In recent times, trilayer graphene has attracted wide attention owing to its stacking and electric-field-dependent electronic properties. However, a direct and well-resolved experimental visualization of its band structure has not yet been reported. In this paper, we present angle-resolved photoemission spectroscopy data which show with high resolution the electronic band structure of trilayer graphene obtained on α-SiC(0001) and β-SiC(111) via hydrogen intercalation. Electronic bands obtained from tight-binding calculations are fitted to the experimental data to extract the interatomic hopping parameters for Bernal and rhombohedral stacked trilayers. Low-energy electron microscopy measurements demonstrate that the trilayer domains extend over areas of tens of square micrometers, suggesting the feasibility of exploiting this material in electronic and photonic devices. Furthermore, our results suggest that, on SiC substrates, the occurrence of a rhombohedral stacked trilayer is significantly higher than in natural bulk graphite.

To establish the mechanism of unconventional superconductivity in Sr${}_2$RuO${}_4$, a prerequisite is direct information concerning the momentum-space structure of the energy gaps ${\Delta }_i\left(k\right)$, and in particular whether the pairing strength is stronger (“dominant”) on the quasi-one-dimensional ($\alpha$ and $\beta$) or on the quasi-two-dimensional ($\gamma$) Fermi surfaces. We present scanning tunneling microscopy measurements of the density of states spectra in the superconducting state of Sr${}_2$RuO${}_4$ for 0.1$T_c$ < $T$ < $T_c$ and analyze them along with published thermodynamic data using a simple phenomenological model. We show that our observation of a single superconducting gap scale with maximum value $2\Delta \approx 5T_c$ along with a spectral shape indicative of line nodes is consistent, within a weak-coupling model, with magnetically mediated odd-parity superconductivity generated by dominant, near-nodal, Cooper pairing on the α and β bands.

URu${}_2$Si${}_2$ is claimed to be a chiral $d$-wave superconductor with a $k_z(k_x\pm i{k}_y)$ time-reversal symmetry broken orbital component for the Cooper pair wave function, which contains both nodal points and lines of nodes. To study the magnetic response of such an unconventional state through a bulk, thermodynamic probe, we measured the magnetic torque $\tau$ in very high-quality, well-characterized URu${}_2$Si${}_2$ single crystals at high magnetic fields $H$ and at very low temperatures $T$. The magnetization $M\left(H\right)\propto \tau \left(H\right)/H$ of URu${}_2$Si${}_2$, in its superconducting state and for angles within ${15}^{\circ }$ from the $\mathit{ab}$ plane, reveals a change in its sign for $H$ approaching $H_{c2}$: from a clear diamagnetic response dominated by the pinning of vortices to a state with a smaller but “paramagneticlike” hysteretic response which disappears at $H_{c2}$, thus implying that it is intrinsically related to the superconducting state. We argue that this anomalous, angular-dependent behavior is evidence for a time-reversal symmetry broken superconducting state in URu${}_2$Si${}_2$, although not necessarily for the $k_z(k_x\pm i{k}_y)$ state.

We report on new superconductors Ba${}_n$${}_{+2}$Ir${}_{4n}$Ge${}_{12n+4}$ ($n$ $=$ 1, 2) with critical temperatures $T_c$ $=$ 6.1 and 3.2 K, respectively, along with their crystal structures, electron transport, and specific heat. The compounds are composed of alternating Ba@Ir${}_8$Ge${}_{16}$ and Ba@Ir${}_2$Ge${}_{16}$ cages, both of which are larger in the $n$ $=$ 1 sample than in the $n$ $=$ 2 sample. The normal-state heat capacity reveals two low-lying vibration modes associated with guest Ba cations, and both characteristic temperatures in Ba${}_3$Ir${}_4$Ge${}_{16}$ are smaller than those in Ba${}_4$Ir${}_8$Ge${}_{28}$. Meanwhile, the density functional theory calculations reveal that the Ge-4$p$ bands dominated the Fermi level in both samples. We propose that the softening of localized phonons due to expansion of the cage strengthens the electron-phonon coupling between Ba cations and Ge anions, leading to the higher $T_c$ in Ba${}_3$Ir${}_4$Ge${}_{16}$.

