Micro-metric electronic patterning of a topological band structure using a photon beam

In an ideal 3D topological insulator (TI), the bulk is insulating and the surface conducting due to the existence of metallic states that are localized on the surface; these are the topological surface states. Quaternary Bi-based compounds of Bi2−xSbxTe3−ySey with finely-tuned bulk stoichiometries are good candidates for realizing ideal 3D TI behavior due to their bulk insulating character. However, despite its insulating bulk in transport experiments, the surface region of Bi2−xSbxTe3−ySey crystals cleaved in ultrahigh vacuum also exhibits occupied states originating from the bulk conduction band. This is due to adsorbate-induced downward band-bending, a phenomenon known from other Bi-based 3D TIs. Here we show, using angle-resolved photoemission, how an EUV light beam of moderate flux can be used to exclude these topologically trivial states from the Fermi level of Bi1.46Sb0.54Te1.7Se1.3 single crystals, thereby re-establishing the purely topological character of the low lying electronic states of the system. We furthermore prove that this process is highly local in nature in this bulk-insulating TI, and are thus able to imprint structures in the spatial energy landscape at the surface. We illustrate this by ‘writing’ micron-sized letters in the Dirac point energy of the system.

Topological insulators (TIs) are a novel state of quantum matter, serving as a platform for the observation of fundamental physics phenomena and possessing high potential for applications ranging from spintronics to quantum computation [1][2][3][4].Their remarkable properties are linked to twodimensional electronic states termed topological surface states (TSS) [5][6][7], which are protected from backscattering and Anderson localization by non-magnetic impurities due to the combined effect of a helical spin texture and time-reversal invariance [8][9][10].In an applications context, controlled tunability of the electronic bands between regimes dominated by either the TSS or bulk-derived states of trivial topology is important.Different approaches have been reported on Bi-based TIs mainly involving surface decoration [11][12][13][14] and tuning the bulk stoichiometry [15,16], both of which involve modification of the (surface) band structure across the whole sample.
Here we report a new approach that not only provides full control over the band structure at the surface of topological insulators but does so on a local, micron-scale level.Our method requires (a) a bulk-insulating TI materials platform, and (b) a patterning tool -in our case an extreme-ultraviolet (EUV) photon beam of flux >10 21 photons/(s m 2 ).We use angle-resolved photoelectron spectroscopy (ARPES) to track deliberate modifications of the electronic structure of two quaternary TI compounds that possess high bulk resistivity, namely Bi 1.46 Sb 0.54 Te 1.7 Se 1.3 (BSTS1.46),demonstrating successful imprinting of a pre-defined, micro-metric spatial pattern -the letters IoP -into the surface electronic band structure of the BSTS samples.
BSTS systems are excellent bulk insulators (see supplemental material SM-1, Fig. S1 and Ref. 16) and possess TSS, which display the characteristic dispersion relation called a Dirac cone [15].Our results for BSTS1.46 are presented in Fig. 1, from which it is clear that surface decoration due to the adsorption of residual gas atoms from UHV (panels a-c) is the cause of downward band bending [17].Thus, in practice, despite the bulk insulating nature of the crystal, within a few 10 nm of the surface the conduction band states are shifted below the Fermi energy (E F ), where they evolve into a parabolic band (Fig. 1c) which is a signature of electrons confined in the potential-well defined by the surface potential and the band bending profile into the bulk.Consequently, the real-life situation for a cleaved surface of BSTS (even in UHV), is that we have an insulating bulk, topologically-protected surface states and topologically-trivial surface-related states related to the dipping down in energy of the conduction band due to band bending.
We now demonstrate that this dual character offers the chance to act on the electronic band structure at the micron spatial scale, with lifetimes exceeding 5 hours.With bandbent BSTS as the starting point, we are able to selectively erase the topologically trivial surface states at the Fermi level, making use only of a beam of photons with energy exceeding the band gap of BSTS.This makes BSTS's combination of a highly-insulating bulk and a metallic surface of mixed topological character (i.e.topologically trivial and non-trivial states) ideal for EUV electronic patterning.
Comparison of Figs.1d and 1e show the effect of a beam of photons with energy exceeding the band gap of BSTS and flux >10 21 photons/(s m 2 ).The starting point is band bent BSTS1.46 (Fig. 1d) after a few hours in UHV at low temperature, with only minimal exposure to synchrotron radiation.Exposing the same surface to a photon flux of 3.2 × 10 21 photons/(s m 2 ) for 4 hours gives the data Fig. 1e in which a pronounced energy shift of the TSS to lower binding energies is evident, whereby the Dirac point (blue arrow), now lies at an energy comparable to E F .
What Fig 1e shows is the result of the surface photovoltage effect (SPV), which is known to reduce band bending at semiconductor surfaces [18][19][20], when the photon energy exceeds the bulk gap (∼400 meV for BSTS).The photon beam cre- ates electrons and holes, which separate along the z-direction in the space charge layer associated with the band bending.This counteracts the adsorbate-induced potential, resulting ultimately in a (non-equilibrium) restoration of the flat-band situation.To induce SPV shifts, the photon flux should exceed a material-dependent threshold [21], and the total SPV-related energy shift tracks the total photon fluence until saturation is attained.This phenomenology allows a quick I(E,k) measurement to 'read' the energy of the surface bands without SPV effects, as in Figs 1a-c.The photon fluence can be controlled either by varying the integrated exposure time or the flux itself.At intermediate exposure to high-flux illumination, significant spectral broadening accompanied the energy shift, as shown in Fig. 1e.This broadening is absent in the initial and final stages of SPV-induced band flattening (SM-2, Fig. S2), and is due to inhomogeneous illumination within the beam profile.The broadening can be modelled successfully (SM-3, Fig. S3), and is an expression of the local nature of photoinduced changes.
SPV effects depend strongly on the bulk resistivity of the TI material.In Fig. S4 we compare the behaviour of BSTS with that of Bi 2 Se 3 , showing that strong and local SPV effects are only seen for the bulk-insulating BSTS and not for Bi 2 Se 3 .Both this dependence on the bulk resistivity and the fact that the observed broadening fits a SPV-based model (SM-3 and Ref. 21) favors SPV over photon-stimulated desorption as the origin of these effects, in agreement with Ref. 22. Further details of the SPV process in BSTS and other TIs will be published elsewhere.The focus of what follows is on the spa-tial sensitivity of this process in BSTS, as this enables micrometric electronic patterning of the band structure, as we will describe below.
