Electron transport in small graphene nanoribbons is studied by microwave emulation experiments and tight-binding calculations. In particular, it is investigated under which conditions a transport gap can be observed. Our experiments provide evidence that armchair ribbons of width $3m+2$ with integer $m$ are metallic and otherwise semiconducting, whereas zigzag ribbons are metallic independent of their width. The contact geometry, defining to which atoms at the ribbon edges the source and drain leads are attached, has strong effects on the transport. If leads are attached only to the inner atoms of zigzag edges, broad transport gaps can be observed in all armchair ribbons as well as in rhomboid-shaped zigzag ribbons. All experimental results agree qualitatively with tight-binding calculations using the nonequilibrium Green's function method.

We have studied a generalized three-band crossing model in 2D, the generalized $\alpha -T_3$ lattice, ranging from the pseudospin-1 Dirac equation through a quadratic+flat band touching to the pseudospin-1/2 Dirac equation. A general method is presented to determine the operator form of the Green's function, being gauge and representation independent. This yields the Landau level structure in a quantizing magnetic field and the longitudinal and transversal magneto-optical conductivities of the underlying system. Although the magneto-optical selection rules allow for many transitions between Landau levels, the dominant one stems from exciting a particle from/to the flat band to/from a propagating band. The Hall conductivity from each valley is rational (not quantized at all), in agreement with Berry phase considerations, though their sum is always integer quantized.

Broken symmetry states in bilayer graphene in perpendicular electric $E_{\perp }$ and in-plane magnetic $B_{\parallel }$ fields are studied in the presence of the dynamically screened long-range Coulomb interaction and the symmetry-breaking contact four-fermion interactions. The integral gap equations are solved numerically, and it is shown that the momentum dependence of gaps is essential: It diminishes by an order of magnitude the gaps compared to the case of momentum-independent approximation, and the obtained gap magnitudes are found to agree well with existing experimental values. We derived a phase diagram of bilayer graphene at the neutrality point in the plane $(B_{\parallel },E_{\perp })$ showing that the (canted) layer antiferromagnetic (LAF) state remains a stable ground state of the system at large $B_{\parallel }$. On the other hand, while the LAF phase is realized at small values of $E_{\perp }$, the quantum valley Hall (QVH) phase is the ground state of the system at values $E_{\perp }>E_{cr}\left(B_{\parallel }\right)$, where a critical value $E_{cr}\left(B_{\parallel }\right)$ increases with in-plane magnetic field $B_{\left|\right|}$.

We consider the spectrum of Andreev bound states (ABSs) in an exemplary four-terminal superconducting structure where four chaotic cavities are connected by quantum point contacts to the terminals and to each other forming a ring. We nickname the resulting device 4T-ring. Such a tunable device can be realized in a 2D electron gas-superconductor or a graphene-based hybrid structure. We concentrate on the limit of a short structure and large conductance of the point contacts where there are many ABS in the device forming a quasicontinuous spectrum. The energies of the ABS can be tuned by changing the superconducting phases of the terminals. We observe the opening and closing of gaps in the spectrum upon changing the phases. This concerns the usual proximity gap that separates the levels from zero energy as well as less usual “smile” gaps that split the levels of the quasicontinuous spectrum. We demonstrate a remarkable crossover in the overall spectrum that occurs upon changing the ratio of conductances of the inner and outer point contacts. At big values of the ratio (closed limit), the levels exhibit a generic behavior expected for the spectrum of a disordered system manifesting level repulsion and Brownian “motion” upon changing the phases. At small values of the ratio (open limit), the levels are squeezed into narrow bunches separated by wide smile gaps. Each bunch consists of almost degenerate ABS formed by Andreev reflection between two adjacent terminals. We study in detail the properties of the spectrum in the limit of a small ratio, paying special attention to the crossings of bunches. We distinguish two types of crossings: (i) with a regular phase dependence of the levels and (ii) crossings where the Brownian motion of the levels leads to an apparently irregular phase dependence. We work out a perturbation theory that explains the observations both at a detailed level of random scattering in the device and at a phenomenological level of positively defined random matrices. The unusual properties of the spectrum originate from rather unobvious topological effects. The topology of the first kind is restricted to the semiclassical limit and related to the winding of the semiclassical Green function. It is responsible for the closing of the proximity gaps. The topology of the second kind comes about the discreteness of the number of modes in the point contacts and is responsible for the smile gaps. The topology of the third kind leads to the emergence of Weyl points in the spectrum and is not discussed in the context of this article.

