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Spontaneous strain and spontaneous folding of thin nanoplatelets are known phenomena whose microscopic mechanisms are still debating. In this work, first-principles calculations are used to study the mechanical stresses that arise in Janus CdSe nanoplatelets and result in their spontaneous strain. Calculations reveal the existence of three microscopic mechanisms of this phenomenon. Two bulk mechanisms are associated with the inverse piezoelectric effect in an electric field created by the difference in electronegativities of ligands and by the depolarizing field resulting from the difference in the potential jumps in electrical double layers on the surfaces of nanoplatelets. These mechanisms account for 5-25% of the observed effect. The third mechanism is associated with the surface strain of nanoplatelets by bridging bonds, and its influence is predominant. It is shown that the latter mechanism cause spontaneous folding of thin CdSe nanoplatelets and, depending on the values of surface stresses and lateral orientation of nanoplatelets, can result in formation of their experimentally observed structures such as scrolls, spirals, and twisted ribbons., Comment: 10 pages, 7 figures, 3 tables

The vibrational spectroscopy of semiconductor nanostructures can provide important information on their structure. In this work, experimental Raman and infrared spectra are compared with vibrational spectra of CdSe/CdS core/shell nanoplatelets calculated from first principles using the density functional theory. The calculations confirm the two-mode behavior of phonon spectra of nanostructures. An analysis of the experimental spectra reveals the absence of modes with a high amplitude of vibrations of surface atoms, which indicates their strong damping. Taking into account the difference in the damping of different modes and their calculated intensities, all bands in the spectra are unambiguously identified. It is found that the frequencies of longitudinal optical modes in heterostructures are close to the frequencies of LO phonons in bulk strained constituents, whereas the frequencies of transverse modes can differ significantly from those of the corresponding TO phonons. It is shown that an anomalous thickness dependence of CdS TO mode is due to a noticeable surface relaxation of the outer Cd layer in the nanostructure., Comment: 9 pages, 9 figures, 2 tables

The stability of high-symmetry $P4mm$ polar phase in eleven ferroelectric perovskite superlattices with the polar discontinuity is studied from first principles. In most superlattices, this phase exhibits either the ferroelectric or the antiferrodistortive instability, or both of them. The structure of the ground state and, for a number of systems, also of metastable phases in these superlattices is found. The spontaneous polarization and piezoelectric properties of superlattices are calculated. The appearance of high piezoelectric coefficients (up to 150-270 pC/N) in some superlattices is associated with the strain-induced local rearrangement of certain atomic groups in the primitive cell., Comment: 8 pages, 3 figures, 4 tables. arXiv admin note: substantial text overlap with arXiv:2012.08817

The stability of a high-symmetry $P4mm$ polar phase in seventeen short-period ferroelectric perovskite superlattices with polar discontinuity is studied from first principles within the density-functional theory. It is shown that in most superlattices this phase exhibits either the ferroelectric instability or the antiferrodistortive one, or both of them. For each superlattice, the ground-state structure, the structure of possible metastable phases, the spontaneous polarization, and piezoelectric properties are calculated. The properties of superlattices with the polar discontinuity are compared with those of superlattices with broken symmetry and of ordinary superlattices, which have no the polar discontinuity. It is shown that high piezoelectric coefficients (up to 150--270 pC/N) in some superlattices with the polar discontinuity are due to the appearance of strong lattice distortions, whose symmetry follows that of a low-lying polar phonon mode of the ground-state structure, under the influence of external strain., Comment: 13 pages, 4 figures, 5 tables

Recently people started to understand that applications of the mathematical formalism of quantum theory are not reduced to physics. Nowadays, this formalism is widely used outside of quantum physics, in particular, in cognition, psychology, decision making, information processing, especially information retrieval. The latter is very promising. The aim of this brief introductory review is to stimulate research in this exciting area of information science. This paper is not aimed to present a complete review on the state of art in quantum information retrieval.