The bright exciton splitting in nanosystems and its origins are of primary importance for quantum-dot-based entangled-photon-pair generation. In this paper, I investigate excitonic energies and fine structure for million-atom InAs/InP quantum dots using many-body theory in conjunction with the empirical tight-binding method. Whereas the phenomenological theories relate the fine-structure splitting to quantum-dot-shape asymmetry, using an atomistic approach I demonstrate that for certain elongated quantum-dot shapes the bright exciton splitting can be significantly reduced. I demonstrate that strain effects play an essential role as the main contribution to the bright exciton splitting in InAs/InP quantum dots and observe highly reduced fine-structure splitting for high-symmetry quantum dots without wetting layer. I report the “intrinsic” fine-structure splitting, due to the underlying crystal lattice, to be generally significantly larger than the values predicted by the empirical pseudopotential calculations. Finally, I study excitonic properties of alloyed InAsP quantum dots and demonstrate that alloying effects can significantly reduce fine-structure splitting even in significantly elongated quantum dots.

We study the free-energy landscape of a minimal model for relaxor ferroelectrics. Using a variational method which includes leading correlations beyond the mean-field approximation as well as disorder averaging at the level of a simple replica theory, we find metastable paraelectric states with a stability region that extends to zero temperature. The free energy of such states exhibits an essential singularity for weak compositional disorder pointing to their necessary occurrence. Ferroelectric states appear as local minima in the free energy at high temperatures and become stable below a coexistence temperature $T_c$. We calculate the phase diagram in the electric-field–temperature plane and find a coexistence line of the polar and nonpolar phases which ends at a critical point. First-order phase transitions are induced for fields sufficiently large to cross the region of stability of the metastable paraelectric phase. These polar and nonpolar states have distinct structure factors from those of conventional ferroelectrics. We use this theoretical framework to compare and gain physical understanding of various experimental results in typical relaxors.

We prepare single-layer potassium-doped iron selenide (110) film by molecular-beam expitaxy. Such a single-layer film can be viewed as a two-dimensional system composed of weakly coupled two-leg iron ladders. Scanning tunneling spectroscopy reveals that superconductivity is developed in this two-leg ladder system. The superconducting gap is similar to that of the multilayer films. However, the Fermi-surface topology in this quasi-one-dimensional system is remarkably different from that of the bulk materials. Our results suggest that superconducting pairing is very short ranged or takes place rather locally in iron chalcogenides. The superconductivity is most likely driven by electron-electron correlation effect and is insensitive to the change of Fermi surfaces.

We present research on the superconducting properties of Nb${}_x$Re${}_{1-x}$ ($x=0.13$–0.38) obtained by measuring the electrical resistivity $\rho \left(T\right)$, magnetic susceptibility $\chi \left(T\right)$, specific heat $C_P\left(T\right)$, and London penetration depth $\Delta \lambda \left(T\right)$. It is found that the superconducting transition temperature $T_c$ decreases monotonically with an increase of $x$. The upper critical field $B_{c2}\left(T\right)$ for various $x$ can be nicely scaled by its corresponding $T_c$. The electronic specific heat $C_e\left(T\right)/T$, penetration depth $\Delta \lambda \left(T\right)$, and superfluid density ${\rho }_s\left(T\right)$ demonstrate exponential behavior at low temperatures and can be well fitted by a one-gap BCS model. The residual Sommerfeld coefficient ${\gamma }_0\left(B\right)$ in the superconducting state follows a linear field dependence. All these properties suggest an $s$-wave BCS-type of superconductivity with a very large $B_{c2}\left(0\right)$ for Nb${}_x$Re${}_{1-x}$ ($0.13\le x\le 0.38$).

The unusual electronic properties of the quantum spin Hall or Chern insulator become manifest in the form of robust edge states when samples with boundaries are studied. In this work, we ask if and how the topologically nontrivial electronic structure of these two-dimensional systems can be passed on to their zero-dimensional relatives, namely, fullerenes or other closed-cage molecules. To address this question, we study Haldane's honeycomb lattice model on polyhedral nanosurfaces. We find that for sufficiently large surfaces, characteristic corner states appear for parameters for which the planar model displays a quantized Hall effect. In the electronic structure, these corner states show up as in-gap modes which are well separated from the quasicontinuum of states. We discuss the role of finite-size effects and how the coupling between the corner states lifts the degeneracy in a characteristic way determined by the combined Berry phases which leads to an effective magnetic monopole of charge 2 at the center of the nanosurface. Experimental implications for fullerenes in the large spin-orbit regime are also pointed out.

