The control of side gates on the quantum electron transport in narrow graphene ribbons of different widths and edge types (armchair and zigzag) is investigated. The conductance exhibits Fano resonances with varying side gate potential. Resonant and antiresonant peaks in the conductance can be associated with the eigenstates of a closed system, and these peaks can be accurately fitted with a Fano line shape. The local density of states (LDOS) and the electron current show a specific behavior at these resonances, which depends on the ribbon edge type. In zigzag ribbons, transport is dominated by intervalley scattering, which is reflected in the transmission functions of individual modes. The side gates induce $p-n$ interfaces near the edges at which the LDOS exhibits peaks. Near the resonance points, the electron current flows uniformly through the constriction, while near the antiresonances it creates vortices. In the armchair ribbons the LDOS spreads in areas of high potential, with current flowing near the edges.

Near-surface two-dimensional electron gases on the topological insulator ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ are induced by electron doping and studied by angle-resolved photoemission spectroscopy. A pronounced spin-orbit splitting is observed for these states. The $k$-dependent splitting is strongly anisotropic to a degree where a large splitting ($\approx 0.06{\AA }^{-1})$ can be found in the $\overline{\Gamma }\overline{M}$ direction while the states are hardly split along $\overline{\Gamma }\overline{K}$. The direction of the anisotropy is found to be qualitatively inconsistent with results expected for a third-order anisotropic Rashba Hamiltonian. However, a $\mathbf{k}·\mathbf{p}$ model that includes the possibility of band structure anisotropy as well as both isotropic and anisotropic third order Rashba splitting can explain the results. The isotropic third order contribution to the Rashba Hamiltonian is found to be negative, reducing the energy splitting at high $k$. The interplay of band structure, higher order Rashba effect, and tunable doping offers the opportunity to engineer not only the size of the spin-orbit splitting but also its direction.

We investigate the extended Heisenberg model on the kagome lattice by using Gutzwiller projected fermionic states and the variational Monte Carlo technique. In particular, when both second- and third-neighbor superexchanges are considered, we find that a gapped spin liquid described by nontrivial magnetic fluxes and long-range chiral-chiral correlations is energetically favored compared to the gapless U(1) Dirac state. Furthermore, the topological Chern number, obtained by integrating the Berry curvature, and the degeneracy of the ground state, by constructing linearly independent states, lead us to identify this flux state as the chiral spin liquid with a $C=1/2$ fractionalized Chern number.

We calculate the beating of $h/2e$ and $h/e$ periodic oscillations of the flux-dependent critical supercurrent $I_c\left(\Phi \right)$ through a quantum spin-Hall insulator between two superconducting electrodes. A conducting pathway along the superconductor connects the helical edge channels via a nonhelical channel, allowing an electron incident on the superconductor along one edge to be Andreev reflected along the opposite edge. In the limit of small Andreev reflection probability the resulting even-odd effect is described by $I_c\propto |cos(e\Phi /\hslash )+f|$, with $\left|f\right|\ll 1$ proportional to the probability for phase-coherent interedge transmission. Because the sign of $f$ depends on microscopic details, a sample-dependent inversion of the alternation of large and small peaks is a distinctive feature of the beating mechanism for the even-odd effect.

We investigate the ground-state wave function of a prototypical strongly correlated system, a three-band $(p-d)$ Hubbard model of cuprates, using full configuration interaction quantum Monte Carlo. We show that the configuration interaction description of the exact ground state wave function is profoundly affected by the choice of single-particle representation, in a counterintuitive manner. Thus a broken-symmetry unrestricted Hartree-Fock basis, which at a single configuration level produces a qualitatively correct description of the antiferromagnet, results in a highly entangled exact solution consisting of high particle-hole excitations of the reference. This wave function is found to be very difficult to approximate using subspace diagonalizations. Conversely, a restricted Hartree-Fock basis, which yields at a single configuration level a qualitatively incorrect paramagnetic metal, results in a relatively rapidly converging configuration interaction expansion. Convergence can be further accelerated by adopting a natural orbital representation. Our results suggest that with the correct single-particle basis, such strongly correlated systems may be described by relatively compact wave functions.

