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Let $\mathcal{H}$ be a linear space equipped with an indefinite inner product $[\cdot, \cdot]$. Denote by $\mathcal{F}_{++}=\{f\in\mathcal{H} \ : \ [f,f]>0\}$ the nonlinear set of positive vectors in $\mathcal{H}$. We demonstrate that the properties of a linear operator $W$ in $\mathcal{H}$ can be uniquely determined by its restriction to $\mathcal{F}_{++}$. In particular, we prove that the bijectivity of $W$ on $\mathcal{F}_{++}$ is equivalent to $W$ being {\em close} to a unitary operator with respect to $[\cdot, \cdot]$. Furthermore, we consider a one-parameter semi-group of operators $W_+ = \{W(t) : t \geq 0\}$, where each $W(t)$ maps $\mathcal{F}_{++}$ onto itself in a one-to-one manner. We show that, under this natural restriction, the semi-group $W_+$ can be transformed into a one-parameter group $U = \{U(t) : t\in\mathbb{R}\}$ of operators that are unitary with respect to $[\cdot, \cdot]$. By imposing additional conditions, we show how to construct a suitable definite inner product $\langle\cdot, \cdot\rangle$, based on $[\cdot, \cdot]$, which guarantees the unitarity of the operators $U(t)$ in the Hilbert space obtained by completing $\mathcal{H}$ with respect to $\langle\cdot, \cdot\rangle$.

Time-resolved terahertz spectroscopy is used to investigate formation and ultrafast long-distance propagation of electron-hole plasma in strongly photoexcited GaAs and InP. The observed phenomena involve fundamental interactions of electron-hole system with light, which manifest themselves in two different regimes: a coherent one with the plasma propagation speeds up to c/10 (in GaAs at 20 K) and an incoherent one reaching up to c/25 (in InP at 20 K), both over a macroscopic distance > 100 micrometers. We explore a broad range of experimental conditions by investigating the two materials, by tuning their band gap with temperature and by controlling the interaction strength with the optical pump fluence. Our interpretation suggests that the observed phenomena should occur in most direct band semiconductors upon strong photoexcitation with low excess energy.

Optical pump-terahertz probe spectroscopy has been used to investigate ultrafast photo-induced charge carrier transport in 3.4 $\mu$m wide graphene ribbons upon scaling the optical pump intensity. For low pump fluences, the deposited pump energy is rapidly redistributed through carrier-carrier scattering, producing secondary hot carriers: the picosecond THz photoconductivity then acquires a negative sign and scales linearly with an increasing pump fluence. At higher fluences, there are not enough equilibrium carriers able to accept the deposited energy, directly generated (excess) carriers start to contribute significantly to the photoconductivity with a positive sign leading to its saturation behavior. This leads to a non-monotonic variation of the carrier mobility and plasmonic resonance frequency as a function of the pump fluence and, at high fluences, to a balance between a decreasing carrier scattering time and an increasing Drude weight. In addition, a weak carrier localization observed for the polarization parallel to the ribbons at low pump fluences is progressively lifted upon increasing the pump fluence as a result of the rise of initial carrier temperature.

The study of magnetic frustration in classical spin systems was motivated by the prediction and discovery of classical spin liquid states. These uncommon magnetic phases are characterized by a massive degeneracy of their ground state implying a finite magnetic entropy at zero temperature. While the classical spin liquid state was originally predicted in the Ising triangular lattice antiferromagnet in 1950, this state has never been experimentally observed in any triangular magnets. We report here the discovery of an electric analogue of classical spin liquids on a triangular lattice of uniaxial electric dipoles in EuAl12O19 . This new type of frustrated antipolar phase is characterized by a highly degenerate state at low temperature implying an absence of long-range antiferroelectric order, despite short-range antipolar correlations. Its dynamics are governed by a thermally activated process, slowing down upon cooling towards a complete freezing at zero temperature.

Dynamics of plasmons in nanoribbons of (hydrogen intercalated) quasi-free-standing single layer graphene is studied by terahertz spectroscopy both in the steady state and upon photoexcitation by an ultrashort near infrared laser pulse. The use of two-dimensional frequency domain analysis of the optical pump - THz probe signals allows us to determine the evolution of carrier temperature and plasmon characteristics with ~100 fs time resolution. Namely, we find that the carrier temperature decreases from more than 5000 K to the lattice temperature within about 7 ps and that during this evolution the carrier mobility remains practically constant. The time-resolved THz conductivity spectra suggest that graphene nanoribbons contain defects which act as low potential barriers causing a weak localization of charges; the potential barriers are overcome upon photoexcitation. Furthermore, the edges of graphene nanoribbons are found to slightly enhance the scattering of carriers. The results are supported by complementary measurements using THz scanning near-field microscopy which confirm a high uniformity of the THz conductivity across the sample and demonstrate high enough sensitivity to resolve even the impact of nanometric terrace steps on SiC substrate under the graphene monolayer.

