Quantum transfer of a 2D state of a surface in a nonsymmorphic semimetal

We have systematically investigated the quantum oscillations of individual ZrSiSe films and have successfully discovered a new 2D trivial surface state that can be attributed to “floating” surface states caused by a decrease in symmetry on the surface. Our results also suggest that these states are trivial, but persistent and probably protected by a new mechanism. Our results open up a new field for studying exotic surface states in topological quantum materials.

The work is published in the journal Nano Lett. 2021, 21, 11, 4887–4893

In the experiment carried out by our colleagues, it was reported that surface states with stable two-dimensional quantum oscillations of Shubnikov-de Haas (SHDH) were observed in thin flakes of ZrSiSe. Oscillations were observed even with the presence of an amorphous oxidized layer, which indicates its stability.​

Figure 1 - (a) ZrSiSe crystal structure showing Se-Zr-Si-Zr-Se layers and a splitting plane (red arrow). (b) Optical microscope image of a 28.2 nm ZrSiSe nanoflake on a Si / SiO2 wafer obtained by micromechanical exfoliation. The inset shows an atomic force microscope image of the Hall bridge. Images of c) a crystal along the [100] plane and d) individual ZrSiSe films along the [110] plane obtained by scanning transmission electron microscopy of an annular dark field with aberration correction

Figure 1 shows the crystal structure of ZrSiSe, which can be considered as stacked layers of Se-Zr-Si-Zr-Se. The weak strength of the interlayer bond makes it possible to mechanically exfoliate ZrSiSe to atomically thin layers, as shown in Figure 1. Using scanning transmission electron microscopy (STEM), images of individual layers were obtained with good crystallinity of the inner regions with small oxidized surface amorphous layers (about 5 nm) on top and bottom surfaces. The arrangement of the Zr, Si and Se atoms exactly matches the expected structure of the ZrSiSe lattice.

The ZrSiSe Hall bridge was fabricated using electron beam lithography. When a magnetic field was applied perpendicular to the sample surface (i.e., along the c axis), clear oscillations of the SHDH in the magnetoresistance were observed for all thin ZrSiSe flakes with different thicknesses at low temperatures. Surprisingly, the oscillatory components of the longitudinal resistivity Δρxx obtained by background subtraction show different signatures for very thick and thin flakes.

In principle, the picture of quantum oscillations with a certain frequency corresponds to the extreme cross section of the Fermi surface. Therefore, the additional frequency in thin samples indicates that an additional electron band begins to play a significant role in measuring the conductivity in samples with a small thickness. Generally speaking, modification of the band structure due to the size effect is widely observed in two-dimensional materials when the monolayer limit is reached. However, it is unlikely that the size effect manifests itself at a thickness of ~ 60 nm. Instead, this unusual frequency is most likely a manifestation of a new surface state.

It is usually assumed that the surface state is formed as a result of the termination of the action of the volume potential or the presence of surface defects / adsorbates in conventional materials. However, origins of this kind can be easily ruled out, since quantum oscillations are usually not expected for "dirty" materials. Considering that defects or adsorbates are strong scattering centers, quantum oscillations from the surface state are often easily destroyed in conventional materials. However, in ZrSiSe, the observed effect is noticeable and well reproducible, even in the presence of significant amorphous surface layers, which are observed by scanning transmission electron microscopy.

This conclusion was confirmed by a direct calculation of the electronic structure of the surface of the ZrSiSe crystal made by our group. On the surface of the crystal, translational symmetry is broken along one direction and lowers the symmetry. In this layered structure, the natural cleavage plane (001) has a symmetry reduced to the P4mm group (no. 99). Consequently, the degeneracy of the upper zones is not protected and can be removed. Such a nonsymorphic decrease in symmetry significantly deforms the orbitals, which removes the degeneracy of the bulk zones at the X point of the Brillouin zone and, consequently, leads to the appearance of an unoriented surface zone "floating" over the zone of the bulk crystal.

