The two-dimensional electron gas at the crystalline ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ ($c$-LAO/STO) interface has sparked large interest due to its exotic properties, including an intriguing gate-tunable superconducting phase. While there is growing evidence of pronounced spatial inhomogeneity in the conductivity at STO-based interfaces, the consequences for superconductivity remain largely unknown. We study interfaces based on amorphous LAO top layers grown at room temperature ($a$-LAO/STO) and demonstrate a superconducting phase similar to $c$-LAO/STO, however, with a gate-tunable critical temperature of $460\mathrm{mK}$. The dependence of the superconducting critical current on temperature, magnetic field, and back-gate-controlled doping is found to be consistently described by a model of a random array of Josephson-coupled superconducting domains.

The Onsager rule determines the relationship between Fermi surface area and frequencies of quantum oscillations in magnetic fields. We show that this rule remains intact to an excellent approximation in the mixed-vortex state of the underdoped cuprates even though the Landau level index $n$ may be fairly low, $n\sim 10$. The models we consider are fairly general, consisting of a variety of density wave states combined with $d$-wave superconductivity within a mean field theory. Vortices are introduced as quenched disorder and averaged over many realizations, which can be considered as snapshots of a vortex liquid state. We also show that the oscillations ride on top of a field independent density of states $\rho \left(B\right)$ for higher fields. This feature appears to be consistent with recent specific heat measurements [C. Marcenat et al., Nature Communications 6, 7927 (2015)]. The experimental data do not go to low fields at the lowest temperature 3 K. Thus, we cannot compare the density of state for the entire field range. Of course, the high temperature data are linear in the field at lower fields, as they should be, but our theory is only valid at very low temperatures, ideally at zero temperature. At lower fields and zero temperature we model the system as an ordered vortex lattice, and show that its density of states follows a dependence $\rho \left(B\right)\propto \sqrt{B}$ in agreement with the semiclassical results [JETP Lett 58, 469 (1993)].

Unconventional phases often occur where two competing mechanisms compensate. An excellent example is the ionic Hubbard model where the alternating local potential $\delta$, favoring a band insulator (BI), competes with the local repulsion $U$, favoring a Mott insulator (MI). By continuous unitary transformations we derive effective models in which we study the softening of various excitons. The softening signals the instability towards new phases that we describe on the mean-field level. On increasing $U$ from the BI in two dimensions, we find a bond-ordered phase breaking orientational symmetry due to a $d$-wave component. Then, antiferromagnetic order appears coexisting with the $d$-wave bond order. Finally, the $d$-wave order vanishes and a Néel-type MI persists.

We study the influence of reflective boundaries on time-dependent responses of one-dimensional quantum fluids at zero temperature beyond the low-energy approximation. Our analysis is based on an extension of effective mobile impurity models for nonlinear Luttinger liquids to the case of open boundary conditions. For integrable models, we show that boundary autocorrelations oscillate as a function of time with the same frequency as the corresponding bulk autocorrelations. This frequency can be identified as the band edge of elementary excitations. The amplitude of the oscillations decays as a power law with distinct exponents at the boundary and in the bulk, but boundary and bulk exponents are determined by the same coupling constant in the mobile impurity model. For nonintegrable models, we argue that the power-law decay of the oscillations is generic for autocorrelations in the bulk, but turns into an exponential decay at the boundary. Moreover, there is in general a nonuniversal shift of the boundary frequency in comparison with the band edge of bulk excitations. The predictions of our effective field theory are compared with numerical results obtained by time-dependent density matrix renormalization group (tDMRG) for both integrable and nonintegrable critical spin-$S$ chains with $S=1/2$, 1, and $3/2$.

The energy gap of a molecular crystal is one of the most important properties since it determines the crystal charge transport when the material is utilized in electronic devices. This is, however, a quantity difficult to calculate and standard theoretical approaches based on density functional theory (DFT) have proven unable to provide accurate estimates. In fact, besides the well-known band-gap problem, DFT completely fails in capturing the fundamental gap reduction occurring when molecules are packed in a crystal structures. The failure has to be associated with the inability of describing the electronic polarization and the real space localization of the charged states. Here we describe a scheme based on constrained DFT, which can improve upon the shortcomings of standard DFT. The method is applied to the benzene crystal, where we show that accurate results can be achieved for both the band gap and also the energy level alignment.