We study the electron transport in open quantum-dot systems described by the interacting resonant-level models with Coulomb interactions. We consider the situation in which the quantum dot is connected to the left and right leads asymmetrically. We exactly construct many-electron scattering eigenstates for the two-lead system, where two-body bound states appear as a consequence of one-body resonances and the Coulomb interactions. By using an extension of the Landauer formula, we calculate the average electric current for the system under bias voltages in the first order of the interaction parameters. Through a renormalization-group technique, we arrive at the universal electric current, where we observe the suppression of the electric current for large bias voltages, i.e., negative differential conductance. We find that the suppressed electric current is restored by the asymmetry of the system parameters.

We observe condensation of exciton polaritons in quantum states composed of concentric rings when exciting cylindrical pillar GaAs/AlGaAs microcavities nonresonantly by a focused laser beam normally incident at the center of the pillar. The number of rings depends on the pumping intensity and the pillar size, and may achieve 5 in the pillar of $40\mu \text{m}$ diameter. Breaking the axial symmetry when moving the excitation spot away from the pillar center leads to transformation of the rings into a number of bright lobes corresponding to quantum states with nonzero angular momenta. The number of lobes, their shape, and location are dependent on the spot position. We describe the out-of-equilibrium condensation of polaritons in the states with different principal quantum numbers and angular momenta with a formalism based on Boltzmann-Gross-Pitaevskii equations accounting for repulsion of polaritons from the exciton reservoir formed at the excitation spot and their spatial confinement by the pillar boundary.

We demonstrate optical spin orientation of an individual ${\mathrm{Mn}}^{2+}$ ion embedded in a CdSe/ZnSe quantum dot. It is achieved through the injection of spin-polarized excitons to the dot under circularly polarized below-the-barrier optical excitation at energy sufficiently close to the dot emission energy. The efficiencies of both the exciton spin-transfer and optical pumping of the ${\mathrm{Mn}}^{2+}$ spin are studied by means of polarization-resolved single-dot spectroscopy performed at magnetic field in a Faraday configuration. The ion spin orientation efficiency is found to increase significantly with the magnetic field, while the spin-polarization degree of injected excitons remains constant and yields about 40%.

Conditions for the appearance of quantized anisotropic magnetoresistance (QAMR) in ferromagnetic conductors have been investigated from the viewpoint of the transmission channels calculated by method of the nonequilibrium Green's function–density functional theory. We demonstrate that the spin-orbital interaction is a precondition and the transverse size is a crucial condition for QAMR to emerge. Furthermore, we show the evolution of QAMR from a stepwise shape (corresponding to small transverse sizes) to a classical smooth cosine shape (corresponding to large transverse sizes). In addition, we prove the strong temperature dependence of QAMR, so a low temperature is necessary. Our research reconciles the different experiments and enlightens experimenters on QAMR.

For graphene interacting with a few-fs intense optical pulse, we predict unique and rich behavior dramatically different from three-dimensional solids. Quantum electron dynamics is shown to be coherent but highly nonadiabatic and effectively irreversible due to strong dephasing. Electron distribution in reciprocal space exhibits hot spots at the Dirac points and oscillations whose period is determined by nonlocality of electron response and whose number is proportional to the field amplitude. The optical pulse causes net charge transfer in the plane pf graphene in the direction of the instantaneous field maximum at relatively low fields and in the opposite direction at high fields. These phenomena promise ultrafast optoelectronic applications with petahertz bandwidth.

Using cryogenic scanning tunneling microscopy, we measured the electronic states and Kondo resonance of single $\mathrm{Fe}\left(\mathrm{II}\right)$-porphyrin molecules adsorbed on a $\mathrm{Au}(111)$ surface with intramolecular resolution. We found that the $\mathrm{Fe}\left(\mathrm{II}\right)$ ion introduces a spin-polarized molecular state near the Fermi level. Tunneling spectroscopy revealed that this state gives rise to Kondo resonance exhibiting characteristics different from those of the $\mathrm{Fe}\left(\mathrm{II}\right)$ spin state. Spin-polarized density functional theory calculations revealed that the molecule was weakly adsorbed on the surface, yet still switches its spin configuration from $S=1\text{to}2$. The spin switching was found to be driven by three effects: a structural distortion of the macrocyclic ring from planar to saddle shaped, a weak chemical bonding between the Fe and the Au surface atom underneath, and weakened Fe-N bonds due to $\mathrm{Au}(111)$-molecule charge transfer.

