Kinetic Stabilization of 1D Surface States near Twin Boundaries in Noncentrosymmetric BiPd

The search for one-dimensional (1D) topologically protected electronic states has become an important research goal for condensed matter physics owing to their potential use in spintronic devices or as a building block for topologically nontrivial electronic states. Using low temperature scanning tunneling microscopy, we demonstrate the formation of 1D electronic states at twin boundaries at the surface of the noncentrosymmetric material BiPd. These twin boundaries are topological defects that separate regions with antiparallel orientations of the crystallographic $b$ axis. We demonstrate that the formation of the 1D electronic states can be rationalized by a change in effective mass of two-dimensional surface states across the twin boundary. Our work therefore reveals a novel route towards designing 1D electronic states with strong spin-orbit coupling.

Figure 1

(a) Topographic STM image of the surface of BiPd [($8.2\times 8.2{\mathrm{nm}}^2$), $V_{\mathrm{t}}=80\mathrm{mV}$, $I_{\mathrm{t}}=0.5\mathrm{nA}$]. (b) Enlarged image of the area marked with a white square in (a), overlaid with ball models for the $(0\overline{1}0)$ termination at the bottom left and the (010) termination at the top right of the image respectively. In the models, blue and orange spheres are Bi atoms, red and green spheres are Pd atoms, yellow spheres are Pd atoms which are connected to the neighboring Bi atoms from the opposite terminations on both sides. (c) Averaged $dI/dV$ spectra measured on the $(0\overline{1}0)$ and (010) domains, as well as at the twin boundary ($V_{\mathrm{t}}=0.5\mathrm{V}$, $I_{\mathrm{t}}=50\mathrm{pA}$). Inset: STM image taken at a twin boundary ($7.9\times 7.9{\mathrm{nm}}^2$), marked by dashed lines. Colored areas mark the regions over which the spectra in (c) were collected. STM images and spectroscopic data were obtained at 1.8 K.

Figure 2

(a) and (b) $dI/dV$ maps at bias voltages of (a) 0.4 V and (b) 0.44 V, measured in the same field of view as the inset in Fig. 1 ($7.9\times 7.9{\mathrm{nm}}^2$). Spectroscopy setpoint: $V_{\mathrm{t}}=0.5\mathrm{V}$, $I_{\mathrm{t}}=50\mathrm{pA}$. Dashed lines enclose the twin boundary. (c) $dI/dV$ spectra extracted from different positions at the left (red), middle (green), and right (blue) of the twin boundary, as indicated in (b). Spectra are vertically offset for clarity. (d) Plot of peak areas of the 2D Dirac states (dark color) and 1D bound states (light color) versus position across the twin boundary. Orange line is the line profile along the same positions across the twin boundary in the topographic image recorded simultaneously with the $dI/dV$ map. Dashed vertical line marks the central position of the twin boundary.

Figure 3

(a) $dI/dV$ map recorded in the vicinity of a curved twin boundary separating domains of (010) and $(0\overline{1}0)$ orientations, at bias voltage of 0.44 V [$(16.6\times 12.7){\mathrm{nm}}^2$]. The twin boundary initially runs along the [101] direction from the top left, then deviates from this direction. (b) Averaged $dI/dV$ spectra extracted from three different sections along the twin boundary marked with rectangles of different colors in (a). The orientation of each section is represented by $\varphi$, the angle of the twin boundary from the [101] direction (see inset). An averaged spectrum extracted from the $(0\overline{1}0)$ domain (gray) is also included. (c) Polar plot of the energy position of the twin boundary bound state peak relative to that of the $(0\overline{1}0)$ domain surface state peak ($\mathrm{\Delta }E$) as a function of the twin boundary orientation ($\varphi$). Blue markers are the values determined from (b). Red markers represent data points extracted from another dataset obtained with a different tip. The corresponding spectra are shown in Fig. S3 of the Supplemental Material [20].

Figure 4

Band structure of the tight binding model incorporating two different effective masses on both sides of the twin boundary, as a function of momentum $k_{||}$ parallel to the boundary, (a) without and (b) with spin-orbit interaction. When the top edges of the surface state bands on the two sides (shown in two different shades of gray) are approximately aligned a band of bound states (shown in red, red-blue lines) appears at the twin boundary, with maximal split-off energy $\mathrm{\Delta }E$. In the bottom panel, spin-orbit interaction has been taken into account leading to a spin-splitting of the surface state bands (gray), but also of the bound state. The color coding in the bottom plot shows the in-plane spin polarization perpendicular to the twin boundary with red and blue for opposite spin directions.