We investigate the full-counting statistics (FCS) of energy flow carried by electrons in the transient regime. Based on a two-measurement scheme, we formulate a nonequilibrium Keldysh Green's function theory to compute the generating function for FCS of energy transport. Specifically, we express the generating function using the path integral along the Keldysh contour and obtain an exact solution of the generating function using the Grassmann algebra. With this formalism, we calculate the transient energy current and higher-order cumulants for both single- and double-quantum-dot (QD) systems in the transient regime. To examine the finite bandwidth effect of leads to the FCS of energy transport, we have used an exact solvable model with a Lorentizian linewidth where all nonequilibrium Green's functions can be solved exactly in the time domain. It is found that the transient energy current exhibits damped oscillatory behavior. For the single quantum dot system the frequency of oscillation is independent of bandwidth of the leads while the decay rate of the oscillation amplitude is determined by the lifetime of resonant state which increases as the bandwidth decreases. At short times, a universal scaling of maximum amplitude of normalized cumulants is identified for the single-QD system. For the double-QD system, the damped oscillation of energy current is dominated by Rabi oscillation with frequency approximately proportional to the coupling constant between two quantum dots. In general, the transient energy current increases when the coupling between two QDs is stronger. However, when the interdot coupling is larger than half of the external bias the transient energy current is suppressed significantly. All these results can be understood analytically.

We show that curvature-induced inhomogeneous strain distributions in nanoscale buckled semiconducting ribbons lead to the existence of end states which are topologically protected by inversion symmetry. These end-state doublets, corresponding to the so-called Maue-Shockley states, are robust against weak disorder. By identifying and calculating the corresponding topological invariants, we further show that a buckled semiconducting ribbon undergoes topological phase transitions between trivial and nontrivial insulating phases by varying its real-space geometry.

We investigate the structural and electronic properties of Li-intercalated monolayer graphene on SiC(0001) using combined angle-resolved photoemission spectroscopy and first-principles density functional theory. Li intercalates at room temperature both at the interface between the buffer layer and SiC and between the two carbon layers. The graphene is strongly $n$-doped due to charge transfer from the Li atoms and two $\pi$ bands are visible at the $\overline{K}$ point. After heating the sample to $300{}^{\circ }\mathrm{C}$, these $\pi$ bands become sharp and have a distinctly different dispersion to that of Bernal-stacked bilayer graphene. We suggest that the Li atoms intercalate between the two carbon layers with an ordered structure, similar to that of bulk ${\mathrm{LiC}}_6$. An AA stacking of these two layers becomes energetically favourable. The $\pi$ bands around the $\overline{K}$ point closely resemble the calculated band structure of a ${\mathrm{C}}_6{\mathrm{LiC}}_6$ system, where the intercalated Li atoms impose a superpotential on the graphene electronic structure that opens gaps at the Dirac points of the two $\pi$ cones.

We study the proximity effect between an $s$-wave superconductor (SC) and the surface states of a Weyl semimetal. An interesting two-dimensional SC forms in such an interface with properties resembling in certain aspects the Fu-Kane superconductor with some notable differences. In a Weyl semimetal with unbroken time-reversal symmetry the interface SC supports completely flat Majorana bands in a linear Josephson junction with a $\pi$ phase difference. We discuss the stability of these bands against disorder and propose ways in which they can be observed experimentally.

Using a set of first-principles calculations, we studied the electronic structures of two-dimensional transition metal carbides and nitrides, so called MXenes, functionalized with F, O, and OH. Our projected band structures and electron localization function analyses reveal the existence of nearly free electron (NFE) states in a variety of MXenes. The NFE states are spatially located just outside the atomic structure of MXenes and are extended parallel to the surfaces. Moreover, we found that the OH-terminated MXenes offer the NFE states energetically close to the Fermi level. In particular, the NFE states in some of the OH-terminated MXenes, such as $\mathrm{T}{\mathrm{i}}_2\mathrm{C}{\left(\mathrm{OH}\right)}_2,\mathrm{Z}{\mathrm{r}}_2\mathrm{C}{\left(\mathrm{OH}\right)}_2,\mathrm{Z}{\mathrm{r}}_2\mathrm{N}{\left(\mathrm{OH}\right)}_2,\mathrm{H}{\mathrm{f}}_2\mathrm{C}{\left(\mathrm{OH}\right)}_2,\mathrm{H}{\mathrm{f}}_2\mathrm{N}{\left(\mathrm{OH}\right)}_2,\mathrm{N}{\mathrm{b}}_2\mathrm{C}{\left(\mathrm{OH}\right)}_2$, and $\mathrm{T}{\mathrm{a}}_2\mathrm{C}{\left(\mathrm{OH}\right)}_2$, are partially occupied. This is in remarkable contrast to graphene, graphane, and $\mathrm{Mo}{\mathrm{S}}_2$, in which their NFE states are located far above the Fermi level and thus they are unoccupied. As a prototype of such systems, we investigated the electron transport properties of $\mathrm{H}{\mathrm{f}}_2\mathrm{C}{\left(\mathrm{OH}\right)}_2$ and found that the NFE states in $\mathrm{H}{\mathrm{f}}_2\mathrm{C}{\left(\mathrm{OH}\right)}_2$ provide almost perfect transmission channels without nuclear scattering for electron transport. Our results indicate that these systems might find applications in nanoelectronic devices. Our findings provide new insights into the unique electronic band structures of MXenes.

