A given fractional quantum Hall state may admit multiple, distinct edge phases on its boundary. We explore the implications that multiple edge phases have for the entanglement spectrum and entropy of a given bulk state. We describe the precise manner in which the entanglement spectrum depends upon local (tunneling) interactions along an entanglement cut and throughout the bulk. The sensitivity to local conditions near the entanglement cut appears not only in gross features of the spectrum, but can also manifest itself in an additive, positive constant correction to the topological entanglement entropy, i.e., it increases its magnitude. A natural interpretation for this result is that the tunneling interactions across an entanglement cut can function as a barrier to certain types of quasiparticle transport across the cut, thereby, lowering the total entanglement between the two regions.

We study the transport properties of a charge qubit coupling two chiral Luttinger liquids, realized by two antidots placed between the edges of an integer $\nu =1$ or fractional $\nu =1/3$ quantum Hall bar. We show that in the limit of a large capacitive coupling between the antidots, their quasiparticle occupancy behaves as a pseudospin corresponding to an orbital Kondo impurity coupled to a chiral Luttinger liquid, while the interantidot tunneling acts as an impurity magnetic field. The latter tends to destabilize the Kondo fixed point for the $\nu =1/3$ fractional Hall state, producing an effective interedge tunneling. We relate the interedge conductance to the susceptibility of the Kondo impurity and calculate it analytically in various limits for both $\nu =1$ and $\nu =1/3$.

Formation of localized impurity levels within the band gap in bigraphene under applied electric field and the conditions for their collectivization at finite impurity concentrations are considered. It is shown that a qualitative restructuring of the quasiparticle spectrum within the initial band gap and subsequent metal-insulator phase transitions are possible for such disordered systems, being effectively controlled by variation of the electric field bias. Since these effects can be expected at low enough impurity concentrations and accessible applied voltages, they can be promising for practical applications in nanoelectronics devices.

We study the electronic properties of twisted bilayer graphene in the tight-binding approximation. The interlayer hopping amplitude is modeled by a function which depends not only on the distance between two carbon atoms, but also on the positions of neighboring atoms as well. Using the Lanczos algorithm for the numerical evaluation of eigenvalues of large sparse matrices, we calculate the bilayer single-electron spectrum for commensurate twist angles in the range $1^{\circ }\lesssim \theta \lesssim {30}^{\circ }$. We show that at certain angles $\theta$ greater than ${\theta }_c\approx 1.{89}^{\circ }$ the electronic spectrum acquires a finite gap, whose value could be as large as 80 meV. However, in an infinitely large and perfectly clean sample the gap as a function of $\theta$ behaves nonmonotonously, demonstrating exponentially large jumps for very small variations of $\theta$. This sensitivity to the angle makes it impossible to predict the gap value for a given sample, since in experiment $\theta$ is always known with certain error. To establish the connection with experiments, we demonstrate that for a system of finite size $\tilde{L}$ the gap becomes a smooth function of the twist angle. If the sample is infinite, but disorder is present, we expect that the electron mean-free path plays the same role as $\tilde{L}$. In the regime of small angles $\theta <{\theta }_c$, the system is a metal with a well-defined Fermi surface which is reduced to Fermi points for some values of $\theta$. The density of states in the metallic phase varies smoothly with $\theta$.

We study alkali-metal adsorption on supported graphene by means of density-functional-theory calculations that include dispersion corrections. Graphene supported by the Au/Ni(111) surface is an important system for fundamental studies because this surface allows one to support graphene, preserving the electronic properties of freestanding graphene. We investigate the binding energetics as well as the structural and electronic properties of Li, Na, K, and Rb atoms adsorbed or intercalated at the graphene/Au/Ni(111) interfaces and compare the results to those obtained on freestanding graphene. Both the adsorption and intercalation of the alkali atoms induce electron doping to the graphene $\pi$ bands that display a quasirigid-energy shift. Electron doping by alkali atoms preserves the Dirac cone of graphene, which shifts downwards due to the negative polarity of the doping. The metallic or ionic character of the alkali dopant is controlled by its position relative to graphene. All of the investigated alkali atoms display an energetic preference to intercalate between graphene and the Au/Ni support. These results shed light on the relationship between graphene electron doping, the alkali-atom adsorption site, and the charge transfers at the graphene/support interface.