Self-assembly of organic molecules represents a fascinating playground to create various liquid crystalline (LC) nanostructures. In this work, we study layer undulations on micrometer scale in smectic A phases for achiral compounds, experimentally demonstrated as regular stripe patterns induced by thermal treatment. Undulations including their anharmonic properties are evaluated by means of polarimetric imaging and light diffraction experiments in cells with various thicknesses. The key role in stripe formation is played by high negative values of the thermal expansion coefficient., Comment: 7 pages, 5 figures, 1 table. To be published in PRL

In \cite{BK} Parseval frames were used to define bounded Hamiltonians, both in finite and in infinite dimesional Hilbert spaces. Here we continue this analysis, with a particular focus on the discrete spectrum of Hamiltonian operators defined as a weighted infinite sum of rank one operators defined by some Parseval frame living in an infinite dimensional Hilbert space. The main difference with \cite{BK} is that, here, the operators we consider are mostly unbounded. This is an useful upgrade with respect to our previous results, since physically meaningful Hamiltonians are indeed often unbounded. However, due to the fact that frames (in general) are not bases, the definition of an Hamiltonian is not so easy, and part of our results goes in this direction. Also, we discuss the eigenvalues of the Hamiltonians, and we discuss some physical applications of our framework.

Antiferromagnetic CuMnAs thin films have attracted attention since the discovery of the manipulation of their magnetic structure via electrical, optical, and terahertz pulses of electric fields, enabling convenient approaches to the switching between magnetoresistive states of the film for the information storage. However, the magnetic structure and, thus, the efficiency of the manipulation can be affected by the film morphology and growth defects. In this study, we investigate the properties of CuMnAs thin films by probing the defect-related uniaxial anisotropy of electric conductivity by contact-free terahertz transmission spectroscopy. We show that the terahertz measurements conveniently detect the conductivity anisotropy, that are consistent with conventional DC Hall-bar measurements. Moreover, the terahertz technique allows for considerably finer determination of anisotropy axes and it is less sensitive to the local film degradation. Thanks to the averaging over a large detection area, the THz probing also allows for an analysis of strongly non-uniform thin films. Using scanning near-field terahertz and electron microscopies, we relate the observed anisotropic conductivity of CuMnAs to the elongation and orientation of growth defects, which influence the local microscopic conductivity. We also demonstrate control over the morphology of defects by using vicinal substrates., Comment: 33 pages, 16 figures

We investigate the origin of the translational symmetry breaking in epitaxially grown single-layer graphene. Despite the surface morphology of homogeneous graphene films influenced by the presence of mutually parallel SiC surface terraces, the far-infrared magneto-plasmon absorption is almost independent of the angle between the probing light polarization and the orientation of terraces. Based on a detailed analysis of the plasmon absorption lineshape and its behavior in the magnetic field, supported by confocal Raman mapping and atomic force microscopy, we explain this discrepancy by spontaneously formed graphene micro flakes. We further support our conclusions using data collected on artificially created graphene nanoribbons: we recognize similar plasmon origin in artificial ribbons and naturally formed grains. An unexpectedly large plasmon resonance redshift was observed in nanoribbons. In a hydrogen-intercalated sample (which does not contain the buffer), this redshift is quantitatively taken into account by a plasmon-plasmon interaction. In non-intercalated samples featuring a buffer layer, this redshift is due to an interplay between the plasmon-plasmon coupling and Coulomb screening by the buffer-induced interface states. This model determines the density of interface states in good agreement with experimentally reported values., Comment: 17 pages, 10 figures, 4 tables

Since the recent discoveries, ferroelectric nematics became of upmost interest due to their outstanding ferroelectric properties. In this work, we prepared a series of polar molecules revealing a ferroelectric nematic phase (NF) with a very high dielectric constant (>104). A new motif, which differs from previously reported molecular structures, was optimized to support the NF phase. For all homologues the NF phase was observed directly on the cooling from the isotropic phase and ferroelectric behaviour was investigated by dielectric spectroscopy, second harmonic generation, polarization current measurements and by analysis of textures in the polarized light. The presented materials combine ferroelectricity with giant permittivity in a fluid media at room temperatures, so they appear to be extremely attractive. Polarity of molecules with the strong susceptibility to the electric field represent high potential for various applications in energy-efficient memory devices or capacitors.

