QAHE Topological Insulators



Severe Dirac Mass Gap Suppression in Sb2Te3-based QAH Materials

 Nano Lett 20, 8001-8007 (2020)


Essence: Atomic-resolution Landau Level spectroscopic imaging is used to compare the electronic structure of the archetypal FMTI Cr0.08(Bi0.1Sb0.9)1.92Te3 to that of its nonmagnetic parent (Bi0.1Sb0.9)2Te3. In (Bi0.1Sb0.9)2Te3 and Cr0.08(Bi0.1Sb0.9)1.92Te3  we find spatially random variations of the Dirac energy, with uncorrelated Dirac mass gap disorder in the latter. We show how these two classes of electronic disorder conspire to drastically suppress the minimum mass gap to below 100 μeV for nanoscale regions separated by <1 μm, fundamentally limiting the fully quantized anomalous Hall effect in Sb2Te3-based FMTI materials to very low temperatures.


Comparison of the archetypal FMTI Cr<sub>0.08</sub>(Bi<sub>0.1</sub>Sb<sub>0.9</sub>)<sub>1.92</sub>Te<sub>3</sub> to that of its nonmagnetic parent (Bi<sub>0.1</sub>Sb<sub>0.9</sub>)<sub>2</sub>Te<sub>3</sub>.

Comparison of the archetypal FMTI Cr0.08(Bi0.1Sb0.9)1.92Te3 to that of its nonmagnetic parent (Bi0.1Sb0.9)2Te3.


The quantum anomalous Hall (QAH) effect appears in ferromagnetic topological insulators (FMTIs) when a Dirac mass gap opens in the spectrum of the topological surface states (SSs). 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 nonmagnetic 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.



Imaging Dirac-Mass Disorder at the Magnetic Dopant-Atoms of the Ferromagnetic Topological Insulator Crx(Bi0.1Sb0.9)2-xTe3

PNAS 112, 1316 (2015)


Essence: In the canonical ferromagnetic topological insulator Cr0.08(Bi0.1Sb0.9)1.92Te3  we visualize the Dirac-mass gap Δ(r) revealing its intense disorder, which we demonstrate directly is related to fluctuations in the Cr dopant-atom areal density n(r). Despite this intense Dirac-mass disorder, the relationship Δ(r)∝n(r) is confirmed throughout. These observations revealed for the first time how magnetic dopant atoms generate the TI mass gap locally and that, to achieve all the novel physics expected of time-reversal-symmetry breaking TI materials, control of the resulting Dirac-mass gap disorder will be essential.


Measured Dirac mass gap versus location in archetypal FMTI Cr<sub>0.08</sub>(Bi<sub>0.1</sub>Sb<sub>0.9</sub>)<sub>1.92</sub>Te<sub>3</sub>. Inset shows the fixed relationship of Dirac mass gap magnitude to density of Cr magnetic dopant atoms (sites indicated by red triangles).

Measured Dirac mass gap versus location in archetypal FMTI Cr0.08(Bi0.1Sb0.9)1.92Te3. Inset shows the fixed relationship of Dirac mass gap magnitude to density of Cr magnetic dopant atoms (sites indicated by red triangles).


To achieve and utilize the most exotic electronic phenomena predicted for the surface states of 3D topological insulators (TI), it is necessary to open a "Dirac-mass gap" in their spectrum by breaking time-reversal symmetry. Use of magnetic dopant atoms to generate a ferromagnetic state is the most widely used approach. But it was 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 Cr0.08(Bi0.1Sb0.9)1.92Te3. Simultaneous visualization of the Dirac-mass gap Δ(r) reveals its intense disorder, which we demonstrate directly is 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)consistent 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*=145meV.nm2.