The threshold displacement energy $E_d$ has been determined for graphene and 216 different ($n, m$) single-walled carbon nanotube chiralities, with $5\le n\le 20$ and $0\le m\le n$, under several model conditions using classical molecular dynamics. The model conditions vary by particle (electron or carbon ion), empirical potential (two parametrizations of Tersoff [J. Tersoff, Phys. Rev. B 39, 5566 (1989); L. Lindsay and D. A. Broido, Phys. Rev. B 81, 205441 (2010)] and one of Brenner et al. [D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni, and S. B. Sinnott, J. Phys.: Condens. Matter 14, 783 (2002)]), and momentum transfer direction (towards or away from the nanotube axis). For electron irradiation simulations, $E_d$ exhibits a smoothly varying chirality dependence and a characteristic curvature influenced by the momentum transfer direction. Changing the empirical potential shifts the magnitude of $E_d$, but the trend is preserved for electron simulations. However, the perturbation in the knock-on dynamics introduced by the carbon ion leads to $E_d$ trends that diverge from the equivalent electron simulation. Thus, the ion interaction has a non-negligible effect on the dynamics of the collision and leads to $E_d$ values that can distinctly vary depending on the selected carbon nanostructure.

The one-dimensional $p$-wave topological superconductor model with open-boundary conditions is examined in its topological phase. Using the eigenbasis of the noninteracting system I show that, provided the interactions are local and do not result in a closing of the gap, then even and odd parity sectors are unitarily equivalent. Following on from this, it is possible to define two many-body operators that connect each state in one sector with a degenerate counterpart in the sector with opposite parity. This result applies to all states in the system and therefore establishes, for a long enough wire, that all even-odd eigenpairs remain essentially degenerate in the presence of local interactions. Building on this observation I then set out a full definition of the related many-body Majorana operators and point out that their structure cannot be fully revealed using cross-correlation data obtained from the ground-state manifold alone. Although all results are formulated in the context of the one-dimensional $p$-wave model, I argue why they should also apply to more realistic realizations (e.g., the multichannel $p$-wave wire and proximity coupled models) of topological superconductivity.

We introduce a mean-field and a perturbative approach, based on clusters, to describe the ground state of fermionic strongly correlated systems. In the cluster mean-field approach, the ground-state wave function is written as a simple tensor product over optimized cluster states. The optimization of the single-particle basis where the cluster mean field is expressed is crucial in order to obtain high-quality results. The mean-field nature of the Ansatz allows us to formulate a perturbative approach to account for intercluster correlations; other traditional many-body strategies can be easily devised in terms of the cluster states. We present benchmark calculations on the half-filled 1D and (square) 2D Hubbard model, as well as the lightly doped regime in 2D, using cluster mean-field and second-order perturbation theory. Our results indicate that, with sufficiently large clusters or to second-order in perturbation theory, a cluster-based approach can provide an accurate description of the Hubbard model in the considered regimes. Several avenues to improve upon the results presented in this work are discussed.

We introduce an approach to derive realistic Coulomb interaction terms in freestanding layered materials and vertical heterostructures from ab initio modeling of the corresponding bulk materials. To this end, we establish a combination of calculations within the framework of the constrained random-phase approximation, Wannier function representation of Coulomb matrix elements within some low-energy Hilbert space, and continuum medium electrostatics, which we call Wannier function continuum electrostatics (WFCE). For monolayer and bilayer graphene we reproduce full ab initio calculations of the Coulomb matrix elements within an accuracy of $0.3$ eV or better. We show that realistic Coulomb interactions in bilayer graphene can be manipulated on the eV scale by different dielectric and metallic environments. A comparison to electronic phase diagrams derived in M. M. Scherer et al. [Phys. Rev. B 85, 235408 (2012)] suggests that the electronic ground state of bilayer graphene is a layered antiferromagnet and remains surprisingly unaffected by these strong changes in the Coulomb interaction.

