Fractionally charged excitations play a central role in condensed matter physics, and can be probed in different ways. If transport occurs via dissipationless supercurrents, they manifest as a fractional Josephson effect, whereas in dissipative transport they can be revealed by the transport statistics. However, in a regime where supercurrents and lossy currents coincide, a full understanding of the relationship between these two transport phenomena is still missing. Moreover, especially for superconducting circuits, the question of how noninteger quasicharges can be reconciled with charge quantization is still not fully resolved, and plays an important role for the circuit dynamics. Here, we aim to unify the above concepts by studying the system-detector dynamics in terms of a Lindbladian capturing both coherent and dissipative transport. Charge quantization is here a conserved property of the detector basis of the Lindbladian, while charge fractionalization is a topological property of its complex-valued eigenspectrum. We show that already conventional superconductor-normal metal hybrid circuits exhibit a variety of topological phases, including an open quantum system version of a fractional Josephson effect. Surprisingly, quasiparticles, usually considered a detrimental side effect, are here a necessary ingredient to observe nontrivial transport behavior.

Nonlocal games yield an unusual perspective on entangled quantum states. The defining property of such games is that a set of players in joint possession of an entangled state can win the game with higher probability than is allowed by classical physics. Here we construct a nonlocal game that can be won with certainty by $2N$ players if they have access to the ground state of the toric code on as many qubits. By contrast, the game cannot be won by classical players more than half the time in the large $N$ limit. Our game differs from previous examples because it arranges the players on a lattice and allows them to carry out quantum operations in teams, whose composition is dynamically specified. This is natural when seeking to characterize the degree of quantumness of nontrivial many-body states, which potentially include states in much more varied phases of matter than the toric code. We present generalizations of the toric code game to states with ${\mathbb{Z}}_M$ topological order.

We investigate the effects of alternating voltage on nonequilibrium quantum systems with localized phonon modes. Nonequilibrium Green's functions are utilized, with electron-phonon coupling being considered with the $GD$ approximation (self-consistent Born approximation). Using a Floquet approach, we assume periodicity of the dynamics. This approach allows us to investigate the influence of the driven electronic component on the nonequilibrium occupation of the vibrations. It was found that signatures of inelastic transport gained photon-assisted peaks. A simplistic model was proposed and found to be in good agreement with the full model in certain parameter ranges. Moreover, it was found that driving the alternating current at resonance with vibrational frequencies caused an increase in phonon occupation.

We report the electronic structure of ${\mathrm{BaIr}}_2{\mathrm{Ge}}_7$ with two types of cage structure by means of angle-resolved photoemission spectroscopy (ARPES) and hard x-ray photoemission spectroscopy. ARPES spectra reveal the three-dimensional and multiband Fermi surfaces (FSs) originating from the hybridized Ir $5d$ and Ge $4p$ orbitals. The observed FSs show $C_2$ symmetry, reflecting the orthorhombic $Ammm$ crystal structure of ${\mathrm{BaIr}}_2{\mathrm{Ge}}_7$. The temperature dependence of the ARPES spectra exhibits the thermal spectral broadening, and the width of the spectral peak shows a concave-downward behavior with temperature. Considering the effect of anharmonic phonon modes, we have reproduced the temperature dependence of the electrical resistivity as well as the thermal spectral broadening. The resultant renormalized phonon frequencies ${\omega }_{\mathrm{r}0}^{\left(1\right)}=146.9\mathrm{K}$ and ${\omega }_{\mathrm{r}0}^{\left(2\right)}=70.6\mathrm{K}$ are comparable to the Einstein temperatures estimated from the previous specific heat measurement. Our results suggest the existence of the weak anharmonic phonon modes in ${\mathrm{BaIr}}_2{\mathrm{Ge}}_7$.

