Majorana bound states in topological superconductors have been predicted to appear in the form of zero-bias conductance peaks of height $2e^2/h$, which represents one of the most studied signatures so far. Here, we show that quasi-zero-energy states, similar to Majorana bound states, can naturally form in any superconducting hybrid junction due to confinement effects, in the absence of spin fields and, thus, without relation to topology. Remarkably, these topologically trivial quasi-zero-energy states produce zero-bias conductance peaks, that could be similar to Majorana signatures, but develop a different peak height ($4e^2/h$) and are less stable under gating or depletion of the confined region. Our results put forward confinement as an alternative mechanism to explain the ubiquitous presence of trivial zero-bias peaks and quasi-zero-energy states in superconductor hybrids.

We present a constrained density-functional perturbation theory scheme for the calculation of structural and harmonic vibrational properties of insulators in the presence of an excited and thermalized electron-hole plasma. The method is ideal to tame ultrafast light-induced structural transitions in the regime where the photocarriers thermalize faster than the lattice, the electron-hole recombination time is longer than the phonon period, and the photocarrier concentration is large enough to be approximated by an electron-hole plasma. The complete derivation presented here includes total energy, forces and stress tensor, variable cell structural optimization, harmonic vibrational properties, and the electron-phonon interaction. We discuss in detail the case of zone-center optical phonons not conserving the number of electrons and inducing a Fermi shift in the photoelectron and hole distributions. We validate our implementation by comparing with finite differences in Te and ${\mathrm{VSe}}_2$. By calculating the evolution of the phonon spectrum of Te, Si, and GaAs as a function of the fluence of the incoming laser light, we demonstrate that even at low fluences, corresponding to approximately 0.05 photocarriers per atom, the phonon spectrum is substantially modified with respect to the ground-state one with new Kohn anomalies appearing and a substantial softening of zone-center optical phonons. Our implementation can be efficiently used to detect reversible transient phases and irreversible structural transitions induced by ultrafast light absorption.

The cubic neodymium-based compound ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20}$ exhibits a first-order antiferromagnetic (AFM) transition at $T_{\text{N}}=0.53$ K. Strong magnetic fluctuations at temperatures up to 5 K were suggested by the downward curvature of the electrical resistivity $\rho \left(T\right)$ and the reduced magnetic entropy $S_{\text{m}}$ of $0.5R\ln 2$ at $T_{\text{N}}$. In this study, we measured $\rho \left(T\right)$, the isothermal magnetization $M\left(B\right)$, magnetic susceptibility $\chi \left(T\right)$, and specific heat $C\left(T\right)$ of ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20-x}{\mathrm{Cd}}_x$ for $x=1$ and ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20-y}{\mathrm{Ga}}_y$ for $y=1$ and 2. The sharp peak of the magnetic specific heat $C_{\text{m}}\left(T\right)$ at $T_{\text{N}}$ for $x$ = 0 is changed to a weak and broad maximum at 0.55 K for $x$ = 1. This drastic change in $C_{\text{m}}\left(T\right)$ suggests that the isovalent Cd substitution for Zn disorders the exchange interactions between the Nd moments to hinder the first-order AFM transition. On the other hand, $C_{\text{m}}\left(T\right)$ for $y=1$ and 2 exhibits a lambda-shaped anomaly, which is a characteristic of a second-order AFM transition, at elevated temperatures of 0.78 and 1.5 K, respectively. The stabilization of the AFM order by the Ga substitution indicates that $4p$ electron doping strengthens the AFM interaction. We therefore propose that the first-order transition in ${\mathrm{NdCo}}_2{\mathrm{Zn}}_{20}$ is maintained by competitive magnetic interactions inherent in the Nd diamond sublattice.

Exact analytical formulas are derived, by means of Keldysh Green functions, for currents and current correlation functions in a Cooper pair splitter modeled on a double quantum dot system coherently coupled to a superconductor and two normal metallic electrodes. Confining to the subspace with the interdot singlet we show perfect entanglement of split electrons in two separated crossed Andreev reflection processes. The studies are focused on the noise power spectrum in a whole bias voltage range. In particular, in the large voltage limit shot noise dominates and its spectrum exhibits two extraordinary side dips related to resonant interlevel current correlations caused by coherent electron-hole recombination processes accompanied by emission and absorption of photons. In the linear response limit we derived the frequency-dependent admittance which shows different interference patterns for the cross and the auto current correlations.