Hybrid semiconductor-superconductor systems are interesting melting pots where various fundamental effects in condensed-matter physics coexist. For example, when a quantum dot is coupled to a superconducting electrode two very distinct phenomena, superconductivity and the Kondo effect, compete. As a result of this competition, the system undergoes a quantum phase transition when the superconducting gap $\Delta$ is of the order of the Kondo temperature $T_K$. The underlying physics behind such transition ultimately relies on the physics of the Anderson model where the standard metallic host is replaced by a superconducting one, namely the physics of a (quantum) magnetic impurity in a superconductor. A characteristic feature of this hybrid system is the emergence of subgap bound states, the so-called Yu-Shiba-Rusinov (YSR) states, which cross zero energy across the quantum phase transition, signaling a switching of the fermion parity and spin (doublet or singlet) of the ground state. Interestingly, similar hybrid devices based on semiconducting nanowires with spin-orbit coupling may host exotic zero-energy bound states with Majorana character. Both parity crossings and Majorana bound states (MBSs) are experimentally marked by zero-bias anomalies in transport, which are detected by coupling the hybrid device with an extra normal contact. We here demonstrate theoretically that this extra contact, usually considered as a nonperturbing tunneling weak probe, leads to nontrivial effects. This conclusion is supported by numerical renormalization-group calculations of the phase diagram of an Anderson impurity coupled to both superconducting and normal-state leads. We obtain this phase diagram for an arbitrary ratio $\frac{\Delta }{T_K}$, which allows us to analyze relevant experimental scenarios, such as parity crossings as well as Kondo features induced by the normal lead, as this ratio changes. Spectral functions at finite temperatures and magnetic fields, which can be directly linked to experimental tunneling transport characteristics, show zero-energy anomalies irrespective of whether the system is in the doublet or singlet regime. We also derive the analytical condition for the occurrence of Zeeman-induced fermion-parity switches in the presence of interactions which bears unexpected similarities with the condition for emergent MBSs in nanowires.

The case of a quantum dot connected to two superconducting leads is studied by using the narrow-band limit to describe the superconducting degrees of freedom. The model provides a simple theoretical framework, almost analytical, to analyze the interplay between the Kondo effect, superconductivity, and finite temperature. In the quantum dot Kondo regime, the model is completely characterized by the ratio $\Delta /J$, with $\Delta$ the superconducting gap and $J$ an effective antiferromagnetic exchange coupling between the dot and the leads. The model allows us to calculate, at any temperature $T$, the equilibrium Josephson current through the dot in a very straightforward way as a function of $\Delta /J$. The behavior of the current allows us to distinguish the four types of hybrid junctions: 0, $0^{\prime },{\pi }^{\prime }$, and $\pi$. The presence of the 0- and $0^{\prime }$-junction configurations are intrinsically linked to the Kondo effect in the quantum dot, while the $\pi$- and ${\pi }^{\prime }$-junction configurations are driven by the superconductivity in the leads. The Josephson critical current has a non-monotonic behavior with temperature, that may be used for the experimental characterization of the fundamental $0-\pi$ transition. The model allows us to obtain easily a phase diagram $\Delta /J$ vs temperature, from where we can obtain an overall picture on the stability of the different types of junctions. From the explicit analytical expressions for the ground-state, low-energy excitations, free energy, and Josephson current, it is easy to understand the physical nature of the main features of the critical current and the phase diagram. The results, obtained with a minimum of numerical effort, are in a good qualitative agreement with more demanding calculational approaches aimed to solve the full model.