We use the synergy of infrared, terahertz, and Raman spectroscopies with DFT calculations to shed light on the magnetic and lattice properties of VI3. The structural transition at TS1 = 79 K is accompanied by a large splitting of polar phonon modes. Below TS1, strong ferromagnetic fluctuations are observed. The variations of phonon frequencies at 55 K induced by magnetoelastic coupling enhanced by spin-orbit interaction indicate the proximity of long-range ferromagnetic order. Below TC = 50 K, two Raman modes simultaneously appear and show dramatic softening in the narrow interval around the temperature TS2 of the second structural transition associated with the order-order magnetic phase transition. Below TS2, a magnon in the THz range appears in Raman spectra. The THz magnon observed in VI3 indicates the application potential of 2D van der Waals ferromagnets in ultrafast THz spintronics, which has previously been considered an exclusive domain of antiferromagnets., Comment: Accepted in Journal of Physical Chemistry Letters

Schr\"{o}dinger operators with nonlocal $\delta$-interaction are studied with the use of the Lax-Phillips scattering theory methods. The condition of applicability of the Lax-Phillips approach in terms of non-cyclic functions is established. Two formulas for the $S$-matrix are obtained. The first one deals with the Krein-Naimark resolvent formula and the Weyl-Titchmarsh function, whereas the second one is based on modified reflection and transmission coefficients. The $S$-matrix $S(z)$ is analytical in the lower half-plane $\mathbb{C_-}$ when the Schr\"{o}dinger operator with nonlocal $\delta$-interaction is positive self-adjoint. Otherwise, $S(z)$ is a meromorphic matrix-valued function in $\mathbb{C_-}$ and its properties are closely related to the properties of the corresponding Schr\"{o}dinger operator. Examples of $S$-matrices are given.

One of a key problems in signal reconstruction process with the use of frames is to find a dual frame. Typically, a canonical dual frame is used. However, there are many applications where this choice appears to be unfortunate. Due to that fact, it is necessary to develop a tool, which helps to find a suitable dual frame. In this paper we give a method to find every dual frames. The proposed method is based on Naimark's dilation theorem and the obtained description of dual frames involves parameters that characterize extension of a Parseval frame to an orthonormal basis. These formulas are simplified for frames in finite-dimensional spaces and for near-Riesz bases. In the latter case, the simplification is based on the extended and supplemented version of the Naimark theorem, which is proved in the last part of the paper.

We analyze special classes of bi-orthogonal sets of vectors in Hilbert and in Krein spaces, and their relations with generalized Riesz systems. In this way, the notion of the first/second type sequences is introduced and studied. We also discuss their relevance in some concrete quantum mechanical system driven by manifestly non self-adjoint Hamiltonians., Comment: submitted to Journal of Physics A. arXiv admin note: text overlap with arXiv:1810.05218

Pseudo-Hermitian Hamiltonians have recently become a field of wide investigation. Originally, the Generalized Riesz Systems (GRS) have been introduced as an auxiliary tool in this theory. In contrast, the current paper, GRSs are analysed in terms of basis theory. The relationship between semi-regular sequences and GRSs is provided. Various characterizations of GRSs are discussed.

Nanosized particles of $\omega$ phase in a $\beta$-Ti alloy were investigated by small-angle X-ray scattering using synchrotron radiation. We demonstrated that the particles are spontaneously weakly ordered in a three-dimensional cubic array along the $\langle 100\rangle$-directions in the $\beta$-Ti matrix. The small-angle scattering data fit well to a three-dimensional short-range-order model; from the fit we determined the evolution of the mean particle size and mean distance between particles during ageing. The self-ordering of the particles is explained by elastic interaction between the particles, since the relative positions of the particles coincide with local minima of the interaction energy. We performed numerical Monte Carlo simulation of the particle ordering and we obtained a good agreement with the experimental data.

A definition of frames in Krein spaces is proposed which extends the concept of $J$-frames defined by J.I. Giribet et al., J. Math. Anal. Appl. ${\textbf{393}}$ (2012), 122-137. The principal difference consists in the fact that a $J$-frame is related to maximal definite subspaces $\mathcal{M}_\pm$ which are not assumed to be uniformly definite. The latter allows one to extend the collection of $J$-frames. In particular, some complete $J$-orthogonal sequences and $J$-orthogonal Schauder bases can be interpreted as $J$-frames., Comment: 15 pages.arXiv admin note: text overlap with arXiv:1703.03665 by other authors