Many of the intriguing properties of bilayer graphene (BLG) are related to interlayer electronic coupling. Since this coupling is sensitive to an applied electric field perpendicular to the layers, we develop a strategy for determining interlayer coupling by decomposing the total electric dipole polarizability, which measures the response of electrons to applied fields, into site-specific contributions and consequently the intralayer and interlayer components. The interlayer polarizability is evaluated from field-induced electron density variations computed with a first-principles approach for twisted BLG quantum dots (QDs). Changes in interlayer polarizability dominate the polarizability variation with twist angle. In addition to the well-recognized strong coupling in the Bernal stackings, enhanced coupling is revealed for the structures at small and size-dependent twist angles when AB stacking first appears in the outermost shell of the QD. The values of these magic angles depend on the QD size. This paper not only provides an approach for measuring interlayer coupling strength but also indicates the existence of strong interlayer coupling even at small twist angles, which could be important for understanding the properties of twisted BLG.

We study a non-Hermitian and nonunitary version of the two-dimensional Chalker-Coddington network model with balanced gain and loss. This model belongs to the class ${\mathrm{D}}^{†}$ with particle-hole ${\mathrm{symmetry}}^{†}$ and hosts both the non-Hermitian skin effect as well as exceptional points. By calculating its two-terminal transmission, we find a contact effect induced by the skin effect, which results in a nonquantized transmission for chiral edge states. In addition, the model exhibits an insulator to “supermetal” transition, across which the transmission changes from exponentially decaying with system size to exponentially growing with system size. In the clean system, the critical point separating insulator from supermetal is characterized by a non-Hermitian Dirac point that produces a quantized critical transmission of 4, instead of the value of 1 expected in Hermitian systems. This change in critical transmission is a consequence of the balanced gain and loss. When adding disorder to the system, we find a critical exponent for the divergence of the localization length $\nu \approx 1$, which is the same as that characterizing the universality class of two-dimensional Hermitian systems in class D. Our work provides a way of exploring the localization behavior of non-Hermitian systems, by using network models, which in the past proved versatile tools to describe Hermitian physics.

When two identical two-dimensional (2D) periodic lattices are stacked in parallel after rotating one layer by a certain angle relative to the other layer, the resulting bilayer system can lose lattice periodicity completely and become a 2D quasicrystal. Twisted bilayer graphene with ${30}^{\circ }$ rotation is a representative example. We show that such quasicrystalline bilayer systems generally develop macroscopically degenerate localized zero-energy states (ZESs) in strong coupling limit where the interlayer couplings are overwhelmingly larger than the intralayer couplings. The emergent chiral symmetry in strong coupling limit and aperiodicity of bilayer quasicrystals guarantee the existence of the ZESs. The macroscopically degenerate ZESs are analogous to the flat bands of periodic systems, in that both are composed of localized eigenstates, which give divergent density of states. For monolayers, we consider the triangular, square, and honeycomb lattices, comprised of homogenous tiling of three possible planar regular polygons: the equilateral triangle, square, and regular hexagon. We construct a compact theoretical framework, which we call the quasiband model, that describes the low-energy properties of bilayer quasicrystals and counts the number of ZESs using a subset of Bloch states of monolayers. We also propose a simple geometric scheme in real space, which can show the spatial localization of ZESs and count their number. Our paper clearly demonstrates that bilayer quasicrystals in strong coupling limit are an ideal playground to study the intriguing interplay of flat band physics and the aperiodicity of quasicrystals.

We present an interpolation method for the specific heat $c_v\left(T\right)$, when there is a phase transition with a logarithmic singularity in $c_v$ at a critical temperature $T=T_c$. The method uses the fact that $c_v$ is constrained both by its high temperature series expansion and just above $T_c$ by the type of singularity. We test our method on the ferro- and antiferromagnetic Ising models on the two-dimensional square, triangular, honeycomb, and kagome lattices, where we find an excellent agreement with the exact solutions. We then explore the XXZ Heisenberg model, for which no exact results are available.

We show that the reduced, dimensionless Yukawa potential $y_{\alpha }$ can be employed as an important ingredient in the construction of the exchange and correlation energy functionals. A functional based on $y_{\alpha }$ provides a better description of the exchange and correlation linear response functions of the homogeneous electron gas, not only at small wave vectors, where gradient expansions are correct, but also at large wave vectors, where semilocal exchange and correlation functionals fail badly. Moreover, the $y_{\alpha }$ ingredient gives a realistic description of the exchange energy and potential at the nuclear cusp and the inner atomic core, where the semilocal ingredients (i.e., the reduced gradient and Laplacian of the density) are not suitable, causing divergence of the potential. Thus, the $y_{\alpha }$ ingredient can be attractive for the development of various exchange-correlation functionals.

We propose general dual-band coordinate transformation media realizing two arbitrary coordinate transformations at two target frequencies and their universal implementation method by LC-based circuit metamaterials with full-tensor anisotropic dispersion controls. The circuit topologies to fully manipulate the material parameters to be realized are discussed. The general quantitative relations of the equivalent material parameters in two arbitrary coordinate transformations are classified into six cases, and the five fundamental branch unit constituents to cover all the six cases are presented. As an example, a dual-band illusion device with peculiar dispersions mimicking a bump and a pothole at each frequency is designed based on the presented implementation method. The illusion operations of the designed medium for 0 and ${45}^{\circ }$ incidences are numerically demonstrated by circuit simulations, and the validities of the proposed concept and the implementation method are confirmed.