Informative recent measurements on the heavy-fermion metal $\beta \text{−}{\mathrm{YbAlB}}_4$ performed with applied magnetic field and pressure as control parameters are analyzed with the goal of establishing a sound theoretical explanation for the inferred scaling laws and non-Fermi-liquid (NFL) behavior, which demonstrate some unexpected features. Most notably, the robustness of the NFL behavior of the thermodynamic properties and of the anomalous $T^{3/2}$ temperature dependence of the electrical resistivity under applied pressure $P$ in zero magnetic field is at variance with the fragility of the NFL phase under application of a field $B$. We show that a consistent topological basis for this combination of observations, as well as the empirical scaling laws, may be found within fermion-condensation theory in the emergence and destruction of a flat band, and explains that the paramagnetic NFL phase takes place without magnetic criticality, not from quantum critical fluctuations. Schematic $T-B$ and $T-P$ phase diagrams are presented to illuminate this scenario.

In this paper we suggest a simple analytical method for description of electromagnetic properties of a geometrically regular two-dimensional subwavelength arrays (metasurfaces) formed by particles with randomly fluctuating polarizabilities. We propose an analytical homogenization method applicable for normal wave incidence on particle arrays with dominating electric dipole responses and validate it with numerical point-dipole modeling using the supercell approach. We demonstrate that fluctuations of particle polarizabilities lead to increased diffuse scattering despite the subwavelength lattice constant of the array.

Based on a local mean-field theory approach at Anderson localization, we find a distribution function of critical temperature from that of disorder. An essential point of this local mean-field theory approach is that the information of the wave-function multifractality is introduced. The distribution function of the Kondo temperature $\left(T_K\right)$ shows a power-law tail in the limit of $T_K\to 0$ regardless of the Kondo coupling constant. We also find that the distribution function of the ferromagnetic transition temperature $\left(T_c\right)$ gives a power-law behavior in the limit of $T_c\to 0$ when an interaction parameter for ferromagnetic instability lies below a critical value. However, the $T_c$ distribution function stops the power-law increasing behavior in the $T_c\to 0$ limit and vanishes beyond the critical interaction parameter inside the ferromagnetic phase. These results imply that the typical Kondo temperature given by a geometric average always vanishes due to finite density of the distribution function in the $T_K\to 0$ limit while the typical ferromagnetic transition temperature shows a phase transition at the critical interaction parameter. We propose that the typical transition temperature serves a criterion for quantum Griffiths phenomena vs smeared transitions: Quantum Griffiths phenomena occur above the typical value of the critical temperature while smeared phase transitions result at low temperatures below the typical transition temperature. We speculate that the ferromagnetic transition at Anderson localization shows the evolution from quantum Griffiths phenomena to smeared transitions around the critical interaction parameter at low temperatures.

We have investigated the magnetoresistance (MR) and Hall resistivity properties of a FeAs single crystal which exhibits magnetic order below $T_N$ = 69 K. We observe nonlinear Hall resistivity and linear MR in the presence of magnetic-order-connected Fermi surface reconstruction. The analysis of the magnetotransport data using a two-carrier model suggests the emergence of an additional minor hole Fermi surface which coexists with major electron carriers below $T_N$. The origin of the linear MR, however, remains inconsistent with current explanations based on the electronic band structure, i.e., the quantum linear MR model from linearly dispersive Dirac cones and linear MR as a result from strong velocity changes of the cyclotron motion near nested Fermi surfaces. While a macroscopic inhomogeneity in a mobility distribution may cause the linear MR as widely observed in other semimetals with high mobilities, the spiral magnetic order of FeAs seems to ask for an alternative description which takes the specific magnetic order and details of the electronic structure of FeAs as well as a possible entanglement between them into account.

