We find theoretically the energy spectrum of a graphene monolayer in a strong constant electric field using a tight-binding model. Within a single band, we find quantized equidistant energy levels (Wannier-Stark ladder), separated by the Bloch frequency. Singular interband coupling results in mixing of the states of different bands and anticrossing of corresponding levels, which is described analytically near Dirac points and is related to the Pancharatnam-Berry phase. The rate of interband tunneling, which is proportional to the anticrossing gaps in the spectrum, is only inversely proportional to the tunneling distance, in a sharp contrast to conventional solids where this dependence is exponential. This singularity will have major consequences for graphene behavior in strong ultrafast optical fields, in particular, leading to nonadiabaticity of electron excitation dynamics.

Theory of weak localization is developed for electrons in semiconductor quantum wells grown along [110] and [111] crystallographic axes. Anomalous conductivity correction caused by weak localization is calculated for symmetrically doped quantum wells. The theory is valid for both ballistic and diffusion regimes of weak localization in the whole range of classically weak magnetic fields. We demonstrate that in the presence of bulk inversion asymmetry the magnetoresistance is negative: The linear in the electron momentum spin-orbit interaction has no effect on the conductivity while the cubic in momentum coupling suppresses weak localization without a change of the correction sign. Random positions of impurities in the doping layers in symmetrically doped quantum wells produce electric fields, which result in a position-dependent Rashba coupling. This random spin-orbit interaction leads to spin relaxation, which changes the sign of the anomalous magnetoconductivity. The obtained expressions allow determination of electron-spin relaxation times in (110) and (111) quantum wells from transport measurements.

We study theoretically the electron states in a system of two vertically stacked quantum dots. We investigate the influence of the geometrical symmetry breaking (caused by the displacement as well as the ellipticity of the dots) on the electron states. Our modeling is based on the eight-band $\mathit{k}·\mathit{p}$ method. We study the coupling of the $s$ state from one dot with the $p$ and $d$ states from the other induced by the absence of axial symmetry. Our findings indicate that this coupling can produce a strong energy splitting at resonance (on the order of several meV) in the case of closely spaced quantum dots. Furthermore, we show that in the presence of a piezoelectric field, the direction of the displacement plays an important role in the character of the coupling.

We present a systematic study on hydrogenated silicon $m$ vacancies above saturation. For each system a global geometry optimization search for low-lying local minima is performed using a newly developed SiH tight binding model. Subsequently a large number of low-energy structures are examined by density functional calculations using a minimal basis set. Finally the energetically favorable structures are reexamined using a systematically extendable basis set with local, semilocal, and hybrid exchange-correlation functionals. Particular attention is paid to the divacancy to which the Raman peak at 3822 ${\mathrm{cm}}^{-1}$ associated with the ${\mathrm{H}}_2$ molecule had previously been assigned. Both the energetics and vibrational analysis of divacancy-related stable configurations suggest a revision of the above conclusion.

We work out theoretically a mechanism for magnetoelectric (ME) coupling driven by a buildup of an interfacial spiral spin density in ferromagnet (FM)/ferroelectric (FE) composites. We infer an intrinsic linear ME coupling that is most pronounced in the vicinity of the FM/FE interface acting within the spin-diffusion length ${\lambda }_m$ of the order of nanometers. Our study delivers a strong coupling strength for $\mathrm{Co}\left(40 \mathrm{nm}\right)/{\mathrm{BaTiO}}_3$ that is in line with experiments. We identify a region of magnetic noncollinearity coupled to dielectric polarization that extends over ${\lambda }_m$ around the interface, functionalizing the interface for electric control of magnetotransport and surface magnetic anisotropy.

We report on high-temperature electron spin resonance studies of a detwinned ${\mathrm{LaMnO}}_3$ single crystal across the Jahn-Teller transition at $T_{\mathrm{JT}}=750$ K. The anisotropy of the linewidth and $g$ factor reflects the local Jahn-Teller distortions in the orbitally ordered phase. A clear jump in the linewidth accompanies the Jahn-Teller transition at $T_{\mathrm{JT}}=750$ K confirming that the transition is of first order. Already at $T^{*}=550$ K a significant decrease of the reduced linewidth is observed. This temperature scale is discussed with respect to the interaction of the $e_g$ electrons of the ${\mathrm{Mn}}^{3+}$ ions and the elastic field of the cooperative distortions. Our results support a partial melting of the orbital order along the antiferromagnetically coupled $b$ axis at $T^{*}$. The remaining two-dimensional orbital ordering within the ferromagnetically coupled $ac$ plane finally disappears together with the cooperative distortion at $T_{\mathrm{JT}}$. Moreover, in our discussion we show that elastic strain field interactions can explain the melting of the orbital order and, thus, have to be taken into account to explain the orbital ordering in ${\mathrm{LaMnO}}_3$.