Figure 2 - (a) Evolution of the bulk band structure (marked in black) into the band structure of the plate (marked in red) with a sequential increase in the vacuum space between the SeZr-Si-ZrSe layers. The inset shows the atomic structure and distribution of the wave function at the marked k-point on the band structure. (b) Band structure and density of electronic states of a six-layer ZrSiSe plate with a ZrSe surface. In the electronic structure, the black solid lines are the zones of bulk states, and the red zones are the contribution from the surface layer. In the density of electronic states, the dotted and solid lines correspond to the contributions of the p and d orbitals, respectively, from the bulk (black) and surface layers (red) states. (c) The zone structure of a wafer with a Si surface and a ZrO surface, where Se is replaced by O, and (d) the same surfaces with passivated dangling bonds with -H and -OH. The red dotted line indicates the contribution from the surface layer. (e) Structure of ZrSiSe with an oxidized layer (ZrSiO4) and its band structure. The Fermi level is taken as zero and is indicated by a horizontal dashed line

The decrease in the crystal symmetry and the removal of degeneracy can be represented as the evolution of the bulk band structure into the structure of the band of a separate layer (shown in Fig. 2). A sequential increase in the vacuum space between the SeZr-Si-ZrSe layers leads to a shift of the electron band in XM with a final drop by ∼1 eV with the formation of two electron pockets centered at point X.

This is due to the Zr 4d orbitals in the plate. In bulk ZrSiSe, the Zr 4d orbitals are linked to the Se p and Zr 4d orbitals in the neighboring unit cell along the (001) direction (see the distribution of wave functions in Figure 2 on the left and the density of electronic states in Figure 2, marked in black), while in a separate plate the orbital Zr d are associated only with Si p orbitals.

To understand the experimental observation of the "floating" zone, we performed a calculation of a model of a plate with a thickness of six unit cells along the c direction. The bulk bands arising from the inner layers are clearly visible in the band structure, but, in addition, a new band appears (marked in red), which crosses the Fermi level, which should lead to the observation of new electron carriers in comparison with the bulk crystal. The distribution of the wave function corresponding to this new zone is located in the upper layer of ZrSe, which indicates the purely surface nature of this state. Thus, as in the case of the monolayer, the dangling bond with the Zr 4d orbitals in the uppermost unit cell results in a downward shift of the electron band by X, which was once called the floating zone. It should be noted here that the band structure of a multilayer plate strongly resembles a superposition of band structures of a bulk crystal and a single-layer plate marked in black and red in Figure 2a (right image) with a shift of the Fermi level of the plate to the valence band of the bulk crystal. This can be viewed as the fact that the top layer of the multilayer plate hardly interacts with the inner layers, but is still doped with electrons. In addition, this observation allows one to study the behavior of the floating zone when only the upper layer is modified.

The floating zone can be adjusted by changing the chemical environment of the Zr by decorating / coating the surface or forming an interface. Figure 2c shows various cases of surface termination that destroys the floating zone or moves it above the Fermi level. However, the termination of the dangling links leads to the restoration of the floating zone. In general, it can be seen that the surface contains many dangling bonds, as in the case of unrealistic silicon termination of the ZrSiSe crystal, which leads to surface states that are very different from those in the bulk or in the plate. In addition, the second (near-surface) ZrSe layer contributes only to the bulk zones. The possibility of rebuilding the floating zone is due to its trivial nature.

On the other hand, it is very likely that the experimentally observed interface between the oxide layer and ZrSiSe has little effect on the floating zone. We modeled the oxide layer as zirconium orthosilicate, in which the Zr and Si atoms are surrounded by O. We modeled the interface between a two-layer ZrSiSe supercell plate (2 × 2 × 1 unit cells) and a ZrSiO4 layer. DFT calculations clearly showed that ZrSiO4 only weakly interacts with the ZrSe surface due to its high chemical stability, which leads to the conservation of the floating band crossing the Fermi level, while the ZrSiO4 bands do not appear near the floating bands due to the large energy gap of the oxide. It can be assumed that the amorphous oxidizing layer does not affect the structure of the ZrSiSe zone and protects the floating zone from any other chemical modifications.

Highly efficient double-sided doping of single-walled carbon nanotubes

Together with the experimental group of Prof. Albert Nasibulin (Skoltech) we proposed and thoroughly investigated a new approach that comprises simultaneous bilateral (outer and inner surfaces) SWCNT doping after their opening by thermal treatment at 400 °C under an ambient air atmosphere. Doping by a chloroauric acid (HAuCl4) ethanol solution allowed us to achieve the record value of sheet resistance of 31 ± 4 Ω/sq at a transmittance of 90% in the middle of visible spectra (550 nm). The strong p-doping was examined measurements and confirmed by ab initio calculations demonstrating a downshift of Fermi level around 1 eV for the case of bilateral doping.