We derive a general expression for the electric and magnetic part of the near-field energy density of $N$ dipoles of temperatures $T_1,...,T_N$ immersed in a background field having a different temperature $T_b$. In contrast to former expressions this inclusion of the background field allows for determining the energy density of heated or cooled isotropic dipolar objects within an arbitrary environment which is thermalized at a different temperature. Furthermore, we show how the energy density is related to the local density of states. We use this general expression to study the near-field enhanced energy density at the edges and corners of one-dimensional (1D) Su-Schrieffer-Heeger chains and 2D Su-Schrieffer-Heeger lattices of plasmonic InSb nanoparticles when the phase transition from a topological trivial to a topological nontrivial state is made. We discuss the robustness of these modes when adding defects and the possibility to measure the topological edge and corner modes.

We have investigated the low-temperature magnetism of sodium superoxide (${\mathrm{NaO}}_2$), in which spin, orbital, and lattice degrees of freedom are closely entangled. The magnetic susceptibility shows anomalies at $T_1=220$ K and $T_2=190$ K, which correspond well to the structural phase transition temperatures, and a sudden decrease below $T_3=34$ K. At 4.2 K, the magnetization shows a clear stepwise anomaly around 30 T with a large hysteresis. In addition, the muon spin relaxation experiments indicate no magnetic phase transition down to $T=0.3$ K. The inelastic neutron scattering spectrum exhibits magnetic excitation with a finite energy gap. These results confirm that the ground state of ${\mathrm{NaO}}_2$ is a spin-singlet state. To understand this ground state in ${\mathrm{NaO}}_2$, we performed Raman scattering experiments. All the Raman-active libration modes expected for the marcasite phase below $T_2$ are observed. Furthermore, we find that several new peaks appear below $T_3$. This directly evidences the low crystal symmetry, namely, the presence of the phase transition at $T_3$. We conclude that the singlet ground state of ${\mathrm{NaO}}_2$ is due to the spin-Peierls instability.

Interfacial electron-phonon coupling in ultrathin films has attracted much interest recently. Here, by combining angle-resolved photoemission spectroscopy and scanning tunneling microscopy, we report quantized electronic states and strong interfacial electron-phonon coupling in ultrathin Yb films on graphite. We observed clear kinks in the energy-momentum dispersion of quantum well states, and the kink positions agree well with the energies of optical phonons of graphite. The extracted coupling strength $\lambda$ is largest for the thinnest film with a preferred (“magic”) thickness of four monolayers and exhibits a strong band dependence, which can be qualitatively accounted for by a simple model. The interfacial electron-phonon coupling also gives rise to characteristic steplike structures in the $dI/dV$ spectra, implying dominant coupling with the phonons with zero in-plane momentum. A Lifshitz transition occurs at higher coverage, where quantum well states derived mainly from $5d$ electrons dominate near the Fermi level and possess large effective mass (up to $\sim 19m_e$). Our results highlight the potentially important role of interfacial electron-phonon interaction for ultrathin films and provide spectroscopic insight to understand this cross-interface fermion-boson interaction.

The long-standing quest to determine the superconducting order of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ (SRO) has received renewed attention after recent nuclear magnetic resonance (NMR) Knight shift experiments have cast doubt on the possibility of spin-triplet pairing in the superconducting state. As a putative solution, encompassing a body of experiments conducted over the years, a $(d+ig)$-wave order parameter caused by an accidental near degeneracy has been suggested [S. A. Kivelson et al., npj Quantum Mater. 5, 43 (2020)]. Here we develop a general Ginzburg–Landau theory for multiband superconductors. We apply the theory to SRO and predict the relative size of the order parameter components. The heat capacity jump expected at the onset of the second-order parameter component is found to be above the current threshold deduced by the experimental absence of a second jump. Our results tightly restrict theories of $d+ig$ order, and other candidates caused by a near degeneracy, in SRO. We discuss possible solutions to the problem.