Fig. 2 summarizes the key result of our research for a crystal of BSTS1.46.In the upper row of images, each rectangular pixel represents an I(E,k) image, recorded using an EUV beamspot of 100 µm (h) × 30 µm (v).Representative I(E,k) images recorded from the individual pixels marked with a white 'X' are shown, center-left, and display the characteristic linear TSS dispersion and signatures of the bulk valence and conduction bands.Due to prior exposure to UHV, essentially saturated band-bent conditions are prevalent here, and the average binding energy of the Dirac point, E D , is ∼370 meV.The three greyscale images in the top-left panel represent a spatial 'readout' of E D (with 10 seconds measuring time per spatial pixel), proving low variation of E D in this 'virgin' state over a mm scale area of the surface.
We subsequently expose pre-selected parts of the sample to a high-fluence photon beam.The target areas are outlined in the top left panels of Fig. 2 using dashed lines and spell the letters "I" , "o" and "P", the acronym for Institute of Physics.The fluence of the writing photon beam is 40× that used for E D -readout, and comparison of the top-left and top-right spatial maps shows that after high fluence exposure, the letters have been successfully imprinted into the E D spatial landscape.
Looking at the I(E,k) images from the three locations centered on the letters (marked with a red '1' and shown in the red-outlined black panel), it is clear that E D has shifted upward by some 150 meV and consequently the bulk conduction band is absent, now being above E F .Artist's impressions for the 'written' and adjoining pixels are shown in the bottom-left panels, illustrating that at the written areas, only the valence band states at higher binding energy and the TSS at E F are seen: the topologically trivial band-bent CB states have effectively been erased.
After SPV-based writing, the nearest-neighbour (NN, blue '2') and next-nearest-neighbour (NNN, green '3') pixels are hardly affected, as can be seen in the spatial maps and the corresponding I(E,k) images.Whilst the NNN pixels show essentially no change with respect to the virgin state, the NN pixels show only a very modest energy shift.For both NN and NNN locations, besides the valence band, both the TSS and the surface-confined bulk conduction band states are still visible at binding energies ≤E F .So, what the data of Fig. 2 show is that for bulk insulating BSTS, the non-topological surface states can be removed along a spatial trajectory that can be chosen at will, leaving behind pure TSS's at E F , which will dominate the transport properties of the system at these locations.This spatially-resolved tunability of the electronic band structure is a novel and additional 'knob', giving us control over the topological states in real 3D topological insulators.Fig. 2 illustrates the creation of micron-sized structures, the spatial extent controlled by the dimensions of the EUV light beam.Use of more finely focused beams or masks, true nanometric patterning of the electronic states should be within reach.written structures, in which the left panel shows the same "P" as in Fig. 2.This sample area then remained unexposed to external illumination until a second readout 330 min later, which is shown in the right-hand panel of Fig. 3.There is a reduction in the definition of the letter, signalling finite in-plane diffusion of the photo-induced carriers, nevertheless, the imprinted pattern is still clearly visible after more than six hours.
In the following, we discuss the outlook for further improving this approach and touch on a few open issues.Firstly, how far could the spatial resolution be improved?The data argue for a strong lateral confinement of the photo-induced charges in the bulk and near-surface region of BSTS at low temperature, as the written structures (Fig. 2) are as small as the photon beam used to write them.The simulations discussed in SM-3 show that the system reacts to the differing photon exposures within the beam profile, pointing to possible sub-micron length scales upon further reduction of the beam size and control over the beam shape.We mention that nano-ARPES measurements would be one way of providing a spectroscopic feasibility test [23,24] of future nanoscale pat- terning applications in TIs.
The second question is: can the lifetime of the photonbased manipulation of the electronic structure be extended?The structures presented here were written in a serial, pixelby-pixel process, during (and after) which, the sample surface is continuously exposed to residual gases, whose adsorption tends to increase, rather than flatten the downward band bending.A parallel strategy in which different sample locations are exposed in a multi-beam device or one with a line focus, would significantly decrease the total time taken to imprint a pattern and would thus improve the 'active' lifetime of the written pattern.Periodic re-illumination or even permanent illumination could be considered to prolong the lifetime of the modification of the electronic structure indefinitely.
A final question: is a 3 rd generation electron storage ring as a light source a necessary condition for this patterning approach?In our case, it was convenient to use the same photon source as both a patterning tool and (at reduced fluence) a readout tool.However, the general nature of the surface photovoltage effect means that other super-band-gap photon sources such as laboratory lasers or LEDs could be used, and a laser pointer or standard LED source is certainly capable of achieving comparable fluxes to those of the EUV source used here.
Consequently, given the feasibility of photon-beam induced modification of the electronic structure at the surface of bulkinsulating TIs using readily available light sources, the way ahead looks clear for exploring how such manipulation of the electronic landscape can be exploited in transport and devicebased experiments.Already some transport experiments on bulk-insulating, 3D TI systems have been interpreted as showing complications from topologically trivial, band-bending induced 2DEG states, besides the TSS [25].Thus, even global spatial tuning of the surface chemical potential may prove to be of use.When considering adding the spatial structuring of the electronic states to transport experiments, careful experimental design will be required so as to avoid short-circuiting the illuminated 'topological only' transport channel by the non-illuminated regions which maintain their metallic character and topologically trivial states at the Fermi level.
In summary, the ARPES data presented here from the 3D, bulk insulating topological insulator Bi 1.46 Sb 0.54 Te 1.7 Se 1.3 present unequivocal evidence that it is possible to exploit a beam of super-band-gap photons (with flux exceeding 10 21 photons/[s m 2 ]) to reverse the downward band bending that results in the bulk conduction band states dipping below E F in the surface region.Furthermore, such a photon beam can also write micron-sized spatial patterns of arbitrary shape in the energy landscape of the topological electronic states in the surface region.This electronic patterning persists on a timescale of several hours, and thus use of this photon-induced reversal of the occupation of surface-confined bulk conduction band states presents a novel route providing local control over the topological character of the states at the Fermi level of bulkinsulating TIs.