Work is published in J. Mater. Chem. C, 2021,9, 4514-4521

Although films of single-walled carbon nanotubes (SWCNTs) are the most promising candidates for the creation of transparent and flexible films, they still do not meet the requirements of optoelectronics. In this work, a new approach was proposed and investigated, which consists in the simultaneous two-sided (from the inner and outer sides) alloying of SWCNTs. This result was experimentally obtained by our colleagues, in which SWCNTs were discovered by heat treatment at 400 ° C in ambient air. Doping with ethanol solution of chloroacetic acid (HAuCl4) made it possible to achieve a record value of leaf resistance (31 ± 4) Ohm / m2 with a transmission of 90% in the middle of the visible spectrum (550 nm).

The origin of the more efficient doping of SWCNTs due to the removal of preformed caps by heat treatment is also confirmed by our observations using transmission electron microscopy (TEM). Figure 1 shows TEM images of films doped with HAuCl4, both intact and thermally treated SWCNTs. In the images of the initial SWCNTs and those treated at 300 C, the surface of the nanotubes is decorated with metallic gold nanoparticles approximately 5 to 10 nm in size (Fig. 1a, b). On the contrary, for samples thermally treated at 400 ºC, in addition to decorating the outer surface with Au0 nanoparticles, one can notice the filling of the inner space of SWCNTs (Figure 1c, d). Measurement of the interplanar distance of the encapsulated material from TEM images gave a result of 0.235 nm. It was found to be metallic gold, which has a (111) interplanar spacing of 0.2355 nm. Gold nanoparticles cover the outer surface of SWCNTs, forming as a result of spontaneous reduction of [AuCl4] - anions. When the heat treatment temperature is high enough to oxidize the caps of the nanotubes, for example, 400 ºC, the alloying solution penetrates into the inner space of the SWCNTs, which leads to improved doping and, in addition, to the formation of a metallic gold phase. This is manifested in a higher doping efficiency of the SWCNT film treated at 400 ºC, which explains its record value of R90.

a) SWCNT without pre-heat treatment and with pre-treatment at b) 300 ºC (b) and c) 400 ºC. e, f) STEM images of open SWCNTs doped with 15 mM HAuCl4 with encapsulated gold nanowires

Figure 1 - TEM images of SWCNT films doped with 15 mM ethanol solution of HAuCl4. Arrows show SWCNTs filled with the Au metal phase

To identify the reasons for the effective doping of heat-treated SWCNTs, we performed a theoretical analysis of their electronic properties for individual cases of either only external or simultaneous external and internal doping. Previous calculations using density functional theory (DFT) showed that the p-type character of doping is due to the adsorption of AuCl4. It can be expected that other Au-containing systems will also participate in the doping process. We have carried out a systematic study of the effect of several types of dopants based on AuClx on the electronic structure of carbon nanotubes. The molecular groups of gold chlorides used in the calculations were taken from the crystal structure of Au (III) and Au (I) chlorides, and a pure Au nanowire was cut from bulk fcc gold. SWCNTs with chirality were chosen as a model of the nanotube for the study (10, 10).

Figure 2 - Atomic structures of pure SWCNT, SWCNT doped outside, and doped both inside and outside with various dopants AuClx. The corresponding shift of the Fermi level is indicated under each structure. Gray, pink and yellow balls represent carbon, chlorine and gold atoms, respectively

Calculations show (Figure 2) that SWCNTs doped only outside (SWCNT @ AuCl4) demonstrate a significant downward shift of the Fermi level by 0.79 eV, which characterizes p-type doping. Additional incorporation of Au nanowires into SWCNTs leads to a redistribution of the electron density from the nanowire to SWCNTs and a general shift of the Fermi level by 0.22 eV, which corresponds to n-type doping. However, no significant effect on charge transfer between SWCNTs and Au nanoparticles located on the surface of nanotubes is observed experimentally. In the case of double-sided doping with AuCl4, the largest shift of the SWCNT Fermi level to 0.97 eV is observed in the case of double-sided doping with AuCl4. the largest shift of the SWCNT Fermi level is observed up to 0.97 eV. This indicates a more efficient p-type doping compared to the sample doped only from the outer surface, which reflects the efficient doping of open SWCNTs.

