Trigger of the Ubiquitous Surface Band Bending in 3D Topological Insulators

The main scientific activity in the field of topological insulators (TIs) consists of determining their electronic structure by means of magnetotransport and electron spectroscopy with a view to devices based on topological transport. There is, however, a caveat in this approach. There are systematic experimental discrepancies on the electronic structure of the most pristine surfaces of TI single crystals as determined by Shubnikov–de Haas oscillations and by angle-resolved photoelectron spectroscopy (ARPES). We identify intense ultraviolet illumination—that is inherent to an ARPES experiment—as the source for these experimental differences. We explicitly show that illumination is the key parameter, or in other words, the trigger, for energetic shifts of electronic bands near the surface of a TI crystal. This finding revisits the common belief that surface decoration is the principal cause of surface band bending and explains why band bending is not a prime issue in illumination-free magnetotransport studies. Our study further clarifies the role of illumination on the electronic band structure of TIs by revealing its dual effect: downward band bending on very small time scales followed by band flattening at large time scales. Our results therefore allow us to present and predict the complete evolution of the band structure of TIs in a typical ARPES experiment. By virtue of our findings, we pinpoint two alternatives of how to approach flat-band conditions by means of photon-based techniques and we suggest a microscopic mechanism that can explain the underlying phenomena.

Popular Summary

Topological insulators (TIs) are novel materials with high potential for exotic applications ranging from the use of electron spins for logic in electronics (spintronics) to quantum computation. The first step in this direction is to achieve electric conduction only from electrons that belong to the topological surface state (an electronic state that is unique to TIs). In order to assess the contribution of those electrons to electric conduction, knowledge of the electronic structure of the material’s surface is crucial. The surface electronic structure of TIs has previously been probed by means of both electron spectroscopy and transport, but after 10 years of experimental research, results from these two techniques systematically disagree. In this work, we determine that this discrepancy is inherent to electron spectroscopy, and we show how to overcome the problem in order to get trustworthy results on the surface electronic structure.

The common belief is that the surface electronic structure of a TI is hypersensitive to molecules from the environment sticking to the surface. Our results prove that exposure to ultraviolet light is instead the real reason for electronic structure changes. As illumination is intrinsic to electron spectroscopy but not to transport experiments, electronic structure changes are generally not encountered in the latter. We explain the complete evolution of the surface electronic structure during an electron spectroscopy experiment by complementing molecular adsorption with illumination-triggered microscopic processes such as photoionization, photodissociation, photoinduced desorption, and surface photovoltage.

Our results set the framework for future work on TIs by means of electron spectroscopy as well as any photon-based techniques.

Figure 1

Discrepancies between the experimentally determined Dirac point energies for TI surface states between ARPES and quantum oscillations. The graphic shows the binding energy of the Dirac point ($E_D$) in five different 3D topological insulator materials as extracted from published transport (blue symbols) and ARPES (red symbols) studies. The border of the inner circle corresponds to zero binding energy of the Dirac point (i.e., $E_D=E_F$). The binding energy increases radially with each tick denoting an increase of 100 meV. Notice the different axes scale for each compound. Filled circles denote data from samples which have not been intentionally aged in UHV, and measurements have been typically performed within an hour of sample cleavage. Empty squares and circles denote that air exposure and intentional aging under UHV conditions have been carried out, respectively. Green circles show the value of $E_D$ extracted from ARPES data presented in this study: these surfaces have been intentionally exposed to UHV residual gases for 3 h, but their total exposure to external illumination was of only a single second. The green data points are taken from the ARPES data presented in Figs. 2 and 3 for each compound, whereby we note a slight variation in the composition of the ${\mathrm{Bi}}_{2-x}{\mathrm{Sb}}_x{\mathrm{Te}}_{3-y}{\mathrm{Se}}_y$ used (i.e., $x=0.54$ instead of 0.5), and that the green ARPES data point in the ${\mathrm{Bi}}_2{\mathrm{TeSe}}_2$ panel is from the related system ${\mathrm{BiSbTeSe}}_2$. The number next to each red and blue marker is the literature reference from which $E_D$ is extracted.

Figure 2

The striking effect of illumination on the evolution of band bending during a typical ARPES experiment on TIs. Left-hand (center) columns of $I(E,k)$ images: Surface band structure of four different TI compounds recorded using an EUV exposure of only 1 s (40 s), after the cleavage surface had been exposed to residual UHV gases for 3 h. Right-hand column: Very rapid evolution of $E_D$ from the first moment of EUV illumination, whereby the left-hand $I(E,k)$ images underlie the first (second for ${\mathrm{BiSbTeSe}}_2$) data point of each curve in the right-hand panel. The pressure before and during the ARPES measurements was $1.0\times {10}^{-10}$ and $5.0\times {10}^{-11}\mathrm{mbar}$, respectively. All data have been acquired at 16 K using a photon flux of $3.2\times {10}^{21}\mathrm{photons}/(\mathrm{s}{\mathrm{m}}^2)$. The photon energy was 30 eV for ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and 27 eV for all the other compounds.