We study transport in an asymmetric superconducting quantum interference device (SQUID) which is composed of a loop with three capacitively and resistively shunted Josephson junctions: two in series in one arm and the remaining one in the other arm. The loop is threaded by an external magnetic flux and the system is subjected to both a time-periodic and a constant current. We formulate the deterministic and, as well, the stochastic dynamics of the SQUID in terms of the Stewart-McCumber model and derive an equation for the phase difference across one arm, in which an effective periodic potential is of the ratchet type, i.e., its reflection symmetry is broken. In doing so, we extend and generalize an earlier study by Zapata et al. [Phys. Rev. Lett. 77, 2292 (1996)] and analyze directed transport in wide parameter regimes: covering the overdamped to the moderate damping regime up to its fully underdamped regime. As a result we detect the intriguing features of a negative (differential) conductance, repeated voltage reversals, noise-induced voltage reversals, and solely thermal noise-induced ratchet currents. We identify a set of parameters for which the ratchet effect is most pronounced and show how the direction of transport can be controlled by tailoring the external magnetic flux.

We study superconductivity on the honeycomb lattice close to the Mott state at half filling. Due to the sixfold lattice symmetry and disjoint Fermi surfaces at opposite momenta, we show that several different fully gapped superconducting states naturally exist on the honeycomb lattice, of which the chiral $d+i{d}^{\prime }$-wave state has previously been shown to appear when superconductivity appears close to the Mott state. Using renormalized mean-field theory to study the $t-J$ model and quantum Monte Carlo calculations of the Hubbard-$U$ model we show that the $d+i{d}^{\prime }$-wave state is the favored superconducting state for a wide range of on-site repulsion $U$, from the intermediate to the strong coupling regime. We also investigate the possibility of a mixed chirality $d$-wave state, where the overall chirality cancels. We find that a state with $d+i{d}^{\prime }$-wave symmetry in one valley but $d-i{d}^{\prime }$-wave symmetry in the other valley is not possible in the $t-J$ model without reducing the translational symmetry, due to the zero-momentum and spin-singlet nature of the superconducting order parameter. Moreover, any extended unit cells result either in disjoint Dirac points, which cannot harbor this mixed chirality state, or the two valleys are degenerate at the zone center, where valley hybridization prevents different superconducting condensates. We also investigate extended unit cells where the overall chirality cancels in real space. For supercells containing up to eight sites, including the Kekulé distortion, we find no energetically favorable $d$-wave solution with an overall zero chirality within the restriction of the $t-J$ model.

Zero-field muon spin rotation and relaxation $\left(\mu \mathrm{SR}\right)$ studies carried out on the strongly coupled, noncentrosymmetric superconductor ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C},T_c=9$ K, did not reveal hints of time-reversal symmetry breaking as was found for a number of other noncentrosymmetric systems. Transverse field measurements performed above and below the superconducting transition temperature defined the temperature dependent London penetration depth, which in turn served to derive from a microscopic point of view a simple $s$-wave superconducting state in ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C}$. The present investigations also provide fairly solid grounds to conclude that time-reversal symmetry breaking is not an immanent feature of noncentrosymmetric superconductors.

From high field electron spin resonance measurements in illuminating polarized light, we have revealed the existence of electromagnon, i.e., magnon excitation by oscillatory electric fields of light, in the field-induced 1/5-plateau phase of the triangular lattice antiferromagnet ${\mathrm{CuFeO}}_2$. We indicate that peculiar magnon modes, which generate uniform fluctuation of the vector spin chirality at wave vector $k=0$, appear in the magnetic ordered phase with a collinear spin structure on triangular lattice. Our experimental results demonstrate that such magnon modes couple with an electric component of light, leading to the emergence of the electromagnon. Moreover, the measurements in circularly polarized light exhibit an anomalous behavior that circular dichroism, which is usually found in magnetic resonance, is absent in the resonance signal of the electromagnon. The microscopic mechanism of the electromagnon in ${\mathrm{CuFeO}}_2$ is also discussed.

