We present a systematic study of the energy spectra of graphene quantum rings having different geometries and edge types in the presence of a perpendicular magnetic field. Results are obtained within the tight-binding (TB) and Dirac models and we discuss which features of the former can be recovered by using the approximations imposed by the latter. Energy levels of graphene quantum rings obtained by diagonalizing the TB Hamiltonian are demonstrated to be strongly dependent on the rings geometry and the microscopical structure of the edges. This makes it difficult to recover those spectra by the existing theories that are based on the continuum (Dirac) model. Nevertheless, our results show that both approaches (i.e., TB and Dirac model) may provide similar results, but only for very specific combinations of ring geometry and edge types. The results obtained by a simplified model describing an infinitely thin circular Dirac ring show good agreement with those obtained for hexagonal and rhombus armchair graphene rings within the TB model. Moreover, we show that the energy levels of a circular quantum ring with an infinite mass boundary condition obtained within the Dirac model agree with those for a ring defined by a ring-shaped staggered potential obtained within the TB model.

We apply a real-space pseudopotential formalism for charged one-dimensional periodic systems to examine the binding energies of P dopants in Ge$\left[110\right]$ nanowires with varying periodicities and diameters. Binding energies calculated by density functional quasiparticle energies of the neutral dopant are severely underestimated whereas those calculated by quasiparticle energies of the ionized defect are overestimated. We find the best method for determining binding energies is to adopt a composite approach that evaluates the total energy difference between charged and neutral systems for the ionization energy of the P dopant, but uses the quasiparticle energy for the electron affinity of the pure Ge nanowire. Our formalism offers a simple density functional method for calculating dopant binding energies of small nanowire systems without the use of computationally intensive many-body perturbation theory calculations.

We study the zero-point and thermal ionic motion in ${\text{La}}_2$${\text{CuO}}_4$ by means of high-resolution neutron-diffraction experiments. Our results demonstrate anisotropic motion of O and, to a lesser extent, Cu ions, both consistent with the structure of coupled ${\text{CuO}}_6$ octahedra, and quantify the relative effects of zero-point and thermal contributions to ionic motion. By substitution of ${}^{18}\mathrm{O}$, we find that the oxygen isotope effect on the lattice dimensions is small and negative ($-0.01\%$), while the isotope effect on the ionic displacement parameters is significant ($-6$ to 50%). We use our results as input for theoretical estimates of the distribution of magnetic interaction parameters, $J$, in an effective one-band model for the cuprate plane. We find that ionic motion causes only small ($1\%$) effects on the average value $\langle J\rangle$, which vary with temperature and O isotope, but results in dramatic (10–20$\%$) fluctuations in $J$ values that are subject to significant (8–12%) isotope effects. We demonstrate that this motional broadening of $J$ can have substantial effects on certain electronic and magnetic properties in cuprates.

The phonon spectrum of stoichiometric Heusler alloy ${\text{Ni}}_2$FeGa is calculated for the high-temperature cubic austenite phase by using first-principles density functional perturbation theory. We also compute the elastic constants of the alloy from the initial slopes of the acoustic phonon branch. The ${\text{TA}}_2$ phonon branch along [110] direction shows softening with a minimum dip at $\zeta =0.58$ which indicates the possibility of modulated phases prior to martensitic transformation. We also map the Fermi surface of this alloy both in 3D and 2D to check the presence of any nesting vectors. The observed nesting parameter is in good agreement with the above value of the wave vector in the [110] direction where phonon softening occurs.

We present an interpretation of zero-field energy integrated (“diffuse”) neutron scattering and of high-field magnetization data at very low temperature in the frustrated pyrochlore system ${\text{Tb}}_2{\text{Ti}}_2{\text{O}}_7$. This material has antiferromagnetic exchange interactions, and it is expected to have an Ising character at low temperature. Contrary to expectations, it shows no magnetic ordering down to 0.05 K, being thus labeled a “spin liquid.” However, the ground state in ${\text{Tb}}_2{\text{Ti}}_2{\text{O}}_7$ is not a mere fluctuating moment paramagnet but, as demonstrated by very recent experiments, a state where the electronic degrees of freedom are hybridized with the phononic variables in an unconventional way. We show here that, by approximating this complex and still unraveled electron-phonon interaction by a dynamic Jahn-Teller coupling, one can account rather well for the diffuse neutron scattering and the low-temperature isothermal magnetization.

We study tunneling through a resonant level connected to two dissipative bosonic baths: one is the resistive environment of the source and drain leads, while the second comes from coupling to potential fluctuations on a resistive gate. We show that several quantum phase transitions (QPT) occur in such a model, transitions which emulate those found in interacting systems such as Luttinger liquids or Kondo systems. We first use bosonization to map this dissipative resonant level model to a resonant level in a Luttinger liquid, one with, curiously, two interaction parameters. Drawing on methods for analyzing Luttinger liquids at both weak and strong coupling, we obtain the phase diagram. For strong dissipation, a Berezinsky-Kosterlitz-Thouless QPT separates strong-coupling and weak-coupling (charge localized) phases. In the source-drain symmetric case, all relevant backscattering processes disappear at strong coupling, leading to perfect transmission at zero temperature. In fact, a QPT occurs as a function of the coupling asymmetry or energy of the resonant level: the two phases are (i) the system is cut into two disconnected pieces (zero transmission), or (ii) the system is a single connected piece with perfect transmission, except for a disconnected fractional degree of freedom. The latter arises from the competition between the two fermionic leads (source and drain), as in the two-channel Kondo effect.