${\mathrm{SmB}}_6$ has been predicted to be a Kondo topological insulator with topologically protected conducting surface states. We have studied quantitatively the electrical transport through surface states in high-quality single crystals of ${\mathrm{SmB}}_6$. We observe a large nonlocal surface signal at temperatures lower than the bulk Kondo gap scale. Measurements and finite-element simulations allow us to distinguish unambiguously between the contributions from different transport channels. In contrast to general expectations, the electrical transport properties of the surface channels were found to be insensitive to high magnetic fields. We propose possible scenarios that might explain this unexpected finding. Local and nonlocal magnetoresistance measurements allowed us to identify possible signatures of helical spin states and strong interband scattering at the surface.

The dynamical mean-field theory (DMFT) combined with the fluctuation exchange (FLEX) method, namely, FLEX+DMFT, is an approach for correlated electron systems to incorporate both local and nonlocal long-range correlations in a self-consistent manner. We formulate FLEX+DMFT in a systematic way starting from a Luttinger-Ward functional, and apply it to study the $d$-wave superconductivity in the two-dimensional repulsive Hubbard model. The critical temperature $\left(T_c\right)$ curve obtained in the FLEX+DMFT exhibits a dome structure as a function of the filling, which has not been clearly observed in the FLEX approach alone. We trace back the origin of the dome to the local vertex correction from DMFT that renders a filling dependence in the FLEX self-energy. We compare the results with those of GW+DMFT, where the $T_c$-dome structure is qualitatively reproduced due to the same vertex correction effect, but a crucial difference from FLEX+DMFT is that $T_c$ is always estimated below the Néel temperature in GW+DMFT. The single-particle spectral function obtained with FLEX+DMFT exhibits a double-peak structure as a precursor of the Hubbard bands at temperatures above $T_c$.

Topological semimetals are gapless states of matter which have robust and unique electromagnetic responses and surface states. In this paper, we consider semimetals which have pointlike Fermi surfaces in various spatial dimensions $D=1,2,3$ which naturally occur in the transition between a weak topological insulator and a trivial insulating phase. These semimetals include those of Dirac and Weyl types. We construct these phases by layering strong topological insulator phases in one dimension lower. This perspective helps us understand their effective response field theory that is generally characterized by a 1-form $b$ which represents a source of Lorentz violation and can be read off from the location of the nodes in momentum space and the helicities/chiralities of the nodes. We derive effective response actions for the two-dimensional (2D) and 3D Dirac semimetals and extensively discuss the response of the Weyl semimetal. We also show how our work can be used to describe semimetals with Fermi surfaces with lower codimension as well as to describe the topological response of 3D topological crystalline insulators.

Tantalum and tungsten, direct neighbors in the periodic table, exhibit a very similar electronic structure. Compared with tungsten, however, the bands of tantalum are less occupied due to the lack of one electron. As a consequence, an exceptional Dirac-cone-like surface state, observed below the Fermi level for W(110), may appear above the Fermi level for Ta(110). To prove this conjecture, we investigate the unoccupied surface electronic structure of Ta(110) by spin- and angle-resolved inverse photoemission and electronic-structure calculations. Surprisingly, our results do not show the expected Dirac-cone-like surface state. Instead, spin-polarized unoccupied surface bands are identified, which have no equivalent in W(110). These findings are explained by the difference in the energetic positions of the surface states relative to the bulk states for Ta(110) and W(110) caused by the different lattice constants.

In this paper, we demonstrate that a wire medium (WM) slab loaded with graphene sheets enables the enhancement of the near field for subwavelength imaging at terahertz frequencies. The analysis is based on the nonlocal homogenization model for WM with the additional boundary condition at the connection of wires to graphene. The principle of the operation of the proposed lens depends on the enhancement of evanescent waves, wherein the excited surface plasmons at the lower and upper graphene interfaces are coupled by an array of metallic wires. The resolution and the operating frequency of the subwavelength imaging device are mainly determined by the tunability of graphene and the structural parameters of the WM slab. The proposed structure has a resolution better than $\lambda /10$ with the advantages of broad bandwidth, low sensitivity to losses, and tunability with respect to the chemical potential even if the distance between two graphene sheets is a significant fraction of wavelength. Severe challenges in the fabrication of the lens have been studied in-depth, and a promising approach for a practical realization has been proposed.