We investigated thermally activated ionization and thermally activated crossover as the two possibilities of quenching of $5d$ luminescence in $\mathrm{P}{\mathrm{r}}^{3+}$-doped ${\mathrm{Y}}_3\mathrm{A}{\mathrm{l}}_{5-x}\mathrm{G}{\mathrm{a}}_x{\mathrm{O}}_{12}$. Varying the Ga content $x$ gives the control over the relative energy level location of the $5d$ and $4f^2:{}^{3}P_J$ states of $\mathrm{P}{\mathrm{r}}^{3+}$ and the host conduction band (CB). Temperature-dependent luminescence lifetime measurements show that the $5d$ luminescence quenching temperature $T_{50\%}$ increases up to $x=2$ and decreases with further increasing Ga content. This peculiar behavior is explained by a unique transition between the two quenching mechanisms which have an opposite dependence of thermal quenching on Ga content. For low Ga content, thermally activated crossover from the $4f5d$ state to the $4f^2\left({}^{3}P_J\right)$ states is the operative quenching mechanism. With increasing Ga content, the activation energy for thermally activated crossover becomes larger, as derived from the configuration coordinate diagram, while from the vacuum referred binding energy diagram the activation energy of thermal ionization becomes smaller. Based on these results, we demonstrated that the thermal quenching of $\mathrm{P}{\mathrm{r}}^{3+}:5d_1-4f$ luminescence in ${\mathrm{Y}}_3\mathrm{A}{\mathrm{l}}_{5-x}\mathrm{G}{\mathrm{a}}_x{\mathrm{O}}_{12}$ with $x=0,1,2$ is a thermally activated crossover while for $x=3,4,5$ it results from the thermal ionization.

Transition metal compounds with the ${\left(t_{2g}\right)}^4$ electronic configuration are expected to be nonmagnetic atomic singlets both in the weakly interacting regime due to spin-orbit coupling, as well as in the Coulomb dominated regime with oppositely aligned $L=1$ and $S=1$ angular momenta. However, starting with the full multiorbital electronic Hamiltonian, we show the low-energy effective magnetic Hamiltonian contains isotropic superexchange spin interactions but anisotropic orbital interactions. By tuning the ratio of superexchange to spin-orbit coupling $J_{\mathrm{SE}}/\lambda$, we obtain a phase transition from nonmagnetic atomic singlets to novel magnetic phases depending on the strength of Hund's coupling, the crystal structure and the number of active orbitals. Spin-orbit coupling plays a non-trivial role in generating a triplon condensate of weakly interacting excitations at antiferromagnetic ordering vector $\vec{k}=\vec{\pi }$, regardless of whether the local spin interactions are ferromagnetic or antiferromagnetic. In the large $J_{\mathrm{SE}}/\lambda$ regime, the localized spin and orbital moments produce anisotropic orbital interactions that are frustrated or constrained even in the absence of geometric frustration. Orbital frustration leads to frustration in the spin channel opening up the possibility of spin-orbital liquids with both spin and orbital entanglement.

${\mathrm{Fe}}_2\mathrm{MnSi}$ exhibits a ferromagnetic transition at $T_C\sim 230$ K and another transition to a phase with antiferromagnetic components at $T_A\sim 60$ K. By substituting V for Mn, so as to obtain ${\mathrm{Fe}}_2{\mathrm{Mn}}_{1-x}{\mathrm{V}}_x\mathrm{Si}$, $T_A$ is revealed to decrease with $x$ and then vanish around $x\sim 0.2$. In this study, the phase boundary of the transition at $T_A$ in the high-field range is found for $0\le x\le 0.15$ with pulsed fields up to $\sim 70$ T. The magnetization of ${\mathrm{Fe}}_2{\mathrm{Mn}}_{1-x}{\mathrm{V}}_x\mathrm{Si}$ slowly increases even at the highest field of $\sim 70$ T, though it occurs more gradually as $x$ increases. We compare the magnetization for $0\le x\le 0.20$ at 62 T with the Slater-Pauling rule, which holds when a Heusler compound is a half-metal, and find fairly good agreement. This suggests an intimate relation between the high-field phase and the half-metallic electronic structure, and that at the high-field limit the phase approaches the half-metallic state, which has been predicted by band-structure calculations.