We propose a hypothesis that the potential energy surface (PES) of interlayer interaction in diverse 2D materials can be universally described by the first spatial Fourier harmonics. This statement (checked previously for the interactions between graphene and hexagonal boron nitride layers in different combinations) is verified in the present paper for the case of hydrofluorinated graphene (HFG) bilayer with hydrogen bonding between fluorine and hydrogen at the interlayer interface. The PES for HFG bilayer is obtained through density functional theory calculations with van der Waals corrections. An analytical expression based on the first Fourier harmonics describing the PES which corresponds to the symmetry of HFG layers is derived. It is found that the calculated PES can be described by the first Fourier harmonics with the accuracy of 3\% relative to the PES corrugation. The shear mode frequency, shear modulus and barrier for relative rotation of the layers to incommensurate states of HFG bilayer are estimated. Additionally it is shown that HFG bilayer is stable relative to the formation of HF molecules as a result of chemical reactions between the layers., Comment: 12 pages, 3 figures

The in-plane coefficient of thermal expansion (CTE) for CdSe nanoplatelets with the zinc-blende structure containing from two to five monolayers is calculated from first principles within the quasiharmonic approximation. A comparison of the obtained results with those for bulk CdSe with both the zinc-blende and wurtzite structures finds a significant increase in the magnitude of negative CTE and the temperature range of its observation in nanoplatelets. The main contribution to the negative thermal expansion in CdSe nanoplatelets is given by the out-of-plane flexural ZA mode and in-plane optical $E$ modes that arise from the folding of TA phonon of bulk CdSe., Comment: 10 pages, 8 figures, 4 tables

The ground-state structure of monolayers and nanoplatelets of SnS with a thickness from two to five monolayers is calculated from first principles. It is shown that nanoobjects with only odd number of monolayers are ferroelectric. The ferroelectric, piezoelectric, and elastic properties of these polar structures are calculated. The appearance of polarization in these nanoobjects is explained by an uncompensated polarization that exists in an antiferroelectric structure of bulk SnS. The mechanism of ferroelectricity, in which the ferroelectric distortion is associated with short-range ordering of lone pairs, can be regarded as a way of creating ferroelectrics with high Curie temperature., Comment: 8 pages, 4 figures, 6 tables

Single-layer and bilayer carbon and hexagonal boron nitride nanoscrolls as well as nanoscrolls made of bilayer graphene/hexagonal boron nitride heterostructure are considered. Structures of stable states of the corresponding nanoscrolls prepared by rolling single-layer and bilayer rectangular nanoribbons are obtained based on the analytical model and numerical calculations. The lengths of nanoribbons for which stable and energetically favorable nanoscrolls are possible are determined. Barriers to rolling of single-layer and bilayer nanoribbons into nanoscrolls and barriers to nanoscroll unrolling are calculated. Based on the calculated barriers nanoscroll lifetimes in the stable state are estimated. Elastic constants for bending of graphene and hexagonal boron nitride layers used in the model are found by density functional theory calculations., Comment: 9 pages, 6 figures

The interlayer interaction in graphene/boron-nitride heterostructures is studied using density functional theory calculations with the correction for van der Waals interactions. It is shown that the use of the experimental interlayer distance allows to describe the potential energy surface at the level of more accurate but expensive computational methods. On the other hand, it is also demonstrated that the dependence of the interlayer interaction energy on the relative in-plane position of the layers can be fitted with high accuracy by a simple expression determined by the system symmetry. The use of only two independent parameters in such an approximation suggests that various physical properties of flat graphene/boron-nitride systems are interrelated and can be expressed through these two parameters. Here we estimate some of the corresponding physical properties that can be accessed experimentally, including the correction to the period of the Moir\'{e} superstructure for the highly incommensurate ground state of graphene/boron-nitride bilayer coming from the interlayer interaction, width of stacking dislocations in slightly incommensurate systems of boron nitride on stretched graphene and shear mode frequencies for commensurate graphene/boron-nitride systems, such as a flake on a layer. We propose that the commensurate-incommensurate phase transition can be observed in boron nitride on stretched graphene and experimental measurements of the corresponding critical strain can be also used to get an insight into graphene/boron-nitride interactions., Comment: 15 pages, 4 figures

