Suppression of the spectral weight of topological surface states on the nanoscale via local symmetry breaking

In topological crystalline insulators the topological conducting surface states are protected by crystal symmetry, in principle making it possible to pattern nanoscale insulating and conductive motifs solely by breaking local symmetries on an otherwise homogeneous, single-phase material. We show, using scanning tunneling microscopy/spectroscopy, that defects that break local symmetry of SnTe suppress electron tunneling over an energy range as large as the bulk band gap, an order of magnitude larger than that produced globally via magnetic fields or uniform structural perturbations. Complementary ab initio calculations show how local symmetry breaking obstructs topological surface states as shown by a threefold reduction of the spectral weight of the topological surface states. The finding highlights the potential benefits of manipulating the surface morphology to create devices that take advantage of the unique properties of topological surface states and can operate at practical temperatures.

Figure 1

Scanning tunneling microscopy images of a SnTe film grown on $\mathrm{SrTi}{\mathrm{O}}_3$. (a) Overview image $\left(U_{\mathrm{bias}}=2.2\mathrm{V}\right)$ demonstrates atomically flat terraces with half-unit-cell step heights (3.2 Å). The ellipses highlight (I) a screw dislocation, (II) paired threading screw dislocations, (III) an island, and (IV) a pit. (b) A screw dislocation at atomic resolution (200 mV) showing broken symmetry. (c) Zoomed-in view of the screw dislocation (200 mV) with the dashed lines and χ showing the half-unit-cell shift of the atomic rows across the dislocation core, while dashed lines at the corner of the image show unperturbed lines of atoms (see Fig. S.I. 6 in the Supplemental Material [12] for further analysis). (d) Atomic resolution image (–100 mV) recorded close to a step edge showing superimposed standing waves that have been reported on topological insulator surfaces [40]. (e) Three-dimensionally rendered STM topography showing standing waves induced by step edges $\left(-750\mathrm{mV}\right)$. Valley (black)-to-peak (white) corrugations are 14.81 (a), 3.67 (b), 2.05 (c), and 4.66 Å (d), and the base to topmost height is 18.54 Å for (e).

Figure 2

(a) Tunneling spectra recorded in the middle of a terrace [blue curve recorded within the blue circle in region III of Fig. 1] showing densities of states for a defect-free region, and at an area with high curvature [red curve recorded within red circle in region IV of Fig. 1] revealing suppression of densities of states. (b) DFT calculated atom-projected DOS averaged over all surface atoms on the surface layer for infinite terraces (blue) and a stepped vicinal (103) surface (red) showing suppressed DOS within 50 meV of the Fermi level. These results are for 19-layer-thick slabs.

Figure 3

(a) Scanning tunneling microscopy topography image of a pit. (b) Scanning tunneling spectroscopy experiments conducted along a line. Numerical derivative of tunneling spectrum shows that the tunneling conductance is suppressed within the pit (I), and $dI/dV$ gradually increases (II) as the tip moves to smoother regions (III) where the symmetry of the crystal is protected. Note that the vertical scale of the tunneling spectra is amplified 25 times compared to Fig. 2 (see Fig. S.I. 5 [12] for comparison) to show the variation around the Fermi level more clearly. The valley (black)-to-peak (white) corrugation is 3.41 nm for (a).

Figure 4

DFT calculations for 19-atomic-layers-thick (001) SnTe slabs. (a),(c) Integrated from $E_F-0.1\mathrm{eV}$ to $E_F+0.1\mathrm{eV}$, capturing predominantly the surface states, and averaged (along [100]) LDOS in real space for the (a) defect-free and (c) the stepped (001) SnTe surfaces. Higher (lower) LDOS is shown by red (blue) colors on the same color scale plot. (b),(d) Theoretical band structure for defect-free (c) and stepped surfaces (d); the green-shaded area refers to the bulk bands while blue lines are computed for finite slabs. The SS forming the Dirac point are shown in thick black color with their weight indicated by the size of the red circles (band projection). The SS exist in both cases but the spectral weight of the topological surface states is greatly reduced for the stepped surface. The small gap for the SS in (b) is due to the finite slab thickness [15].