Figure 3

The effect of surface decoration on the evolution of surface band bending during a typical ARPES experiment on 3D TIs. Left-hand column: Binding energy of the Dirac point in ${\mathrm{Bi}}_{1.46}{\mathrm{Sb}}_{0.54}{\mathrm{Te}}_{1.7}{\mathrm{Se}}_{1.3}$ as a function of illumination time after the surface has been exposed for differing times to UHV residual gas molecules, as given in the legend. Center (right-hand) panels: $I(E,k)$ images showing the surface band structure of ${\mathrm{Bi}}_{1.46}{\mathrm{Sb}}_{0.54}{\mathrm{Te}}_{1.7}{\mathrm{Se}}_{1.3}$ which underlie the data points in the left-hand graphic for EUV exposure times of 1 s (20 s). The pressure before and during measurements was $1.0\times {10}^{-10}$ and $5.0\times {10}^{-11}\mathrm{mbar}$, respectively. All data have been acquired at 16 K using a photon flux of $3.2\times {10}^{21}\mathrm{photons}/(\mathrm{s}{\mathrm{m}}^2)$, with a photon energy of 27 eV.

Figure 4

The local character of EUV-induced surface band structure changes in 3D TIs, and the effect of photon flux. The upper panels show the evolution of $E_D$ in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ on exposure of four different sample locations labeled A–D to low (red) and high (blue) photon flux. Vertical dashed lines denote the change of sample location. The lower panels show the $I(E,k)$ images corresponding to the numbered points (1–6) superimposed on the curves in the uppermost panels. The pressure during measurements was $1.5\times {10}^{-10}\mathrm{mbar}$. The flux corresponding to the red data points was 3–4 times lower than the flux corresponding to the blue data points. All data have been acquired at 38 K using a photon energy of 30 eV.

Figure 5

The complete evolution of the band structure of TIs under intense illumination and a schematic of the underlying mechanism. Top: Evolution of $E_D$ at different time scales obtained on a single surface location of ${\mathrm{BiSbTeSe}}_2$ during a standard ARPES experiment. From left to right: Intense illumination promotes downward band bending until a saturation point and from then on further exposure tends to flatten the bands again. Red arrows indicate that true flat-band conditions in an ARPES experiment on these materials can only be achieved at very short or very long time scales. The insets in the upper panel show the corresponding $I(E,k)$ diagrams at different illumination times. Prior to illuminating the surface location that was finally studied with ARPES, the sample had been exposed to residual gas molecules for 3 h, represented by the gray shaded area in the upper panel. The base pressure before and during measurements was, respectively, $1.0\times {10}^{-10}$ and $5.0\times {10}^{-11}\mathrm{mbar}$. All data have been acquired at 16 K using a 27 eV photon flux of $3.2\times {10}^{21}\mathrm{photons}/(\mathrm{s}{\mathrm{m}}^2)$. Bottom: Schematics of the five steps underlying our observations. Vertical dashed lines denote the time period to which each step corresponds. Step 1: immediately after cleavage, the sample surface is free of adsorbates. Step 2: residual gas molecules adsorb on the sample surface during the period while the latter is held in the “dark." Step 3: under the influence of the intense EUV photon beam required to do ARPES, adsorbed molecules start to dissociate into single adatoms in the illuminated sample location [38]. Step 4: all adsorbed molecules are dissociated and/or photoionized, and band bending reaches a maximum. Step 5: Photostimulated desorption of adatoms and surface photovoltage (not illustrated) come into play and the bands shift back up again.

Figure 6

A quantitative model of the microscopic procedures behind the surface band bending in 3D TIs. Top: Time-dependent coverage or density of adsorbed molecules and created charges. Black, red, and green curves follow the coverage or density of, respectively, adsorbed molecules, charges created by photoinduced processes, and molecules desorbed due to incoming photons. Center: Corresponding time-dependent energy value of the Fermi level with respect to the Dirac point. Red and green curves follow the energy variation due to photoinduced processes of charge creation and molecular desorption, respectively. In both the top and center panels, the blue curve shows the total dynamics under the assumption that photostimulated desorption at a local site occurs only after the “activation” of the specific molecule. The dashed curve describes the total dynamics if in the absence of photostimulated desorption the maximum value of surface band bending were to stay unaltered. Bottom: Time-dependent energy variation of the Fermi level in comparison with the experimental data of Fig. 4 showing that the down-shift and up-shift rates are well reproduced. Details on the model parameters are given in the text.

Figure 7

The simulated effect of photon flux and surface decoration on the surface band bending in 3D TIs. Top: Time-dependent energy value of the Fermi level with respect to the Dirac point for various values of the incoming photon flux. Bottom: Time-dependent energy value of the Fermi level with respect to the Dirac point for various time intervals of the surface decoration while the sample was still in the dark. All other parameters of the model are described in the text and they are identical to those used in Fig. 6.