The goal of this paper is to provide an intuitive and useful tool for analyzing the impurity-bound-state problem. We develop a semiclassical approach and apply it to an impurity in two-dimensional systems with parabolic or Dirac-like bands. Our method consists of reducing a higher-dimensional problem into a sum of one-dimensional ones using the two-dimensional Green's functions as a guide. We then analyze the one-dimensional effective systems in the spirit of the wave-function-matching method as in the standard one-dimensional quantum model. We demonstrate our method on two-dimensional models with parabolic and Dirac-like dispersion, with the later specifically relevant to topological insulators.

I study the dynamical correlations that a quantum impurity induces in the Fermi sea to which it is coupled. I consider a quantum transport setup in which the impurity can be realized in a double quantum dot. The same Hamiltonian describes tunneling states in metallic glasses, and can be mapped onto the Ohmic spin-boson model. It exhibits a Fermi edge singularity, i.e., many fermion correlations result in an impurity decay rate with a nontrivial power-law energy dependence. I show that there is a simple relation between temporal impurity correlations on the one hand and the linear response of the Fermi sea to external perturbations on the other. This results in a power-law singularity in the space and time dependence of the nonlocal polarizability of the Fermi sea, which can be detected in transport experiments.

Using hybrid functional calculations, we investigate the formation of $DX$ centers in GaN and AlN. We find that O, Si, and Ge are shallow donors in GaN, but form stable $DX$ centers in AlN for Fermi-level positions near the conduction band. Using a linear interpolation, we estimate the composition at which the onset of $DX$ behavior will occur in AlGaN alloys. Based on these predictions, we identify Si as the most effective donor for high Al-content AlGaN, and explain a number of seemingly conflicting experimental results for Si-doped AlGaN. Although based on size matching Ge was expected to be superior to Si as a shallow donor, it actually turns out to be more prone to $DX$-center formation.

Using an effective medium approach, we describe how, by combining mercury-cadmium-telluride semiconductor alloys with band gap energies of opposite signs, it may be possible to design a superlattice where the electrons have isotropic zero-effective mass and a single valley linear energy-momentum dispersion. We demonstrate that, because of the zero-mass property, the superlattice may have a strong nonlinear optical response.

The helical Dirac states on the surface of a topological insulator are protected by topology and display significant particle-hole asymmetry. This asymmetry arises from a subdominant Schrödinger-type contribution to the Hamiltonian which provides a small perturbation to a dominant Dirac contribution. This changes the Landau level energies in an external magnetic field ($B$) and provides modifications to the usual relativistic optical matrix elements. Nevertheless we find that the relativistic quantization of the Hall plateaus remains even when the ratio of the Schrödinger ($E_0$) to Dirac ($E_1$) magnetic energy scale increases either through an increase in $B$, a decrease in the Schrödinger mass, or a decrease of the Dirac Fermi velocity. First corrections to the optical matrix elements (OMEs) in the relativistic case drop out at least to order ${(E_0/E_1)}^3$. In the opposite limit $E_1$ small, the quantization remains classical but there is a split into two series. The first corrections to the OMEs in this case cancel out at least to order ${(E_1/E_0)}^4$.

We theoretically investigate the spectrum of a single electron double quantum dot, defined by top gates in a graphene with a substrate-induced gap. We examine the effects of electric and magnetic fields on the spectrum of localized states, focusing on the tunability of the interdot coupling. We find that the substrate-induced gap allows for electrostatic control, with some limitations that for a fixed interdot distance, the interdot coupling cannot be made arbitrarily small due to the Klein tunneling. On the other hand, the proximity of the valence band in graphene allows for new regimes, such as an $npn$ double dot, which have no counterparts in GaAs.

Screening is one of the fundamental concepts in solid-state physics. It has a great impact on the electronic properties of graphene, where huge mobilities were observed in spite of the large concentration of charged impurities. While static screening has successfully explained dc mobilities, screening properties can be significantly changed at infrared or optical frequencies. In this paper, we discuss the influence of dynamical screening on the optical absorption of graphene and other two-dimensional electron systems such as metallic monolayers. This research is motivated by recent experimental results that pointed out that graphene plasmon linewidths and optical scattering rates can be much larger than scattering rates determined by dc mobilities. Specifically, we discuss a process in which a photon incident on a graphene plane can excite a plasmon by scattering from an impurity, or a surface optical phonon of the substrate.