We study how the universal properties of quantum quenches across critical points are modified by a weak coupling to a thermal bath, focusing on the paradigmatic case of the transverse field Ising model. Beyond the standard quench-induced Kibble-Zurek defect production in the absence of the bath, the bath contributes extra thermal defects. We show that spatial correlations in the noise produced by the bath can play a crucial role: one obtains quantitatively different scaling regimes depending on whether the correlation length of the noise is smaller or larger than the Kibble-Zurek length associated with the quench speed, and the thermal length set by the temperature. For the case of spatially correlated bath noise, additional thermal defect generation is restricted to a window that is both quantum critical and excluded from the nonequilibrium regime surrounding the critical point. We map the dissipative quench problem to a set of effectively independent dissipative Landau-Zener problems. Using this mapping along with both analytic and numerical calculations allows us to find the scaling of the excess defect density produced in the quench, and it suggests a generic picture for such dissipative quenches.

We present a local probe study of the magnetic superconductor ${\mathrm{ErNi}}_2{\mathrm{B}}_2\mathrm{C}$, using magnetic force microscopy at sub-Kelvin temperatures. ${\mathrm{ErNi}}_2{\mathrm{B}}_2\mathrm{C}$ is an ideal system to explore the effects of concomitant superconductivity and ferromagnetism. At 500 mK, far below the transition to a weakly ferromagnetic state, we directly observe a structured magnetic background on the micrometer scale. We determine spatially resolved absolute values of the magnetic penetration depth $\lambda$ and study its temperature dependence as the system undergoes magnetic phase transitions from paramagnetic to antiferromagnetic, and to weak ferromagnetic, all within the superconducting regime. In addition, we estimate the absolute pinning force of Abrikosov vortices, which shows a position dependence and temperature dependence as well, and discuss the possibility of the purported spontaneous vortex formation.

We investigate the impact of impurity scattering on superconductivity in an anisotropic multiorbital model with spin-orbit coupling, which describes the electron fluid at two-dimensional oxide interfaces. As the pairing mechanism is under debate, both conventional and unconventional superconducting states are analyzed. We consider magnetic and nonmagnetic spin-dependent intra- and interorbital scattering and discuss possible microscopic realizations leading to these processes. It is found that, for magnetic disorder, the unconventional superconductor is protected against interband scattering and, thus, it is more robust than the conventional condensate. In case of nonmagnetic impurities, the conventional superconductor is protected as expected from the Anderson theorem and the critical scattering rate of the unconventional state is enhanced by a factor of four due to the spin-orbit coupling and anisotropic masses in oxide interfaces.

We experimentally study the superconducting proximity effect in high-temperature superconductor/half-metallic ferromagnet $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_7/\mathrm{L}{\mathrm{a}}_{2/3}\mathrm{C}{\mathrm{a}}_{1/3}\mathrm{Mn}{\mathrm{O}}_3$ junctions, using conductance measurements. In particular, we investigate the magnetic-field dependence of the spectroscopic signatures that evidence the long-range penetration of superconducting correlations into the half-metal. Those signatures are insensitive to the applied field when this is below the ferromagnet's saturation fields, which demonstrates that they are uncorrelated with its macroscopic magnetization. However, the application of more intense fields progressively washes away the fingerprint of long-range proximity effects. This is consistent with the fact that the well-known magnetic inhomogeneities at the $c$-axis $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_7/\mathrm{L}{\mathrm{a}}_{2/3}\mathrm{C}{\mathrm{a}}_{1/3}\mathrm{Mn}{\mathrm{O}}_3$ interface play a role in the proximity behavior.

Recent experiments show that the Nernst-Ettingshausen effect is orders of magnitude stronger than the thermoelectric Seebeck effect in superconductors above the critical temperature. We explain different magnitudes of the two effects accounting for the magnetization current of virtual Cooper pairs. The method allows for detailed understanding of the surprising nonmonotonic dependence of the Nernst-Ettingshausen coefficient on the magnetic field.

Circuit quantum electrodynamics systems are typically built from resonators and two-level artificial atoms, but the use of multilevel artificial atoms instead can enable promising applications in quantum technology. Here we present an implementation of a Josephson junction circuit dedicated to operate as a V-shape artificial atom. Based on a concept of two internal degrees of freedom, the device consists of two transmon qubits coupled by an inductance. The Josephson nonlinearity introduces a strong diagonal coupling between the two degrees of freedom that finds applications in quantum nondemolition readout schemes, and in the realization of microwave cross-Kerr media based on superconducting circuits.