We perform and analyze a series of time-resolved Faraday rotation measurements of coherent spin dynamics in a room-temperature ensemble of CdSe nanocrystal quantum dots (NCQDs) to study the decoherence and dephasing mechanisms that limit the transverse spin lifetime. Coherent spin lifetimes on the order of nanoseconds have been previously observed in CdSe NCQDs, but the presence of multiple components with distinct dynamics and strong inhomogeneous dephasing have made it difficult to study the relevant spin decay mechanisms quantitatively. Here, we obtain reliable fitting results by ensuring that cross-correlations between model parameters are minimized for the parameters of interest. Furthermore, we characterize the morphological inhomogeneity of the NCQD ensemble using transmission electron microscopy to constrain the model parameters that specify inhomogeneous dephasing. We find that $g$-factor inhomogeneity-induced dephasing (gID) is not sufficient to explain the magnetic-field-dependent decay of the spin signal. We propose an additional decoherence mechanism arising from rapid transitions between the fine structure states of the exciton referred to as fine-structure decoherence (FSD). By including both gID and FSD in the model, excellent fits are obtained to the data, including a prominent short-time-scale feature, which has typically been excluded from the fits in previous work.

The change of the quasiparticle density of states in a superconductor due to the Zeeman splitting can lead to highly responsive spintronic devices. This is demonstrated here in the magnetotunneling studies of a supercondcutor/insulator/ferromagnet tunnel junction. A tunnel magnetoresistance (TMR) as large as 36% is obtained, resulting from the conductance variation due to spin-split quasiparticle tunneling, and only occurs in the superconducting state. Our results show that in addition to the naturally existent spin imbalance in ferromagnets (upon which conventional TMR is obtained), we can manipulate tunnel conductance by tailoring spin dependent density of states with interfacial exchange fields, and even with a tunnel junction with both superconducting electrodes.

We investigate spin and charge transport in both single and bilayer graphene nonlocal spin-valve devices. An inverse dependence of the spin lifetime ${\tau }_s$ on the carrier mobility $\mu$ is observed in devices with large contact-resistance-area products ($R_{c}A>1\mathrm{k}\Omega \mu {\mathrm{m}}^2$). Furthermore, we observe an increase of ${\tau }_s$ with increasing $R_{c}A$ values, demonstrating that spin transport is limited by spin dephasing underneath the electrodes. In charge transport, we measure a second contact-induced Dirac peak at negative gate voltages in devices with larger $R_{c}A$ values, demonstrating different transport properties in contact-covered and bare graphene parts. We argue that the existence of the second Dirac peak complicates the analysis of the carrier mobilities and the spin scattering mechanisms.

We show, using an ab initio approach, that the quantum zero-point atomic motion has strong effects on the electronic properties of carbon and silicon nanoclusters. The ensuing band-gap renormalization is between 0.3 and 0.9 eV and is as large as the corresponding exciton binding energy. These results call for a critical reassessment of the quality of nanocluster calculations performed assuming frozen atom positions, even in the zero-temperature limit. Our approach allows to separate the effect into different spatial contributions (surface, core, passivants) and to quantify on which electronic states (according to their symmetries) the effect is strongest.

Recently, it has been suggested that topological superconductivity and Majorana end states can be realized in a chain of magnetic impurities on the surface of an $s$-wave superconductor when the magnetic moments form a spin helix as a result of the RKKY interaction mediated by the superconducting substrate. Here, we investigate this scenario theoretically by developing a tight-binding Bogoliubov-de Gennes description starting from the Shiba bound states induced by the individual magnetic impurities. While the resulting model Hamiltonian has similarities with the Kitaev model for one-dimensional spinless $p$-wave superconductors, there are also important differences, most notably the long-range nature of hopping and pairing as well as the complex hopping amplitudes. We use both analytical and numerical approaches to explore the consequences of these differences for the phase diagram and the localization properties of the Majorana end states when the Shiba chain is in a topological superconducting phase.

In this work, we extend recent inverse statistical-mechanical methods developed for many-particle systems to the case of spin systems. For simplicity, we focus in this initial study on the two-state Ising model with radial spin-spin interactions of finite range (i.e., extending beyond nearest-neighbor sites) on the square lattice under periodic boundary conditions. Our interest herein is to find the optimal set of shortest-range pair interactions within this family of Hamiltonians, whose corresponding ground state is a targeted spin configuration such that the difference in energies between the energetically closest competitor and the target is maximized. For an exhaustive list of competitors, this optimization problem is solved exactly using linear programming. The possible outcomes for a given target configuration can be organized into the following three solution classes: unique (nondegenerate) ground state (class I), degenerate ground states (class II), and solutions not contained in the previous two classes (class III). We have chosen to study a general family of striped-phase spin configurations comprised of alternating parallel bands of up and down spins of varying thicknesses and a general family of rectangular block checkerboard spin configurations with variable block size, which is a generalization of the classic antiferromagnetic Ising model. Our findings demonstrate that the structurally anisotropic striped phases, in which the thicknesses of up- and down-spin bands are equal, are unique ground states for isotropic short-ranged interactions. By contrast, virtually all of the block checkerboard targets are either degenerate or fall within class III solutions. The degenerate class II spin configurations are identified up to a certain block size. We also consider other target spin configurations with different degrees of global symmetries and order. Our investigation reveals that the solution class to which a target belongs depends sensitively on the nature of the target radial spin-spin correlation function. In the future, it will be interesting to explore whether such inverse statistical-mechanical techniques could be employed to design materials with desired spin properties.