We present a controlled rare-weak-link theory of the superfluid-to-Bose/Mott glass transition in one-dimensional disordered systems. The transition has Kosterlitz-Thouless critical properties but may occur at an arbitrary large value of the Luttinger parameter $K$. The hydrodynamic description is valid under the correlation radius and defines criticality via mutual renormalization of the strength of microscopic weak links and superfluid stiffness. The link strength renormalizes along the lines of Kane and Fisher [Phys. Rev. Lett. 68, 1220 (1992)], while the renormalization of superfluid stiffness follows the lines of classical-field flow. The hallmark of the theory is the relation $K^{\left(c\right)}=1/\zeta$ between the critical value of the Luttinger parameter at macroscopic scales and the microscopic (irrenormalizable) exponent $\zeta$ describing the scaling $\propto 1/N^{1-\zeta }$ for the strength of the weakest link among the $N\gg L$ disorder realizations in a system of fixed mesoscopic size $L$.

Domain structures and the magnetic reversals of micrometer stripe patterns embedded in a weakly antiferromagnetically exchange coupled ${\text{Co}}_{90}$${\text{Fe}}_{10}$/Ru/${\text{Co}}_{90}$${\text{Fe}}_{10}$ trilayer were investigated. Patterning was achieved by means of ion irradiation through a lithographically defined mask. In this process, irradiated parts become ferromagnetic due to interfacial intermixing. The embedded stripes fabricated by this technique are compared to stripes patterned by reactive ion etching. Using magneto-optical Kerr microscopy, the domain structure and the shape of the magnetic reversal for both kinds of stripes have been studied. Observed differences in the switching behavior are explained by modifications of the magnetic material properties, e.g., anisotropy and saturation magnetization due to the ion irradiation. Irradiated 2-µm-wide stripes show a collective switching with quasidomains during the magnetic reversal. This observation indicates interactions of the internal magnetization of embedded stripes with the adjacent ones in the nonirradiated antiferromagnetically coupled trilayers. Two possible mechanisms suspected to mediate these interactions are discussed: a deviation of the antiparallel magnetic orientation in the synthetic antiferromagnetic material leading to an effective magnetic moment, as well as a domain wall at the boundary of two different kinds of stripes. The latter investigation is supported by micromagnetic simulations.

We study theoretically the dynamics of magnons in the presence of a single skyrmion in chiral magnets featuring Dzyaloshinskii-Moriya interaction. We show by micromagnetic simulations that the scattering process of magnons by a skyrmion can be clearly defined although both originate in the common spins. We find that (i) the magnons are deflected by a skyrmion, with the angle strongly dependent on the magnon wave number due to the effective magnetic field of the topological texture, and (ii) the skyrmion motion is driven by magnon scattering through exchange of the momenta between the magnons and a skyrmion: the total momentum is conserved. This demonstrates that the skyrmion has a well-defined, though highly non-Newtonian, momentum.

Rare-earth tri-tellurium $R$${\text{Te}}_3$ is a typical quasi-two-dimensional system which exhibits obvious charge-density-wave (CDW) orders. So far, $R$${\text{Te}}_3$ with heavier $R$ ions (Dy, Ho, Er, and Tm) are believed to experience two CDW phase transitions, while the lighter ones only hold one. ${\text{TbTe}}_3$ is claimed to belong to the latter. However, in this work we present evidences that ${\text{TbTe}}_3$ also possesses more than one CDW order. Aside from the one at 336 K, which was extensively studied and reported to be driven by imperfect Fermi surface nesting with a wave vector $q=(2/7c^{*})$, a new CDW energy gap (260 meV) develops at around 165 K, revealed by both infrared reflectivity spectroscopy and ultrafast pump-probe spectroscopy. More intriguingly, the origin of this energy gap is different from the second CDW order in the heavier $R$ ions-based compounds $R$${\text{Te}}_3$ ($R=\mathrm{Dy}$, Ho, Er, and Tm).

We provide a description of the interaction between light and a three-dimensional electron gas in the framework of the Power-Zienau-Wooly (PZW) formulation of the quantum electrodynamics. The existence of the collective plasmon and plasmon-polariton modes of the gas appears as a consequence of the general properties of the PZW Hamiltonian. Our description enables a fully microscopic theory of the surface plasmon-polariton excitations, based on a quantum Hamiltonian that is free from any additional hypothesis regarding the material dispersion. This theory can therefore be applied to study the quantum optical properties of plasmon and surface plasmon waves.

We investigate the entanglement spectrum in HOTRG—tensor renormalization group (RG) method combined with the higher order singular value decomposition—for two-dimensional (2D) classical vertex models. In the off-critical region, it is explained that the entanglement spectrum associated with the RG transformation is described by “doubling” of the spectrum of a corner transfer matrix. We then demonstrate that the doubling actually occurs for the square-lattice Ising model by HOTRG calculations up to $D=64$, where $D$ is the cutoff dimension of tensors. At the critical point, we also find that a nontrivial $D$ scaling behavior appears in the entanglement entropy. We mention about the HOTRG for the 1D quantum system as well.