Tetragonal phase of CuMnAs progressively appears as one of the key materials for antiferromagnetic spintronics due to efficient current-induced spin-orbit torques whose existence can be directly inferred from crystal symmetry. Theoretical understanding of spintronic phenomena in this material, however, relies on the detailed knowledge of electronic structure (band structure and corresponding wave functions) which has so far been tested only to a limited extent. We show that AC permittivity (obtained from ellipsometry) and UV photoelectron spectra agree with density functional calculations. Together with the x-ray diffraction and precession electron diffraction tomography, our analysis confirms recent theoretical claim [Phys.Rev.B 96, 094406 (2017)] that copper atoms occupy lattice positions in the basal plane of the tetragonal unit cell., Comment: 5 pages, 5 figures + Supplementary Information

The spin-conserving length-scale is a key parameter determining functionalities of a broad range of spintronic devices including magnetic multilayer spin-valves in the commercialized magnetic memories or lateral spin transistors in experimental spin-logic elements. Spatially resolved optical pump-and-probe experiments in the lateral devices allow for the direct measurement of the lengthscale and the time-scale at which spin-information is transferred from the injector to the detector. Using this technique, we demonstrate that in an undoped GaAs/AlGaAs layer spins are detected at distances reaching more than ten microns from the injection point at times as short as nanoseconds after the pump-pulse. The observed unique combination of the long-range and highrate electronic spin-transport requires simultaneous suppression of mechanisms limiting the spin life-time and mobility of carriers. Unlike earlier attempts focusing on elaborate doping, gating, or heterostructures we demonstrate that the bare GaAs/AlGaAs layer intrinsically provides superior spin-transport characteristics whether deposited directly on the substrate or embedded in complex heterostructures.

A common way of speeding up powder diffraction measurements is the use of one or two dimensional detectors. This usually goes along with worse resolution and asymmetric peak profiles. In this work the influence of a straight linear detector on the resolution function in the Bragg-Brentano focusing geometry is discussed. Due to the straight nature of most modern detectors geometrical defocusing occurs which heavily influences the line shape of diffraction lines at low angles. An easy approach to limit the resolution degrading effects is presented. The presented algorithm selects an adaptive range of channels of the linear detector at low angles, resulting in increased resolution. At higher angles still the whole linear detector is used and the data collection remains fast. Using this algorithm a well-behaved resolution function is obtained in the full angular range, whereas using the full linear detector the resolution function varies within one pattern which hinders line shape and Rietveld analysis., Comment: 20 pages, 5 figures

Polarized Raman, IR and time-domain THz spectroscopy of orthorhombic lead zirconate single crystals yielded a comprehensive picture of temperature-dependent quasiharmonic frequencies of its low-frequency phonon modes. It is argued that these modes primarily involve vibration of Pb and/or oxygen octahedra librations and their relation to particular phonon modes of the parent cubic phase is proposed. Counts of the observed IR and Raman active modes belonging to distinct irreducible representations agree quite well with group-theory predictions. The most remarkable finding is the considerably enhanced frequency renormalization of the y-polarized polar modes, resulting in a pronounced low temperature dielectric anisotropy. Results are discussed in terms of contemporary phenomenological theory of antiferroelectricity.

We studied a thin superconducting NbN film in magnetic fields up to 8 T above the zero- temperature limit by means of time-domain terahertz and scanning tunneling spectroscopies in order to understand the vortex response. Scanning tunneling spectroscopy was used to determine the optical gap and the upper critical field of the sample. The obtained values were subsequently used to fit the terahertz complex conductivity spectra in the magnetic field in the Faraday geometry above the zero temperature limit. These spectra are best described in terms of the Coffey-Clem self-consistent solution of a modified London equation in the flux creep regime., Comment: 8 pages, 7 figures

THz-range dielectric spectroscopy and first-principle-based effective-Hamiltonian molecular dynamics simulations were employed to elucidate the dielectric response in the paraelectric phase of (Ba,Sr)TiO3 solid solutions. Analysis of the resulting dielectric spectra suggests the existence of a crossover between two different regimes: a higher-temperature regime governed by the soft mode only versus a lower-temperature regime exhibiting a coupled soft mode/central mode dynamics. Interestingly, a single phenomenological coupling model can be used to adjust the THz dielectric response in the entire range of the paraelectric phase (i.e., even at high temperature). We conclude that the central peak is associated with thermally activated processes, and that it cannot be discerned anymore in the dielectric spectra when the rate of these thermally activated processes exceeds certain characteristic frequency of the system.