The $5d$-transition-metal pyrochlore oxide $\mathrm{C}{\mathrm{d}}_2\mathrm{R}{\mathrm{e}}_2{\mathrm{O}}_7$, which was recently suggested to be a prototype of the spin-orbit-coupled metal [Phys. Rev. Lett. 115, 026401 (2015)], exhibits an inversion-symmetry-breaking (ISB) transition at 200 K and a subsequent superconductivity below 1 K at ambient pressure. We study the crystal structure at high pressures up to 5 GPa by means of synchrotron x-ray powder diffraction. A rich structural phase diagram is obtained, which contains at least seven phases, and is almost consistent with the electronic phase diagram determined by previous resistivity measurements. Interestingly, the ISB transition vanishes at $\sim 4\mathrm{GPa}$ where the enhancement of the upper critical field was observed in resistivity. Moreover, it is shown that the point groups at 8 K, probably kept in the superconducting phases, sequentially transform into piezoelectric, ferroelectric, and centrosymmetric structures on the application of pressure.

The linear and nonlinear phononic interactions between an optically excited infrared (IR) or hyper-Raman mode and a driven Raman mode are computed for the $d^0 \left({\mathrm{CaTiO}}_3\right)$ and $d^1 \left({\mathrm{LaTiO}}_3\right)$ titanates within a first-principles density functional framework. We calculate the potential energy surface expanded in terms of the $A_g$ or $B_{1g}$ mode amplitudes coupled to the $A_u$ or the $B_{3u}$ mode and determine the coupling coefficients for these multimode interactions. We find that the linear-quadratic coupling dominates the anharmonicities over the quadratic-quadratic interaction in the perovskite titanates. The IR and Raman modes both modify the electronic structure with the former being more significant but occurring on a different time scale; furthermore, the coupled-mode interactions lead to sizable perturbations to the valence bandwidth ($\sim 100\text{meV}$) and band gap ($\sim 50$  meV). By comparing the coupling coefficients of undoped ${\mathrm{CaTiO}}_3$ and ${\mathrm{LaTiO}}_3$ to those for electron-doped $\left({\mathrm{CaTiO}}_3\right)$ and hole-doped $\left({\mathrm{LaTiO}}_3\right)$ titanates, we isolate the role of orbital filling in the nonlinear coupling process. We find that with increasing occupancy of the $d$ manifold, the linear-quadratic interaction decreases by approximately 30% with minor changes induced by the cation chemistry (that mainly affect the phonon mode frequencies) or by electron correlation. We identify the importance of the Ti-O bond stiffness, which depends on the orbital filling, in governing the lattice anharmonicitiy. This microscopic understanding can be used to increase the nonlinear coupling coefficient to facilitate more facile access of nonequilibrium structures and properties through ionic Raman scattering processes.

A study of the zero field and field induced magnetic states of the frustrated rare earth tetraboride ${\mathrm{HoB}}_4$ has been carried out using single crystal neutron diffraction complemented by magnetization measurements. In zero field, ${\mathrm{HoB}}_4$ shows magnetic phase transitions at $T_{\mathrm{N}1}=7.1$ K to an incommensurate state with a propagation vector $(\delta ,\delta ,{\delta }^{\prime })$, where $\delta =0.02$ and ${\delta }^{\prime }=0.43$ and at $T_{\mathrm{N}2}=5.7$ K to a noncollinear commensurate antiferromagnetic structure. Polarized neutron diffraction measurements in zero field have revealed that the incommensurate reflections, albeit much reduced in intensity, persist down to 1.5 K despite antiferromagnetic ordering at 5.7 K. At lower temperatures, application of a magnetic field along the $c$ axis initially re-establishes the incommensurate phase as the dominant magnetic state in a narrow field range, just prior to ${\mathrm{HoB}}_4$ ordering with an up-up-down ferrimagnetic structure characterized by the $\left(hk\frac{1}{3}\right)$-type reflections between 18 and 24 kOe. This field range is marked by the previously reported $M/M_{\mathrm{sat}}=\frac{1}{3}$ magnetization plateau, which we also see in our magnetization measurements. The region between 21 and 33 kOe is characterized by the increase in the intensity of the antiferromagnetic reflections, such as (100), the maximum of which coincides with the appearance of the narrow magnetization plateau with $M/M_{\mathrm{sat}}\approx \frac{3}{5}$. Further increase of the magnetic field results in the stabilization of a polarized state above 33 kOe, while the incommensurate reflections are clearly present in all fields up to 59 kOe. We propose the $H-T$ phase diagram of ${\mathrm{HoB}}_4$ for the $H\parallel c$ containing both stationary and transitionary magnetic phases which overlap and show significant history dependence.