FIG. 1 :
FIG. 1: Tunability of the electronic structure of bulk-insulating Bi1.46Sb0.54Te1.7Se1.3 by adatom adsorption and by exposure to high-flux photons.(a-c) Near-EF electronic structure on increasing exposure to residual gases in a UHV environment.(d,e) Strong changes occur in the near-EF electronic structure after long exposure to a high-fluence photon beam [flux 3.2 × 10 21 photons/(s m 2 ) for 4 hours].After exposure, the Dirac point has shifted upward to lie very close to EF, as indicated by the red/blue arrows.The sample temperature for all data was 17K.

Fig. 3 FIG. 2 :
FIG. 2: Demonstration of micro-metric electronic patterning of the electronic states of the topological insulator Bi1.46Sb0.54Te1.7Se1.3(BSTS1.46).The three top-left panels represent the spatial dependence of the Dirac point energy (ED) under saturated band bending conditions, before high-fluence photon exposure.The grey-scale shows that the spatial variations in this ED-landscape are negligible.Each pixel corresponds to an I(E,k)-measurement, with examples (white 'X' locations) shown in the center-left, black-framed panel.The regions defined by the dashed lines were then exposed to a high-fluence photon beam, and after low-fluence ARPES 'readout', the new spatial ED-landscape is shown in the top-left panels, indicating that the letters I, o and P (IoP, the acronym for Institute of Physics) have been successfully imprinted into the electronic states of the BSTS1.46surface.The numbers '1', '2', '3' on the post-writing areas label pixels on the written line, the nearest-neighbor and next-nearest neighbour sites, respectively, and the respective I(E,k) images are shown in the lower-right red-, blue-and green-framed boxes.Comparison of the black-and red-framed I(E,k) images reveals that the writing process has pushed the topologically trivial band-bent states above EF.The neighboring pixels (blue-framed data-box) are only moderately affected, while the 2 nd -nearest neighbors (green-framed data-box) show negligible change in ED.The graphical illustrations (bottom-left) illustrate the low-lying, occupied electronic structure at the red, blue and green pixels, showing that only for the BSTS receiving high-fluence exposure are the states shifted significantly towards EF and the conduction band depopulated.The greyscale pixel images in the upper panels are scaled in units of the beam diameter along the x(y) axes, which was 100(30) µm.The sample temperature was 17K and the photon flux was greater than 10 21 photons/(s m 2 ).The fluence per pixel in the spatial ED maps used for readout was 40× lower than the corresponding fluence used for writing.

FIG. 3 :
FIG. 3: The lifetime of photo-induced micro-metric patterns.(left) The imprinted character is "P" reproduced from Fig. 2. The grey-scale encodes the energy shift of ED after exposure to an EUV beam of super-band-gap energy and high photon fluence (see text).(right) Readout of the same area after leaving the sample in the dark for 6.5 hours.The sample temperature was 17K.