We assess the ground-state phase diagram of the $J_1\text{−}{J}_2$ Heisenberg model on the Kagome lattice by employing Gutzwiller-projected fermionic wave functions. Within this framework, different states can be represented, defined by distinct unprojected fermionic Hamiltonians that include hopping and pairing terms, as well as a coupling to local Zeeman fields to generate magnetic order. For $J_2=0$, the so-called U(1) Dirac state, in which only hopping is present (such as to generate a $\pi$-flux in the hexagons), has been shown to accurately describe the exact ground state [Y. Iqbal, F. Becca, S. Sorella, and D. Poilblanc, Phys. Rev. B 87, 060405(R) (2013); Y.-C. He, M. P. Zaletel, M. Oshikawa, and F. Pollmann, Phys. Rev. X 7, 031020 (2017).]. Here we show that its accuracy improves in the presence of a small antiferromagnetic superexchange $J_2$, leading to a finite region where the gapless spin liquid is stable; then, for $J_2/J_1=0.11\left(1\right)$, a first-order transition to a magnetic phase with pitch vector $\mathbf{q}=(0,0)$ is detected by allowing magnetic order within the fermionic Hamiltonian. Instead, for small ferromagnetic values of $|J_2|/J_1$, the situation is more contradictory. While the U(1) Dirac state remains stable against several perturbations in the fermionic part (i.e., dimerization patterns or chiral terms), its accuracy clearly deteriorates on small systems, most notably on 36 sites where exact diagonalization is possible. Then, on increasing the ratio $|J_2|/J_1$, a magnetically ordered state with $\sqrt{3}\times \sqrt{3}$ periodicity eventually overcomes the U(1) Dirac spin liquid. Within the ferromagnetic $J_2$ regime, evidence is shown in favor of a first-order transition at $J_2/J_1=-0.065\left(5\right)$.

In recent years qubit designs such as transmons have approached fidelities of up to 0.999. However, even these devices are still insufficient for realizing quantum error correction requiring better than 0.9999 fidelity. Topologically protected superconducting qubits are arguably the most prospective for building a realistic quantum computer as they are intrinsically protected from noise and leakage errors that occur in transmons. We propose a topologically protected qubit design based on a $\pi$-periodic Josephson element and a universal set of gates: A protected Clifford group and highly robust (with infidelity $\lesssim {10}^{-4}$) nondiscrete holonomic phase gate. The qubit is controlled via charge $Q$ and flux $\mathrm{\Phi }$ biases. The holonomic gate is realized by quickly, but adiabatically, going along a particular closed path in the two-dimensional $\{\mathrm{\Phi },Q\}$ space—a path where computational states are always degenerate but Berry curvature is localized inside the path. This gate is robust against currently achievable noise levels. This qubit architecture allows building a realistic scalable superconducting quantum computer with leakage and noise-induced errors below ${10}^{-4}$, which allows performing realistic error correction codes with currently available fabrication techniques.

In this paper, we theoretically investigated the electronic properties of monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ by combining first-principles calculations and symmetry analyses. Spin-orbital coupling resulted in band splitting, whereas a horizontal mirror symmetry constrained the spin polarization to be along the $z$ direction. In addition, a three-band tight-binding model was constructed to describe the low-energy quasiparticle states of monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$, which can be generalized to strained $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ and its derivatives. The calculations using the tight-binding model showed an undamped $\sqrt{q}$-dependent plasmon mode, consistent with the results of first-principles calculations. The developed model is suitable for future theoretical and numerical investigations of low-energy properties in $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ family materials. Furthermore, the study of the electronic properties of monolayer $\mathrm{Mo}{\mathrm{Si}}_2{\mathrm{N}}_4$ paves a way for its applications in spintronics and plasmonics.

The effect of spin-orbit interaction was studied in a high-quality $p$-AlGaAs/GaAs/AlGaAs structure with a square quantum well using acoustic methods. The structure grown on a GaAs (100) substrate was symmetrically doped with carbon on both sides of the quantum well. Shubnikov–de Haas–type oscillations of the ac conductance of two-dimensional holes were measured. At a low magnetic field $B<2$ T, conductance oscillations undergo beating induced by a spin-orbit interaction. Analysis of the beating character made it possible to separate the conductance contributions from the two heavy-hole subbands split by the spin-orbit interaction. For each of the subbands the values of the effective masses and quantum relaxation times were determined, and then the energy of the spin-orbit interaction was obtained. The quantum well profile, as well as the small magnitude of the spin-orbit interaction, allowed us to conclude that the spin-orbit splitting is governed by the Dresselhaus mechanism.

We study single-channel continuum models of one-dimensional insulators induced by periodic potential modulations which are either terminated by a hard wall (the boundary model) or feature a single region of dislocations and/or impurity potentials breaking translational invariance (the interface model). We investigate the universal properties of excess charges accumulated near the boundary and the interface, respectively. We find a rigorous analytic proof for the earlier observed linear dependence of the boundary charge on the phase of the periodic potential modulation as well as extend these results to the interface model. The linear dependence on the phase shows a universal value for the slope and is intersected by discontinuous jumps by plus or minus one electron charge at the phase points where localized states enter or leave a band of extended states. Both contributions add up such that the periodicity of the excess charge in the phase over a $2\pi$ cycle is maintained. While in the boundary model this property is usually associated with the bulk-boundary correspondence, in the interface model a correspondence of scattering state and localized state contributions to the total interface charge are unveiled on the basis of the so-called nearsightedness principle.