Sci. U.S.A.

et al. 2015

Self Cite

233

Proc. Natl. Acad. Sci. U.S.A.

“…A new opportunity to address these questions has emerged recently, through studies of the CDM phenomena now widely observed in underdoped cuprates (15,20,21). Pioneering studies of CDMs in La 2-x Ba x CuO 4 and La 2-x-y Nd y Sr x CuO 4 near p = 0.125 discovered charge modulations of period 4a 0 or Q = ((1/4,0);(0,1/ 4))2π/a 0 (14,21).…”

Section: Cdms In the Pseudogap Phasementioning

confidence: 99%

“…Understanding the cuprate CDM phenomenology has proved challenging (28-30) because its q-space peaks are typically broad with spectral weight distributed over many wavevectors (15)(16)(17)(18)(19)(20)(21) and also because of the form factor symmetry (17,(31)(32)(33). For example, Fig.…”

Section: Cdms and Phase Discommensurationsmentioning

confidence: 99%

“…Phasesensitive transmission electron microscopy can achieve DC visualization (34), whereas coherent X-ray diffraction might (35), but neither one has been used on cuprates. Instead, we consider CDM visualization using spectroscopic imaging scanning tunneling microscopy (20) because it offers full access to both the amplitude and phase ofψðqÞ, with the definition of phase referenced to the underlying atomic lattice (33). Then, based on such phase visualization capabilities, we introduce an approach for identifying the fundamental wavevector of the cuprate CDM state.…”

Section: Cdms and Phase Discommensurationsmentioning

confidence: 99%

“…A variety of powerful theoretical techniques (2-11) support this strongly interacting r-space viewpoint. In the interim, however, CDM phenomena have been discovered within the pseudogap regime of many other underdoped cuprates (15,20,21). …”

mentioning

confidence: 99%

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Commensurate 4 a ₀ -period charge density modulations throughout the Bi ₂ Sr ₂ CaCu ₂ O _8+x pseudogap regime

Mesaroš

Fujita

Edkins

et al. 2016

Self Cite

Theories based upon strong real space (r-space) electron-electron interactions have long predicted that unidirectional charge density modulations (CDMs) with four-unit-cell (4a 0 ) periodicity should occur in the hole-doped cuprate Mott insulator (MI). Experimentally, however, increasing the hole density p is reported to cause the conventionally defined wavevector Q A of the CDM to evolve continuously as if driven primarily by momentum-space (k-space) effects. Here we introduce phase-resolved electronic structure visualization for determination of the cuprate CDM wavevector. Remarkably, this technique reveals a virtually doping-independent locking of the local CDM wavevector at jQ 0 j = 2π=4a 0 throughout the underdoped phase diagram of the canonical cuprate Bi 2 Sr 2 CaCu 2 O 8 . These observations have significant fundamental consequences because they are orthogonal to a k-space (Fermi-surface)-based picture of the cuprate CDMs but are consistent with strong-coupling r-space-based theories. Our findings imply that it is the latter that provides the intrinsic organizational principle for the cuprate CDM state.CuO 2 pseudogap | commensurate charge density modulation | phase discommensuration S trong Coulomb interactions between electrons on adjacent Cu sites result in complete charge localization in the cuprate Mott insulator (MI) state (1). When holes are introduced, theories based upon the same strong r-space interactions have long predicted a state of unidirectional modulation of spin and charge (2-11), with latticecommensurate periodicity for the charge component. Experimentally, it is known that even the lightest hole doping of the MI state produces nanoscale clusters of charge density modulations (CDMs) (12, 13), which implies immediately that r-space interactions predominate. However, with increasing hole density p, the conventionally defined wavevector Q A of the CDM is reported to increase (14) or diminish (15) continuously as if driven primarily by k-space (Fermi surface) effects. Distinguishing between the r-space and k-space theoretical perspectives is critical to identifying the correct fundamental theories for the phase diagram and Cooper pairing mechanism in underdoped cuprates. Here we introduce an approach to this challenge by applying phase-resolved electronic structure visualization (16-18) in combination with the technique of phase demodulation-residue minimization, to explore the CDM wavevector. Using these methods, we visualize the phase discommensurations (19) and their influence on the doping dependence of both the conventionally defined Q A and the fundamental local wavevector Q 0 of the underdoped cuprate CDM state. CDMs in the Pseudogap PhaseAs holes are introduced into the CuO 2 plane of the MI, the first nonmagnetic state to appear is the pseudogap (PG) phase (Fig. 1A). It contains nanoscale CDM clusters (12, 13) even at lowest hole-density p; near p = 0.06 these CDM clusters percolate and the superconducting state appears (12). X-ray scattering experiments (15) now report a robust ...

Severe Dirac Mass Gap Suppression in Sb₂Te₃-Based Quantum Anomalous Hall Materials

et al. 2020

Quantum anomalous Hall (QAH) effect appears in ferromagnetic topological insulators (FMTI) when a Dirac mass gap opens in the spectrum of the topological surface states (SS). Unaccountably, although the mean mass gap can exceed 28 meV (or ~320 K), the QAH effect is frequently only detectable at temperatures below 1 K. Using atomic-resolution Landau level spectroscopic imaging, we compare the electronic structure of the archetypal FMTI Cr0.08(Bi0.1Sb0.9)1.92Te3 to that of its non-magnetic parent (Bi0.1Sb0.9)2Te3, to explore the cause. In (Bi0.1Sb0.9)2Te3, we find spatially random variations of the Dirac energy. Statistically equivalent Dirac energy variations are detected in Cr0.08(Bi0.1Sb0.9)1.92Te3 with concurrent but uncorrelated Dirac mass gap disorder. These two classes of SS electronic disorder conspire to drastically suppress the minimum mass gap to below 100 µeV for nanoscale regions separated by <1 µm. This fundamentally limits the fully quantized anomalous Hall effect in Sb2Te3-based FMTI materials to very low temperatures.