Graphene can be turned into a semimetal with broken time-reversal symmetry by adding a valley-dependent pseudoscalar potential that shifts the Dirac point energies in opposite directions, as in the modified Haldane model. We consider a bilayer obtained by stacking two time-reversed copies of the modified Haldane model, where conduction and valence bands cross to give rise to a nodal line in each valley. In the AB stacking, the interlayer hopping lifts the degeneracy of the nodal lines and induces a band repulsion, leading surprisingly to a chiral insulator with a Chern number $C=\pm 2$. As a consequence, a pair of chiral edge states appears at the boundaries of a ribbon bilayer geometry. In contrast, the AA stacking does not show nontrivial topological phases. We discuss possible experimental implementations of our results.

Decagonal quasiperiodic ordering of Sn thin films on $d$-Al-Ni-Co is shown based on scanning tunneling microscopy (STM), low-energy electron diffraction, and density functional theory (DFT). Interestingly, the decagonal structural correlations are partially retained even up to a large film thickness of 10 nm grown at $165\pm 10\mathrm{K}$. The nucleation centers called “Sn white flowers” identified by STM at submonolayer thickness are recognized as valid patches of the decagonal clathrate structure with low adsorption energies of these motifs. Due to the excellent lattice matching (to within 1%) between columns of Sn dodecahedra in the clathrate structure and pentagonal motifs at the $d$-Al-Ni-Co surface, the interfacial energy favors clathrate over the competing Sn crystalline forms. DFT study of the Sn/Al-Ni-Co composite model shows good mechanical stability, as shown by the work of separation of Sn from Al-Ni-Co slab that is comparable to the clathrate self-separation energy. The relaxed surface terminations of the ${\mathrm{R}}_2{\mathrm{T}}_4$ clathrate approximant are in self-similarity correspondence with the motifs observed in the STM images from monolayer to the thickest Sn film.

Recent theories predicted that $1{\mathrm{T}}^{\prime }\text{−}\mathrm{MoT}{\mathrm{e}}_2$ is a higher-order topological insulator (HOTI) exhibiting one-dimensional (1D) conducting edge states, and that ${\mathrm{T}}_d\text{−}\mathrm{MoT}{\mathrm{e}}_2$ becomes a HOTI with broken inversion symmetry under strain or lattice distortion. Here, we report the transport evidence for 1D helical edge states in ${\mathrm{MoTe}}_2$ thin flakes. Under an in-plane magnetic field perpendicular to the current, Altshuler-Aronov-Spivak interference of edge states is observed, in which the oscillating period corresponding to magnetic flux $h/2e$ agrees with the lateral cross-sectional area. The absence of Aharonov-Bohm interference stems from the helical nature of the edge states. Temperature evolution of the fast Fourier transform amplitude is further obtained, indicating the quasiballistic transport mode. Our work deepens the understanding of higher-order topological properties of ${\mathrm{MoTe}}_2$, paving the way for further topological electronics.

The parity game is an example of a nonlocal game: By sharing a Greenberger-Horne-Zeilinger (GHZ) state before playing this game, the players can win with a higher probability than is allowed by classical physics. The GHZ state of $N$ qubits is also the ground state of the ferromagnetic quantum Ising model on $N$ qubits in the limit of vanishingly weak quantum fluctuations. Motivated by this observation, we examine the probability that $N$ players who share the ground state of a generic quantum Ising model, which exhibits nonvanishing quantum fluctuations, still win the parity game using the protocol optimized for the GHZ state. Our main result is a modified parity game for which this protocol asymptotically exhibits quantum advantage in precisely the ferromagnetic phase of the quantum Ising model. We further prove that the ground state of the exactly soluble $d=1+1$ transverse-field Ising model can provide a quantum advantage for the parity game over an even wider region, which includes the entire ferromagnetic phase, the critical point and part of the paramagnetic phase. By contrast, we find examples of topological phases and symmetry-protected topological (SPT) phases of matter, namely the deconfined phase of the toric code Hamiltonian and the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ SPT phase in one dimension, that do not exhibit an analogous quantum advantage away from their fixed points.