Essential to understanding the cuprate pseudogap phase is a study of the charge (and spin) response functions, which we address here via a consistent approach to the Fermi arcs and the Fermi pockets scenario of Yang, Rice, and Zhang (YRZ). The two schemes are demonstrated to be formally similar, and to share a common physics platform; we use this consolidation to address the inclusion of vertex corrections which have been omitted in YRZ applications. We show vertex corrections can be easily implemented in a fashion analytically consistent with sum rules and that they yield important contributions to most observables. A study of the charge ordering susceptibility of the YRZ scenario makes their simple physics evident: They represent the inclusion of charged bosonic, spin singlet degrees of freedom, and are found to lead to a double peak structure.

The question of whether one can systematically identify (previously unknown) ferroelectric phases of a given material is addressed, taking hafnia $\left({\mathrm{HfO}}_2\right)$ as an example. Low free energy phases at various pressures and temperatures are identified using a first-principles based structure search algorithm. Ferroelectric phases are then recognized by exploiting group theoretical principles for the symmetry-allowed displacive transitions between nonpolar and polar phases. Two orthorhombic polar phases occurring in space groups $Pca{2}_1$ and $Pmn{2}_1$ are singled out as the most viable ferroelectric phases of hafnia, as they display low free energies (relative to known nonpolar phases), and substantial switchable spontaneous electric polarization. These results provide an explanation for the recently observed surprising ferroelectric behavior of hafnia, and reveal pathways for stabilizing ferroelectric phases of hafnia as well as other compounds.

We study many-body-localized (MBL) systems that are weakly coupled to thermalizing environments, focusing on the spectral functions of local operators. These spectral functions carry signatures of localization even away from the limit of perfectly isolated systems. We find that, in the limit of vanishing coupling to a bath, MBL systems come in two varieties, with either discrete or continuous local spectra. Both varieties of MBL systems exhibit a “soft gap” at zero frequency in the spatially averaged spectral functions of local operators, which serves as a diagnostic for localization. We estimate the degree to which coupling to a bath broadens these spectral features, and we find that some characteristics of incipient localization survive as long as the system-bath coupling is much weaker than the characteristic energy scales of the system. We discuss the crossover to localization that occurs as the coupling to the external bath is tuned to zero. Since perfect isolation is impossible, we expect the ideas discussed in this paper to be relevant for experiments on many-body localization.

We present a systematic study of the static and dynamic magnetization behavior of interlayer-coupled ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$(200 Å)/Ru($t_{\mathrm{Ru}}$)/${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$(100 Å) trilayers as a function of the Ru spacer layer thickness $t_{\mathrm{Ru}}$. As $t_{\mathrm{Ru}}$ was varied in the range from 0 to 15.8 Å, we observe a strong antiferromagnetic (AFM) exchange coupling between the two ferromagnetic (FM) layers for $t_{\mathrm{Ru}}$ = 5 Å, which becomes weak for $t_{\mathrm{Ru}}$ = 10 Å. For $t_{\mathrm{Ru}}$ = 14.1 Å, the coupled magnetic system changes from AFM to FM ordering. Using broadband ferromagnetic resonance spectroscopy, we have probed the effects of the different coupling mechanisms on both the acoustic and optic magnetic modes. We found that the biquadratic exchange coupling has a negligible effect compared to Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange coupling, while the uniaxial anisotropy at the ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$/Ru interfaces also plays an important role in determining the behaviors of the modes. A mode anticrossing phenomenon is observed when the RKKY exchange interaction term is above a critical value. A theoretical framework developed is in very good agreement with our experimental results.

Magnetization oscillations excited by microwave voltages in ferromagnetic nanostructures having electric-field-dependent interfacial anisotropy are described theoretically. By calculating frequency dependencies of complex susceptibilities we show that this dynamic magnetoelectric effect acquires anomalous characteristics near thickness-induced spin reorientation transitions (SRTs) in nanolayers of cubic ferromagnets. Most importantly, the peak magnetoelectric susceptibilities may reach giant values exceeding ${10}^{-6}$ s/m, and the tunability of the resonance frequency of the magnetization precession by a dc voltage increases drastically near the critical thickness or voltage inducing an SRT.