Terahertz and far-infrared electric and magnetic responses of hexagonal piezomagnetic YMnO3 single crystals are investigated. Antiferromagnetic resonance is observed in the spectra of magnetic permeability mu_a [H(omega) oriented within the hexagonal plane] below the Neel temperature T_N. This excitation softens from 41 to 32 cm-1 on heating and finally disappears above T_N. An additional weak and heavily-damped excitation is seen in the spectra of complex dielectric permittivity epsilon_c within the same frequency range. This excitation contributes to the dielectric spectra in both antiferromagnetic and paramagnetic phases. Its oscillator strength significantly increases on heating towards room temperature thus providing evidence of piezomagnetic or higher-order couplings to polar phonons. Other heavily-damped dielectric excitations are detected near 100 cm-1 in the paramagnetic phase in both epsilon_c and epsilon_a spectra and they exhibit similar temperature behavior. These excitations appearing in the frequency range of magnon branches well below polar phonons could remind electromagnons; however, their temperature dependence is quite different. We have used density functional theory for calculating phonon dispersion branches in the whole Brillouin zone. A detailed analysis of these results and of previously published magnon dispersion branches brought us to the conclusion that the observed absorption bands stem from phonon-phonon and phonon- paramagnon differential absorption processes. The latter is enabled by a strong short-range in-plane spin correlations in the paramagnetic phase., Comment: subm. to PRB

We report on a systematic study of optical properties of (Ga,Mn)As epilayers spanning the wide range of accessible substitutional Mn_Ga dopings. The growth and post-growth annealing procedures were optimized for each nominal Mn doping in order to obtain films which are as close as possible to uniform uncompensated (Ga,Mn)As mixed crystals. We observe a broad maximum in the mid-infrared absorption spectra whose position exhibits a prevailing blue-shift for increasing Mn-doping. In the visible range, a peak in the magnetic circular dichroism blue shifts with increasing Mn-doping. These observed trends confirm that disorder-broadened valence band states provide a better one-particle representation for the electronic structure of high-doped (Ga,Mn)As with metallic conduction than an energy spectrum assuming the Fermi level pinned in a narrow impurity band., Comment: 22 pages, 14 figures

After decades of research, the low Curie temperature of ferromagnetic semiconductors remains the key problem in the development of magnetic semiconductor spintronic technologies. Removing this roadblock might require a change of the field's basic materials paradigm by looking beyond ferromagnets. Recent studies of relativistic magnetic and magnetotransport anisotropy effects, which in principle are equally well present in materials with ferromagnetically and antiferromagnetically ordered spins, have inspired our search for antiferromagnetic semiconductors suitable for high-temperature spintronics. Since these are not found among the magnetic counterparts of common III-V or II-VI semi- conductors, we turn the attention in this paper to high N \'eel temperature I-II-V magnetic compounds whose electronic structure has not been previously identified. Our combined experimental and theoretical work on LiMnAs provides basic prerequisite for the systematic research of this class of materials by demonstrating the feasibility to grow single crystals of group-I alkali metal compounds by molecular beam epitaxy, by demonstrating the semiconducting band structure of the I-Mn-V's, and by analyzing their spin-orbit coupling characteristics favorable for spintronics., Comment: 11 pages, 5 figures

We report an investigation of hexagonal Y_(1-x)Eu_xMnO_3 ceramics with x=0, 0.1 and 0.2 using infrared and THz spectroscopies in the temperature range between 5 and 900 K. The temperature dependence of the THz permittivity reveals a kink near the antiferromagnetic phase transition temperature T_N ~ 70 K giving evidence of a strong spin-lattice coupling. Below T_N two absorption peaks were revealed in the THz spectra close to 43 and 73 cm-1. While the first peak corresponds to a sharp antiferromagnetic resonance exhibiting softening on heating towards TN, the second one may be attributed to an impurity mode or a multiphonon absorption peak. High-temperature THz spectra measured up to 900 K reveal only small gradual increase of the permittivity in agreement with a weak phonon softening observed in the infrared reflectance spectra upon heating. This corresponds to an improper ferroelectric character of the phase transition proposed from first principle calculations by Fennie and Rabe [Phys. Rev. B 72 (2005), pp. 100103(R)]., Comment: Phase Transitions, accepted

Time-domain THz transmission experiment was performed on a $\rm SrBi_2Ta_2O_9$ film deposited on sapphire substrate. Temperatures between 300 and 923 K were investigated and complex permittivity spectra of the film were determined. The lowest frequency optic phonon near 28 cm$^{-1}$ reveals a slow monotonic decrease in frequency on heating with no significant anomaly near the phase transitions. We show that the dielectric anomaly near the ferroelectric phase transition can be explained by slowing down of a relaxational mode, observed in the THz spectra. A second harmonic generation signal observed in a single crystal confirms a loss of center of symmetry in the ferroelectric phase and a presence of polar clusters in the intermediate ferroelastic phase., Comment: subm. to J. Phys.: Condens. Matter