Atomically thin films: current progress (Review)

A review has been published in Physics-Uspekhi (with 423 references ) devoted to the current state of research of atomically thin films. The structure and properties of atomically thin monoelemental films, such as 2D Fe, Au, Li, as well as Si, Ge, B etc., are described in detail. Two-dimensional films of metallic compounds like FeO, CuO, ZnO and FeC, CoC and CuC are considered. The main approaches to the stabilization of monoatomic films inside pores or between layers of other 2D materials are presented, and the exfoliation mechanism of ionic-covalent films with a polar surface into weakly bounded monolayers is described.

Paper have published in Physics-Uspekhi 64, 1, 28 (2021) ​ The isolation and subsequent detailed study of graphene have shown its significant prospects and potential for use in a wide range of technologies, such as composite materials, low-dimensional catalysts, touch screens, conductive ink, electronic paper, and organic light-emitting diodes. In 10-20 years, the introduction of graphene-based transistors and other logic units is expected. ​ The main obstacles to the wide use of graphene in electronics are the requirements of high quality of the synthesized atomic structure and the absence of a bandgap. The latter is a fundamental problem, to which no universal solution has been found yet. Each of the approaches proposed, e.g., functionalization, the introduction of defects into the structure, or graphene splitting into separate ribbons, has its drawbacks. Indeed, the chemical adsorption of atoms on graphene leads to a change in the hybridization of carbon atoms from sp2 to sp3 accompanied by destruction of the p-system responsible for graphene conductivity. The proposed partial functionalization by forming hydrated or fluorinated regions (in a limiting case, separate periodically arranged chains of hydrogen) solves the problem, because a bandgap opens between the regions due to the dimensional effect. However, in spite of experimental confirmation of the effect, this technique requires adsorption with atomic precision, which at present is hardly a solvable problem. ​ Using monolayers of different compositions can be an alternative way, especially as pioneering study has demonstrated the flexibility of the micromechanical exfoliation approach for obtaining planar two-dimensional structures from any crystals with weakly bound layers. The resulting materials have a planar structure as thin as one or a few atomic layers, whereas the lateral size can exceed a few micrometers. The atomic-size thickness, quantum dimensional effects, and high anisotropy of the optical properties of two-dimensional nanomaterials, as well as prospects of their application, have continuously attracted great interest of the world scientific community. ​ Studies on finding new quasi-2D films turned out to be so efficient that up to 2020 they numbered a few hundred. This led to a paradoxical situation of a lack of resources in the scientific community sufficient for their thorough investigation. Moreover, the latest theoretical studies predict the possibility of five to six thousand more compounds in a quasi-2D state, which ultimately makes 2D materials one of the most vast and poorly studied areas of up-to-date materials science. ​ The aim of the present review is to inform a wide range of readers about the current state of materials science in the field of noncarbon 2D structures. However, because of the great number of discovered and predicted two-dimensional crystals mentioned above, the discussion is focused on atomically thin films only. This gives rise to a certain difficulty in classifying the compounds described; for example, whether the films of phosphorene or silicene are atomically thin or not? Indeed, both structures have a thickness of a single atom and differ only by the degree of lattice corrugation. Therefore, a criterion should be introduced, according to which the present review will consider only those compounds with the corrugation degree (the out-of-plane displacement of atoms D) much smaller than the lattice parameter of the crystal a, i.e., D<<a. Notably, this criterion excludes phosphorene from consideration, but requires describing silicene and other allied materials. The review consists of three main sections. Section 2 considers single-layer films consisting exclusively of metal atoms (Fe, Au, etc.) and the possibility of their stabilization using other two-dimensional materials (mainly graphene). Section 3 presents a detailed description of various two-dimensional metal compounds, in particular, oxides and carbides of transition metals. Section 4 is devoted to films consisting of elements of groups 13-16 of the periodic table: silicene, borophene, and allied materials. ​