Nondiagonal couplings to a bosonic bath completely change polaronic dynamics, from the usual diagonally coupled paradigm of smoothly varying properties. We study, using analytic and numerical methods, a model having both diagonal Holstein and nondiagonal Su-Schrieffer-Heeger (SSH) couplings. The critical coupling found previously in the pure SSH model, at which the $k=0$ effective mass diverges, now becomes a transition line in the coupling constant plane—the form of the line depends on the adiabaticity parameter. Detailed results are given for the quasiparticle and ground-state properties, over a wide range of couplings and adiabaticity ratios. The new paradigm involves a destabilization, at the transition line, of the simple Holstein polaron to one with a finite ground-state momentum, but with everywhere a continuously evolving band shape. No “self-trapping transition” exists in any of these models. The physics may be understood entirely in terms of competition between different hopping terms in a simple renormalized effective band theory. The possibility of further transitions is suggested by the results.

The dielectric function is one of the most important quantities that describes the electrical and optical properties of solids. Accurate modeling of the frequency-dependent dielectric function has great significance in the study of the long-range van der Waals (vdW) interaction for solids and adsorption. In this work we calculate the frequency-dependent dielectric functions of semiconductors and insulators using the $GW$ method with and without exciton effects, as well as efficient semilocal density functional theory (DFT), and compare these calculations with a model frequency-dependent dielectric function. We find that for semiconductors with moderate band gaps, the model dielectric functions, $GW$ values, and DFT calculations all agree well with each other. However, for insulators with strong exciton effects, the model dielectric functions have a better agreement with accurate $GW$ values than the DFT calculations, particularly in high-frequency region. To understand this, we repeat the DFT calculations with scissors correction, by shifting the DFT Kohn-Sham energy levels to match the experimental band gap. We find that scissors correction only moderately improves the DFT dielectric function in the low-frequency region. Based on the dielectric functions calculated with different methods, we make a comparative study by applying these dielectric functions to calculate the vdW coefficients ($C_3$ and $C_5$) for adsorption of rare-gas atoms on a variety of surfaces. We find that the vdW coefficients obtained with the nearly free electron gas-based model dielectric function agree quite well with those obtained from the $GW$ dielectric function, in particular for adsorption on semiconductors, leading to an overall error of less than 7% for $C_3$ and 5% for $C_5$. This demonstrates the reliability of the model dielectric function for the study of physisorption.

We present an analytical and numerical investigation of the spectral and transport properties of a quadruple quantum-dot (QQD) structure which is one of the popular low-dimensional systems in the context of fundamental quantum physics study, future electronic applications, and quantum calculations. The density of states, occupation numbers, and conductance of the structure were analyzed using the nonequilibrium Green's functions in the tight-binding approach and the equation-of-motion method. In particular the anisotropy of hopping integrals and on-site electron energies as well as the effects of the finite intra- and interdot Coulomb interactions were investigated. It was found out that the anisotropy of the kinetic processes in the system leads to the Fano-Feshbach asymmetrical peak. We demonstrated that the conductance of the QQD device has a wide insulating band with steep edges separating triple-peak structures if the intradot Coulomb interactions are taken into account. The interdot Coulomb correlations between the central QDs result in the broadening of this band and the occurrence of an additional band with low conductance due to the Fano antiresonances. It was shown that in this case the conductance of the anisotropic QQD device can be dramatically changed by tuning the anisotropy of on-site electron energies.

The electronic conductance of graphene-based bilayer flake systems reveals different quantum interference effects, such as Fabry-Pérot resonances and sharp Fano antiresonances on account of competing electronic paths through the device. These properties may be exploited to obtain spin-polarized currents when the same nanostructure is deposited above a ferromagnetic insulator. Here, we study how the spin-dependent conductance is affected when a time-dependent gate potential is applied to the bilayer flake. Following a Tien-Gordon formalism, we explore how to modulate the transport properties of such systems via appropriate choices of the ac-field gate parameters. The presence of an oscillating field opens the possibility of tuning the original antiresonances for a large set of field parameters. We show that interference patterns can be partially or fully removed by the time-dependent gate voltage. The results are reflected in the corresponding weighted spin polarization, which can reach maximum values for a given spin component. We found that differential conductance maps as functions of bias and gate potentials show interference patterns for different ac-field parameter configurations. The proposed bilayer graphene flake systems may be used as a frequency detector in the THz range.

