Master thesis defence of the 6th year student of the NUST MISIS Jose J. PAIS-PEREDA

Congratulations to Jose J. PAIS-PEREDA for the excellent defense of his master's thesis "Theoretical investigation of magnetic properties of heterojunctions between 2D films and half-metallic Heusler alloy"!

The defense took place on June 17, 2021 in the Direction of Quantum Physics for Advanced Materials Engineering, Department of Theoretical Physics and Quantum Technologies, NUST MISIS

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 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. Using 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.

For most of the twentieth century, it was known that electrons that create current in an electrical circuit have their own magnetic moment, but in practice this was not used for any purpose. With the onset of the new millennium, a new direction of science has appeared - magnetoelectronics, or, as it is now commonly called, spintronics. It is based on the concept of an electronic spin. According to this concept, electrons are divided into two types of current carriers: electrons with spin up and electrons with spin down (½ or -½). Spintronics is currently studying magnetic and magneto-optical interactions in metallic and semiconductor heterostructures, the dynamics and coherent properties of spins in condensed media, as well as quantum magnetic phenomena in nanosized structures. Along with the previously known magnets, with the development of spintronics, new ones appeared - magnetic semiconductors, substances in which magnetic, semiconducting and optical properties can be controlled. The experimental mental technique of spintronics includes magneto-optical spectroscopy with high (femtosecond) time resolution, micromechanical magnetometer, atomic and magnetic force scanning microscopy of subatomic resolution, nuclear magnetic resonance spectroscopy, and much more. Chemical, lithographic, physical, and molecular cluster technologies make it possible to create various nanostructures with the required magnetic properties for spintronics.

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. ​ 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. 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, 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.

Funding application supported

Ultra-thin diamond films, diamanes, represent a diamond with a thickness of one unit cell. As a method for their preparation, the effect of a chemically induced phase transition was proposed, according to which multilayer graphene can be converted into a diamond film only under the action of chemical adsorption of adatoms on the surface (hydrogen, fluorine, etc.). We have studied the stability of diamanes and constructed a phase diagram of the transition of multilayer graphene to diamane depending on the thickness of the films and the type of surface.

A controlled tuning the structure of nanomaterials at the atomic level is the most important problem of modern materials science. Description of nanostructures stability requires to take into account their size and surface effects. This problem is especially clearly seen in the study of the phase transformation of nanomaterials, when the phase transition depends not only on external conditions, but also on the contribution of surface effects. For example, the classical Bundy’s carbon phase diagram changes with decreasing carbon film thickness, the graphite-diamond phase transition pressure increases, which reflects an increase in the instability of diamond with size reduction. Upon reaching the atomic thickness, diamond films should demonstrate a number of extremely attractive physical properties, but their synthesis requires fundamentally different approach. Two ways of synthesis of nanomaterial usually considered: the “top-down” and “bottom-up” approaches. The top-down paradigm, when macroscopic material is separated to the required nanostructure probably is not the case, since it is impossible to obtain diamond films of nanometer thickness by separating the bulk diamond. The bottom-up approach (the required nanostructure is synthesized from smaller nanostructures) seems to be the most relevant for this case, although it certainly requires overcoming a number of non-trivial scientific problems. The traditional method of chemical vapor deposition is not applicable for solving the problem of obtaining diamond films of atomic thickness due to the high growth rate and their imperfection at the atomic level. In this project, we will consider another option for producing diamond films, when the initial material is not gas, but a bilayer graphene film. Their formation occurs through a controlled chemical reaction of two graphene sheets with reference atoms, mainly hydrogen and fluorine. We will try this method in an experiment, and we will study theoretically in details the mechanism of transformation of graphene layers not only in the case of bilayer graphene, but also other structures based on weakly coupled layers, double-walled carbon nanotubes and other related nanomaterials.

The project PI is Dr. habil. Pavel Sorokin.

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.