Exchange-correlation functionals with corrections for van der Waals interactions (PBE-D2, PBE-D3, PBE-D3(BJ), PBE-TS, optPBE-vdW and vdW-DF2) are tested for graphene and hexagonal boron nitride, both in the form of bulk and bilayer. The characteristics of the potential energy surface, such as the barrier to relative sliding of the layers and magnitude of corrugation, and physically measurable properties associated with relative in-plane and out-of-plane motion of the layers including the shear modulus and modulus for axial compression, shear mode frequency and frequency of out-of-plane vibrations are considered. The PBE-D3(BJ) functional gives the best results for the stackings of hexagonal boron nitride and graphite that are known to be ground-state from the experimental studies. However, it fails to describe the order of metastable states of boron nitride in energy. The PBE-D3 and vdW-DF2 functionals, which reproduce this order correctly, are identified as the optimal choice for general studies. The vdW-DF2 functional is preferred for evaluation of the modulus for axial compression and frequency of out-of-plane vibrations, while the PBE-D3 functional is somewhat more accurate in calculations of the shear modulus and shear mode frequency. The best description of the latter properties, however, is achieved also using the vdW-DF2 functional combined with consideration of the experimental interlayer distance. In the specific case of graphene, the PBE-D2 functional works very well and can be further improved by adjustment of the parameters., Comment: 22 pages, 4 figues

Phonon spectra of CdSe nanoplatelets (2-6 ML) with the zinc-blende structure were calculated from first principles within the density-functional theory. It turned out that the Lamb modes in nanoplatelets are in fact optical rather than acoustic vibrations. Phonon spectra of the nanoplatelets show the appearance of a large number of low-frequency modes inherited from TA phonons in bulk CdSe. Calculations of the Raman spectra indicate a need to revise the interpretation of available experimental data. The largest contribution to the Raman spectra is provided by the quasi-Lamb modes with the $A_1$ symmetry. The $B_2$ modes whose frequencies depend on the environment of nanoplatelets and whose properties are closest to the properties of LO phonons explain the results obtained in the "nanoparticle-on-mirror" geometry. The features in Raman spectra previously attributed to surface optical (SO) modes should be interpreted as a manifestation of lower-order quasi-Lamb $A_1$ modes. Calculations of the infrared spectra find, in addition to the TO phonon line, the appearance of intense lines from surface modes originating from terminating F(Cl) atoms on the surface of nanoplatelets and true SO-modes., Comment: 8 pages, 8 figures

Semiconductor nanoparticles of cadmium chalcogenides are known to exhibit pronounced thickness-dependent $E_0$ series of exciton transitions at the $\Gamma$ point of the Brillouin zone (BZ). In this work, we report an experimental evidence for high-energy series of exciton transitions, which originates from BZ points different from the $\Gamma$ point, in the family of cadmium chalcogenide quasi-2D nanoplatelets (NPLs). Intensive UV absorption bands demonstrating a pronounced size effect are observed for CdTe, CdSe, and CdS NPLs in addition to the $E_0$ exciton bands in the visible region. These new bands are attributed to transitions analogous to the $E_1$, $E_1+\Delta_1$, and $E_2$ series observed in bulk crystals. First-principles DFT calculations of the electronic structure and absorption spectra support this explanation and show that the main contribution to these optical transitions comes from $X$ and $M$ points of the 2D BZ, which originate from $L$ and $X$ points of the 3D BZ. At the same time, the $E_0$ series of transitions at the $\Gamma$ point is well described by the multiband effective-mass model. The observation of the UV exciton bands reveals tunable optical properties of cadmium chalcogenide NPLs in UV spectral region, which may be interesting for practical applications., Comment: 8 pages, 4 figures, 1 table; to appear in Phys. Rev. B

