Evidence for Topological Edge States in a Large Energy Gap near the Step Edges on the Surface of ${\mathrm{ZrTe}}_5$

Two-dimensional topological insulators with a large bulk band gap are promising for experimental studies of quantum spin Hall effect and for spintronic device applications. Despite considerable theoretical efforts in predicting large-gap two-dimensional topological insulator candidates, none of them have been experimentally demonstrated to have a full gap, which is crucial for quantum spin Hall effect. Here, by combining scanning tunneling microscopy/spectroscopy and angle-resolved photoemission spectroscopy, we reveal that ${\mathrm{ZrTe}}_5$ crystal hosts a large full gap of $\sim 100\mathrm{meV}$ on the surface and a nearly constant density of states within the entire gap at the monolayer step edge. These features are well reproduced by our first-principles calculations, which point to the topologically nontrivial nature of the edge states.

Popular Summary

Two-dimensional topological insulators conduct electrons on their surfaces and act as insulators in their bulk. In the edge states, electrons propagating in opposite directions have opposite spins, leading to a quantum spin Hall effect. To maximize the quantum spin Hall effect, the bulk band gap must be large enough so that thermally excited carriers in the bulk are sufficiently few to contribute to the electron and spin transport. However, such two-dimensional topological insulators with a large fully opened band gap have not been experimentally demonstrated, and the quantum spin Hall effect has only been demonstrated at ultralow temperatures in previous experiments. Here, we show that ${\mathrm{ZrTe}}_5$ crystals exhibit a large energy gap with topological edge states above 4 K.

Using scanning tunneling microscopy/spectroscopy and angle-resolved photoemission spectroscopy of single ${\mathrm{ZrTe}}_5$ crystals, we observe a large full band gap of approximately 0.1 eV on the surface of the ${\mathrm{ZrTe}}_5$ crystal and a finite density of states, which is nearly constant within the entire gap, at the monolayer step edge. We show that the conductance attains a maximum at the edge of the sample and that the edge states decay exponentially into the bulk. These observations are well reproduced by our first-principles calculations, which point to the topologically nontrivial nature of the edge states.

Such a large energy gap with topological edge states observed in ${\mathrm{ZrTe}}_5$ is promising for the quantum spin Hall devices and ideal (i.e., dissipationless) wires operating at relatively high temperatures. We expect that our findings will stimulate applications of topological insulators and propel “topotronics” as the next generation of microelectronics and spintronics.

Figure 1

(a) 3D structure of ${\mathrm{ZrTe}}_5$ crystal. (b) Top view of the single-layer structure. (c) STM constant current topographic image of the cleaved $a\text{−}c$ (010) surface of ${\mathrm{ZrTe}}_5$ crystal ($I=100\mathrm{pA}$, $V=-800\mathrm{mV}$). Right top inset: High-resolution topography ($I=50\mathrm{pA}$, $V=400\mathrm{mV}$) showing the details of the surface structure. Bottom left inset: Tunneling differential conductance spectrum on the $a\text{−}c$ surface ($I=500\mathrm{pA}$, $V=500\mathrm{mV}$) showing a large energy gap of $\sim 100\mathrm{meV}$ above $E_F$ with zero conductance inside the gap.

Figure 2

Band structure of pristine ${\mathrm{ZrTe}}_5$. (a) Band dispersions along $\mathrm{\Gamma }-X$ measured at 24 K. For comparison, the calculated band structure along $\mathrm{\Gamma }-X$ is plotted on top of the experimental data. The calculated bands are shifted up by 70 meV to match the experimental data. (b) Same as (a) but recorded at 200 K. (c) Same as (a) but measured after the deposition of potassium atoms for 2 min. (d) Momentum distribution curve plot of (a) showing two peaks at $E_F$, confirming the $E_F$ crossing of the valence bands. (e) Momentum distribution curves at $-250\mathrm{meV}$ recorded with different incident photon energies from 45 to 95 eV. (f) Fermi surface intensity plot measured on the (010) surface at 24 K showing a small hole pocket at $\mathrm{\Gamma }$. The directions of $k_x$ and $k_y$ are parallel and perpendicular to the ${\mathrm{ZrTe}}_3$ chains in the (010) plane, respectively, while $k_z$ is along the (010) surface normal direction.

Figure 3

Band structure of lightly substituted ${\mathrm{ZrTe}}_5$ with a nominal composition $({\mathrm{Zr}}_{0.9975}{\mathrm{Ta}}_{0.0025}){\mathrm{Te}}_5$ recorded at 190 K. (a) Intensity plot of the band dispersions along $\mathrm{\Gamma }\text{−}X$. Dashed curves represent the extracted bands of the pristine ${\mathrm{ZrTe}}_5$ recorded at 200 K, which are shifted down by 50 meV to match the band dispersions of the substituted one. (b),(c) Intensity plots of the band dispersions along $Y\text{−}M$ and $\mathrm{\Gamma }\text{−}X$, respectively, divided by the FD distribution function ($T=190\mathrm{K}$) convoluted with the energy resolution Gaussian function ($\mathrm{\Delta }E=25\mathrm{meV}$). The red curve in (c) is the energy distribution curve at $\mathrm{\Gamma }$. (d) Energy distribution curve plot of (c).

Figure 4

(a) Tunneling differential conductance spectra along a line perpendicular to a monolayer step edge ($I=500\text{pA}$, $V=500\mathrm{mV}$). Red curves are tunneling spectra measured near the step edge, while the blue and green curves are measured away from the step edge on the lower and upper terraces, respectively. The inset shows the topographic image of the step ($I=30\mathrm{pA}$, $V=300\mathrm{mV}$) and data point locations. (b) Calculated DOS of the top monolayer. The inset shows the calculated DOS of the edge states of the monolayer along the chain direction. (c) Evolution of the edge states. For clarity, the spectra from the 12th to 22nd points are offset with equal intervals of 0.4 nS. Black lines indicate the zero-conductance level for each spectrum. (d) Calculated band dispersions of the edge states of the monolayer along the chain direction. (e) Normalized conductance integral within the gap plotted as a function of the distance from the edge. The black curve is an exponential function fit to the data with a characteristic decay length $\xi =1.5\mathrm{nm}$. The inset plots the calculated mode of the wave function for the edge state close to $\mathrm{\Gamma }$ as a function of the distance from the edge. The black curve is an exponential function with a characteristic decay length $\xi =1.6\mathrm{nm}$.

Figure 5

A ${\mathrm{ZrTe}}_5$ ribbon terminated with a Te-Te zigzag chain (top left) and a ${\mathrm{ZrTe}}_3$ chain (top right) is put on a six-layer-thick bulk ${\mathrm{ZrTe}}_5$. The width of the ribbon shown here is five c-lattice constants. The interlayer distance is 7.5 Å, which leads 3D ${\mathrm{ZrTe}}_5$ to be in a weak TI [24].

Figure 6

Tight-binding model band structure along $\mathrm{\Gamma }\text{−}X$ with fixed ribbon width of 15 $c$ unit cells. (a) Freestanding ribbon. (b), (c) Supported with 1- and 5-layer-thick substrates, respectively. (d)–(f) 7-, 9-, and 11-layer-thick substrates, respectively, but only $1/10$ of the path from $\mathrm{\Gamma }$ to $X$.