Disorder is known to suppress the gap of a topological superconducting state that would support non-Abelian Majorana zero modes. In this paper, we study using the self-consistent Born approximation the robustness of the Majorana modes to disorder within a suitably extended Eilenberger theory, in which the spatial dependence of the localized Majorana wave functions is included. We find that the Majorana mode becomes delocalized with increasing disorder strength as the topological superconducting gap is suppressed. However, surprisingly, the zero bias peak seems to survive even for disorder strength exceeding the critical value necessary for closing the superconducting gap within the Born approximation.

We have experimentally studied the renormalized effective mass $m^{*}$ and Dingle temperature $T_D$ in two spin subbands with essentially different electron populations. Firstly, we found that the product $m^{*}{T}_D$ that determines the damping of quantum oscillations, to the first approximation, is the same in the majority and minority subbands even at a spin polarization degree as high as 66%. This result confirms the theoretical predictions that the interaction takes place at high energies $\sim E_F$ rather than within a narrow strip of energies $E_F\pm k_{B}T$. Secondly, to the next approximation, we revealed a difference in the damping factor of the two spin subbands, which causes skewness of the oscillation line shape. In the absence of the in-plane magnetic field $B_{\parallel }$, the damping factor $m^{*}{T}_D$ is systematically smaller in the spin-majority subband. The difference, quantified with the skew factor $\gamma =(T_{D\downarrow }-T_{D\uparrow })/2T_{D0}$ can be as large as 20%. The skew factor tends to decrease as $B_{\parallel }$ or temperature grow, or $B_{\perp }$ decreases; for low electron densities and high in-plane fields, the skew factor even changes sign. Finally, we compared the temperature and magnetic field dependencies of the magneto-oscillation amplitude with predictions of the interaction correction theory, and found, besides some qualitative similarities, several quantitative and qualitative differences. To explain qualitatively our results, we suggested an empirical model that assumes the existence of easily magnetized triplet scatterers on the Si/${\mathrm{SiO}}_2$ interface.

We demonstrate that in quantum-dot cavity systems, the interplay between acoustic phonons and photon losses introduces novel features and characteristic dependencies in the system dynamics. In particular, the combined action of both dephasing mechanisms strongly affects the transition from the weak- to the strong-coupling regime as well as the shape of the spectral triplet that represents the quantum-dot occupation in Fourier space. The width of the central peak in the triplet is expected to decrease with rising temperature, while the widths and heights of the side peaks depend nonmonotonically on the dot-cavity coupling.

Path-integral Monte Carlo calculations have been performed to study the ${}^4\mathrm{He}$ adsorption on $\gamma$-graphyne, a planar network of benzene rings connected by acetylene bonds. Assuming the ${}^4\mathrm{He}$-substrate interaction described by a pairwise sum of empirical ${}^4\mathrm{He}$-carbon interatomic potentials, we find that unlike $\alpha$-graphyne, a single sheet of $\gamma$-graphyne is not permeable to ${}^4\mathrm{He}$ atoms in spite of its large surface area. One-dimensional density distributions computed as a function of the distance from the graphyne surface reveal a layer-by-layer growth of ${}^4\mathrm{He}$ atoms. A partially-filled ${}^4\mathrm{He}$ monolayer is found to exhibit different commensurate solid structures depending on the helium coverage; it shows a ${\mathrm{C}}_{2/3}$ commensurate structure at an areal density of 0.0491 $\AA {}^{-2}$, a ${\mathrm{C}}_{3/3}$ structure at 0.0736 $\AA {}^{-2}$, and a ${\mathrm{C}}_{4/3}$ structure at 0.0982 $\AA {}^{-2}$. While the promotion to the second layer starts beyond the ${\mathrm{C}}_{4/3}$ helium coverage, the first ${}^4\mathrm{He}$ layer is found to form an incommensurate triangular solid when compressed with the development of the second layer.

Black phosphorus thin films might offer attractive alternatives to narrow-gap compound semiconductors for optoelectronics across mid- to near-infrared frequencies. In this work, we calculate the optical conductivity tensor of multilayer black phosphorus thin films using the Kubo formula within an effective low-energy Hamiltonian. The optical absorption spectra of multilayer black phosphorus are shown to vary sensitively with thickness, doping, and light polarization. In conjunction with experimental spectra obtained from infrared absorption spectroscopy, we also discuss the role of interband coupling and disorder on the observed anisotropic absorption spectra.