Dislocations corresponding to a change of stacking in two-dimensional hexagonal bilayers, graphene and boron nitride, and associated with boundaries between commensurate domains are investigated using the two-chain Frenkel-Kontorova model on top of ab initio calculations. Structural transformations of bilayers in which the bottom layer is stretched and the upper one is left to relax freely are considered for gradually increased elongation of the bottom layer. Formation energies of dislocations, dislocation width and orientation of the boundary between commensurate domains are analyzed depending on the magnitude and direction of elongation. The second-order phase transition from the commensurate phase to the incommensurate one with multiple dislocations is predicted to take place at some critical elongation. The order parameter for this transition corresponds to the density of dislocations, which grows continuously upon increasing the elongation of the bottom layer above the critical value. In graphene and metastable boron nitride with the layers aligned in the same direction, where elementary dislocations are partial, this transition, however, is preceded by formation of the first dislocation at the elongation smaller than the critical one. The phase diagrams including this intermediate state are plotted in coordinates of the magnitude and direction of elongation of the bottom layer., Comment: 15 pages, 9 figures

Principal characteristics of interlayer interaction and relative motion of hexagonal boron nitride (h-BN) layers are investigated by the first-principles method taking into account van der Waals interactions. Dependences of the interlayer interaction energy on relative translational displacement of h-BN layers (potential energy surfaces) are calculated for two relative orientations of the layers, namely, for the layers aligned in the same direction and in the opposite directions upon relative rotation of the layers by 180 degrees. It is shown that the potential energy surfaces of bilayer h-BN can be approximated by the first Fourier components determined by symmetry. As a result, a wide set of physical qualintities describing relative motion of h-BN layers aligned in the same direction including barriers to their relative sliding and rotation, shear mode frequency and shear modulus are determined by a single parameter corresponding to the roughness of the potential energy surface, similar to bilayer graphene. The properties of h-BN layers aligned in the opposite directions are described by two such parameters. The possibility of partial and full dislocations in stacking of the layers is predicted for h-BN layers aligned in the same and opposite directions, respectively. The extended two-chain Frenkel-Kontorova model is used to estimate the width and formation energy of these dislocations on the basis of the calculated potential energy surfaces., Comment: 13 pages, 6 figures

The sequence of ground states for SrTiO3 film subjected to epitaxial strain as well as to mechanical stress along the [001] and [110] axes is calculated from first principles within the density functional theory. Under the fixed-strain boundary conditions, an increase in the lattice parameter of a substrate results in the $I4cm \to I4/mcm \to Ima2 \to Cm \to Fmm2 \to Ima2$(II) sequence of ground states. Under the fixed-stress boundary conditions, the phase sequence is different and depends on how the stress is applied. It is revealed that the simultaneous presence of competing ferroelectric and antiferrodistortive instabilities in SrTiO3 gives rise to the appearance of metastable phases, whose number increases dramatically under the fixed-stress conditions. In the metastable phases, the octahedral rotation patterns are shown to differ substantially from those in the ground state. It is suggested that in systems with competing instabilities, each polar phase has its optimal octahedral rotation pattern which stabilizes this phase and creates a potential barrier preventing this phase to be transformed into other structures., Comment: 14 pages, 5 figures, 1 table plus 12 tables of supplemental material

The crystal structures and phonon spectra of orthorhombic cadmium titanate with the $Pbnm$ structure and of its two possible ferroelectrically distorted phases with $Pbn2_1$ and $Pb2_1m$ space groups were calculated from first principles within the density functional theory. The obtained structural parameters and frequencies of Raman- and infrared-active modes are in good agreement with available experimental data for the $Pbnm$ phase. Expansion of the total energy in a Taylor series of two order parameters showed that the ground state of the system corresponds to the $Pbn2_1$ structure into which the $Pbnm$ phase transforms through a second-order phase transition without intermediate phases. A substantial discrepancy between the calculated and experimentally observed lattice distortions and spontaneous polarization in the polar phase was explained by quantum fluctuations as well as by existence of twinning and competing long-period structures., Comment: 7 pages, 3 figures, 5 tables