The current through a helical edge state of a quantum spin Hall insulator may be fully transmitted through a magnetically gapped region due to a combination of spin-transfer torque and spin pumping [Meng et al., Phys. Rev. B 90, 205403 (2014)]. Using a scattering approach, we here argue that in such a system the current is effectively carried by electrons with energies below the magnet-induced gap and well below the Fermi energy. This has striking consequences, such as the absence of shot noise, an exponential suppression of thermal noise, and an obstruction of thermal transport. For two helical edges covered by the same quantum magnet, the device can act as a robust noiseless current splitter.

Anion substitution with bismuth (Bi) in III-V semiconductors is an effective method for experimental engineering of the band gap $E_g$ at low Bi concentrations $\left(\le 2\%\right)$, in particular in gallium arsenide (GaAs). The inverse Bi-concentration dependence of $E_g$ has been found to be linear at low concentrations $x$ and dominated by a valence band defect level anticrossing between As and Bi occupied $p$ levels. Predictive models for the valence band hybridization require a first-principle understanding which can be obtained by density functional theory with the main challenges being the proper description of $E_g$ and the spin-orbit coupling. By using an efficient method to include these effects, it is shown here that at high concentrations $E_g$ is modified mainly by a Bi-Bi $p$ orbital interaction and by the large Bi atom-induced strain. In particular, we find that at high concentrations, the Bi-Bi interactions depend strongly on model periodic cluster configurations, which are not captured by tight-binding models. Averaging over various configurations supports the defect level broadening picture. This points to the role of different atomic configurations obtained by varying the experimental growth conditions in engineering arsenide band gaps, in particular for telecommunication laser technology.

We extend the nested sampling algorithm to simulate materials under periodic boundary and constant pressure conditions, and show how it can be used to determine the complete equilibrium phase diagram for a given potential energy function, efficiently and in a highly automated fashion. The only inputs required are the composition and the desired pressure and temperature ranges, in particular, solid-solid phase transitions are recovered without any a priori knowledge about the structure of solid phases. We benchmark and showcase the algorithm on the periodic Lennard-Jones system, aluminum, and NiTi.

We have investigated the focusing of the lowest-order antisymmetric Lamb mode ($A_0$) behind a positive gradient-index (GRIN) acoustic metalens consisting of air holes drilled in a silicon plate with silicon pillars erected on one face of the lens. We have analyzed the focusing in the near field as the result of the coupling between the flexural resonant mode of the pillars and the vibration mode of the air/silicon phononic crystal. We highlight the role played by the polarization coherence between the resonant mode and the vibration of the plate. We demonstrate both numerically and experimentally the focusing behind the lens over a spot less than half a wavelength, paving a way for performance of acoustic lenses beyond the diffraction limit. Our findings can be easily extended to other types of elastic wave.

Although it has been known for decades that magnetocrystalline anisotropy is linked to spin-orbit coupling (SOC), the mechanism of how it arises for specific systems is still a subject of debate. We focused on finding markers of SOC in the density of states (DOS) and on using them to understand the source of magnetocrystalline anisotropy for the case of adatoms and monolayers. Fully relativistic ab initio Korringa-Kohn-Rostoker Green's-function calculations were performed for Fe, Co, and Ni adatoms and monolayers on Au(111) to investigate changes in the orbital-resolved DOS due to a rotation of magnetization. In this way, one can see that a significant contribution to magnetocrystalline anisotropy for adatoms comes from pushing the SOC-split states above or below the Fermi level. As a result of this, the magnetocrystalline anisotropy energy depends crucially on the position of the energy bands of the adatom with respect to the Fermi level of the substrate. This view is supported by model crystal-field Hamiltonian calculations.

We propose to realize an exotic Haldane superfluid (HSF) phase in an extended Bose-Hubbard model on the two-leg ladder (i.e., a two-species mixture of interacting bosons). The proposal is confirmed by means of large-scale quantum Monte Carlo simulations, with a significant part of the ground-state phase diagram being revealed. Most remarkably, the newly discovered HSF phase features both superfluidity and nonlocal topological Haldane order. The effects induced by varying the number of legs are furthermore explored. Our results shed light on how topological superfluid emerges in bosonic systems.