The resistivities of the dilute, strongly interacting two-dimensional electron systems in the insulating phase of a silicon MOSFET are the same for unpolarized electrons in the absence of magnetic field and for electrons that are fully spin polarized by the presence of an in-plane magnetic field. In both cases the resistivity obeys Efros-Shklovskii variable range hopping $\rho \left(T\right)={\rho }_0\text{exp}\left[{(T_{ES}/T)}^{1/2}\right]$, with $T_{ES}$ and $1/{\rho }_0$ mapping onto each other if one applies a shift of the critical density $n_{\text{c}}$ reported earlier. With and without magnetic field, the parameters $T_{ES}$ and $1/{\rho }_0={\sigma }_0$ exhibit scaling consistent with critical behavior approaching a metal-insulator transition.

After more than a decade, direct observation of the odd frequency triplet pairing state in superconducting hybrid structures remains elusive. We propose an experimentally feasible setup that can unambiguously reveal the zero energy peak due to proximity-induced equal spin superconducting triplet correlations. We theoretically investigate a two-dimensional Josephson junction in the diffusive regime. The nanostructure consists of a normal metal sandwiched between two ferromagnetic layers with spiral magnetization patterns. By applying an external magnetic field perpendicular to the junction plane, vortices nucleate in the normal metal. The calculated energy and spatially resolved density of states, along with the pair potential, reveal that remarkably, only triplet Cooper pairs survive in the vortex cores. These isolated odd frequency triplet correlations result in well defined zero energy peaks in the local density of states that can be identified through tunneling spectroscopy experiments. Moreover, the diffusive regime considered here rules out the possibility of Andreev bound states in the vortex core as contributors to the zero energy peaks.

We perform a magnetoinfrared spectroscopy study of the semiconductor to semimetal transition of InAs/GaSb double quantum wells from the normal to the inverted state. We show that owing to the low carrier density of our samples, the magnetoabsorption spectra evolve from a single cyclotron resonance peak in the normal state to multiple absorption peaks in the inverted state with distinct magnetic field dependence. Using an eight-band Pidgeon-Brown model, we explain all the major absorption peaks observed in our experiment. We demonstrate that the semiconductor to semimetal transition can be realized by manipulating the quantum confinement, the strain, and the magnetic field. Our work paves the way for band engineering of optimal InAs/GaSb structures for realizing novel topological states as well as for device applications in the terahertz regime.

In spite of their relatively high lattice thermal conductivity ${\kappa }_{\ell }$, the $X\mathrm{NiSn}$ ($X=\text{Ti}$, Zr, or Hf) half-Heusler compounds are good thermoelectric materials. Previous studies have shown that ${\kappa }_{\ell }$ can be reduced by sublattice alloying on the $X$ site. To cast light on how the alloy composition affects ${\kappa }_{\ell }$, we study this system using the phonon Boltzmann-transport equation within the relaxation time approximation in conjunction with density functional theory. The effect of alloying through mass-disorder scattering is explored using the virtual crystal approximation to screen the entire ternary ${\mathrm{Ti}}_x{\mathrm{Zr}}_y{\mathrm{Hf}}_{1-x-y}\mathrm{NiSn}$ phase diagram. The lowest lattice thermal conductivity is found for the ${\mathrm{Ti}}_x{\mathrm{Hf}}_{1-x}\mathrm{NiSn}$ compositions; in particular, there is a shallow minimum centered at ${\mathrm{Ti}}_{0.5}{\mathrm{Hf}}_{0.5}\mathrm{NiSn}$ with ${\kappa }_{\ell }$ taking values between 3.2 and 4.1 W/mK when the Ti content varies between 20% and 80%. Interestingly, the overall behavior of mass-disorder scattering in this system can only be understood from a combination of the nature of the phonon modes and the magnitude of the mass variance. Mass-disorder scattering is not effective at scattering acoustic phonons of low energy. By using a simple model of grain boundary scattering, we find that nanostructuring these compounds can scatter such phonons effectively and thus further reduce the lattice thermal conductivity; for instance, ${\mathrm{Ti}}_{0.5}{\mathrm{Hf}}_{0.5}\mathrm{NiSn}$ with a grain size of $L=100$ nm experiences a 42% reduction of ${\kappa }_{\ell }$ compared to that of the single crystal.