We consider the absorption of microwaves by a quantum Hall droplet. We show that the number and velocities of charged edge modes can be directly measured from a droplet of known shape. In contrast to standard transport measurements, different edge equilibration regimes can be accessed in the same device. If there is a quantum point contact in the droplet, then quasiparticle properties, including braiding statistics, can be observed. Their effects are manifested as modulations of the microwave absorption spectrum that are, notably, first-order in the tunneling amplitude at the point contact.

The electronic structure of Ce${}_{1-x}$Yb${}_x$CoIn${}_5$ has been studied by a combination of photoemission, x-ray absorption, and bulk property measurements. Previous findings of a Ce valence near 3$+$ for all $x$ and of an Yb valence near 2.3$+$ for $x⩾0.3$ were confirmed. One new result of this study is that the Yb valence for $x⩽0.2$ increases rapidly with decreasing $x$ from 2.3 toward 3+, which correlates well with de Haas van Alphen results showing a change of Fermi surface around $x=0.2$. Another new result is the direct observation by angle resolved photoemission Fermi surface maps of $\approx$50$\%$ cross-sectional area reductions of the $\alpha$ and $\beta$ sheets for $x=1$ compared to $x=0$, and a smaller, essentially proportionate, size change of the $\alpha$ sheet for $x=0.2$. These changes are found to be in good general agreement with expectations from simple electron counting. The implications of these results for the unusual robustness of superconductivity and Kondo coherence with increasing $x$ in this alloy system are discussed.

Classifying phases of local quantum systems is a general problem that includes special cases such as free fermions, commuting projectors, and others. An important distinction in this classification should be made between classifying periodic and aperiodic systems. A related distinction is that between homotopy invariants (invariants which remain constant so long as certain general properties such as locality, gap, and others hold) and locally computable invariants (properties of the system that can not change from one region to another without producing a gapless edge between them). We attack this problem using a technique inspired by Kirby's “torus trick” in topology. We use this trick to reproduce results for free fermions (in particular, using the trick to reduce the aperiodic classification to the simpler problem of periodic classification). We also show that a similar trick works for interacting phases which are nontrivial but lack anyons; these results include symmetry-protected phases. A key part of this work is an attempt to classify quantum cellular automata.

We discuss the general formalism and validity of weak-coupling perturbation theory as an impurity solver for nonequilibrium dynamical mean-field theory. The method is implemented and tested in the Hubbard model, using expansions up to fourth order for the paramagnetic phase at half filling and third order for the antiferromagnetic and paramagnetic phase away from half filling. We explore various types of weak-coupling expansions and examine the accuracy and applicability of the methods for equilibrium and nonequilibrium problems. We find that in most cases an expansion of local self-energy diagrams including all the tadpole diagrams with respect to the Weiss Green's function (bare-diagram expansion) gives more accurate results than other schemes such as self-consistent perturbation theory using the fully interacting Green's function (bold-diagram expansion). In the paramagnetic phase at half filling, the fourth-order bare expansion improves the result of the second-order expansion in the weak-coupling regime, while both expansions suddenly fail at some intermediate interaction strength. The higher-order bare perturbation is especially advantageous in the antiferromagnetic phase near half filling. We use the third-order bare perturbation expansion within the nonequilibrium dynamical mean-field theory to study dynamical symmetry breaking from the paramagnetic to the antiferromagnetic phase induced by an interaction ramp in the Hubbard model. The results show that the order parameter, after an initial exponential growth, exhibits an amplitude oscillation around a nonthermal value followed by a slow drift toward the thermal value. The transient dynamics seems to be governed by a nonthermal critical point, associated with a nonthermal universality class, which is distinct from the conventional Ginzburg-Landau theory.

We develop a theoretical description of the spin dynamics of resident holes in a $p$-doped semiconductor quantum well (QW) subject to a magnetic field slightly tilted from the Voigt geometry. We find the expressions for the signals measured in time-resolved Faraday rotation (TRFR) and resonant spin amplification (RSA) experiments and study their behavior for a range of system parameters. We find that an inversion of the RSA peaks can occur for long hole spin dephasing times and tilted magnetic fields. We verify the validity of our theoretical findings by performing a series of TRFR and RSA experiments on a $p$-modulation doped GaAs/Al${}_{0.3}$Ga${}_{0.7}$As single QW and showing that our model can reproduce experimentally observed signals.