The electronic, magnetic, thermodynamical, and transport properties of FeRh alloys are studied from first principles. We present a unified approach to the phase stability, an estimate of exchange interactions in various magnetic phases, and transport properties including the effect of temperature which are all based on the same electronic-structure model. Emphasis is put on the transition between the ferromagnetic (FM) and antiferromagnetic (AFM) phases. Such a study is motivated by a recent suggestion of FeRh as a room-temperature antiferromagnetic memory resistor. The theory predicts the order-disorder transformation from the hypothetical disordered bcc phase into ordered B2 phase. Comparison of exchange interactions in the magnetically ordered FM and AFM phases with corresponding spin-disordered counterparts allows us to identify relevant interactions which are precursors of magnetically ordered phases. The most important result is the explanation of a dramatic decrease of the resistivity accompanying the AFM to FM phase transition which is due to the spin disorder present in the system. The study of the anisotropic magnetoresistance in the AFM phase found recently experimentally is extended also to finite temperatures.

We study properties of a helimagnetic thin film with a quantum Heisenberg spin model by using the Green's-function method. Surface spin configuration is calculated by minimizing the spin interaction energy. It is shown that the angles between spins near the surface are strongly modified with respect to the bulk configuration. Taking into account this surface spin reconstruction, we calculate self-consistently the spin-wave spectrum and the layer magnetizations as functions of temperature up to the disordered phase. The spin-wave spectrum shows the existence of a surface-localized branch which causes a low surface magnetization. We show that quantum fluctuations give rise to a crossover between the surface magnetization and interior-layer magnetizations at low temperatures. We calculate the transition temperature and show that it depends strongly on the helical angle. Results are in agreement with existing experimental observations on the stability of helical structure in thin films and on the insensitivity of the transition temperature with the film thickness. We also study effects of various parameters such as surface exchange and anisotropy interactions. Monte Carlo simulations for the classical spin model are also carried out for comparison with the quantum theoretical result.

The suppression of magnetic order with pressure concomitant with the appearance of pressure-induced superconductivity was recently discovered in CrAs. Here we present a neutron diffraction study of the pressure evolution of the helimagnetic ground state towards and in the vicinity of the superconducting phase. Neutron diffraction on polycrystalline CrAs was employed from zero pressure to 0.65 GPa and at various temperatures. The helimagnetic long-range order is sustained under pressure and the magnetic propagation vector does not show any considerable change. The average ordered magnetic moment is reduced from 1.73(2) ${\mu }_B$ at ambient pressure to 0.4(1) ${\mu }_B$ close to the critical pressure $P_c\approx 0.7$ GPa, at which magnetic order is completely suppressed. The width of the magnetic Bragg peaks strongly depends on temperature and pressure, showing a maximum in the region of the onset of superconductivity. We interpret this as associated with competing ground states in the vicinity of the superconducting phase.

The geometric arrangement of interacting (magnetic) dipoles is a question of fundamental importance in physics, chemistry, and engineering. Motivated by recent progress concerning the self-assembly of magnetic structures, the equilibrium orientation of eight interacting dipoles in a cubic cluster is investigated in detail. Instead of discrete equilibria we find a type of ground state consisting of infinitely many orientations. This continuum of energetically degenerate states represents a yet unknown form of magnetic frustration. The corresponding dipole rotations in the flat potential valley of this Goldstone mode enable the construction of frictionless magnetic couplings. Using computer-assisted algebraic geometry methods, we moreover completely enumerate all equilibrium configurations. The seemingly simple cubic system allows for exactly 9536 unstable discrete equilibria falling into 183 distinct energy families.

The inverse Faraday effect (IFE) describes the spontaneous magnetization of a conducting or dielectric medium due to irradiation with a circularly polarized electromagnetic wave. The effect has recently been discussed in the context of laser-induced magnetic switching of solids. We analyze analytically the electron dynamics induced by a circularly polarized laser beam within the framework of plasma theory. A macroscopic drift current is obtained, which circulates around the perimeter of the laser beam. The magnetic moment due to this macroscopic current has an opposite sign and half of the magnitude of the magnetic moment that is generated directly by the IFE. This constitutes an important contribution of angular momentum transferred from the wave to the medium and a classical mechanism for the light-induced generation of magnetic fields.