The study of symmetry-protected topological phases of matter has been extended from fermionic electron systems to various bosonic systems. Bosonic topological magnon phases in magnetic materials have received much attention because of their exotic uncharged topologically protected boundary modes and the potential for dissipationless magnonics and spintronic applications. Here, we establish twisted bilayer honeycomb magnets as a platform for hosting second-order topological magnon insulators (SOTMIs) without fine-tuning. We employ a simple, minimal Heisenberg spin model to describe misaligned bilayer sheets of honeycomb ferromagnetic magnets with a large commensurate twist angle. We found that the higher-order topology in this bilayer system shows a significant dependence on the interlayer exchange coupling. The SOTMI, featuring topologically protected magnon corner states that go beyond the conventional bulk-boundary correspondence, appears for ferromagnetic interlayer couplings, while the twisted bilayer exhibits a nodal phase in the case of antiferromagnetic interlayer coupling. At last, relevance to twisted bilayer ${\mathrm{CrI}}_3$ is also discussed.

We have examined the electronic structure of twisted bilayers of ${\mathrm{WSe}}_2$ within ab initio electronic structure calculations. Flat bands are found to emerge above a set of dispersing bands at a twist angle of $3.48{}^{\circ }$, whereas they are absent at $19.03{}^{\circ }$ which has a similar-sized moiré cell. The presence of the flat bands at the valence-band maximum are traced to the strong perturbations from zone-boundary scattering found for small angles. This follows from the fact that the strongest Fourier components of the lattice potential are associated with the primitive cell vectors, justifying a description of the electronic structure as a perturbation to the unrotated limit. The layer polarization of the charge density associated with the valence-band maximum also allows for tuning the electronic structure with an electric field, thereby driving a semiconductor-metal-semiconductor transition.

In this paper, we discuss in the framework of a mechanoelastic model the electronic and mechanical behavior of a single layer of spin crossover molecules self-organized on a substrate. We consider the molecules situated in a face-centered-cubic structure interacting in between and with sites in the substrate by the way of connecting springs with given elastic constants. The main experimental results are reproduced, i.e., typical thermal transitions with their incompleteness of the hysteresis loop, residual fractions after low-temperature relaxations, cooperativity, or kinetic features. However, we prove that the simple model, implying fixed neighbors on the substrate for every spin crossover molecule, leads in some cases to unphysical situations, corresponding to unexpected large curvatures of the spin crossover layer. Therefore, to go further, we allow every spin crossover molecule to change its adsorption site on the substrate at every moment, by connecting to the closest molecules on the substrate. This approach, corroborated with the use of different densities of the sites on the substrate, allows us to simulate further experimental observations, such as the appearance of cracks inside the layer or periodic arrangements of apparent heights of spin crossover molecules on the layer leading to moiré patterns, for which experimental data are also provided.

The superconducting state of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ was once thought to be a leading candidate for $p$-wave superconductivity. A constant Knight shift below the transition temperature provided evidence for spin-triplet pairing, and a $\pi$ phase shift observed in Josephson junction tunneling experiments suggested odd-parity pairing, both of which are described by $p$-wave states. However, with recent experiments observing a significant decrease in the Knight shift below the transition temperature, signifying a spin-singlet state, the odd-parity results are left to be reconciled. In this work, we show that an even-parity pseudospin-singlet state originating from interorbital pairing via spin-orbit coupling can explain what has been assumed to be evidence for an odd-parity state. In the presence of small mirror symmetry breaking, interorbital pairing is uniquely capable of displaying odd-parity characteristics required to explain these experimental results. Further, we discuss how these experiments may be used to differentiate the proposed pairing states of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$.

We report a detailed investigation of the superconducting properties of the kagome-honeycomb lattice compound $\mathrm{La}{\mathrm{Ru}}_3{\mathrm{Si}}_2$ by systematically tuning the spin-orbit coupling (SOC) via doping of heavier elements Rh and Ir at the Ru site. All doped samples (for a doping level of 10 at. %) preserve the pristine hexagonal crystal structure in the space group $P{6}_3/mmc$, though a marginal lattice compression was noted for Rh doping. Based on the results of dc magnetization, resistivity, and heat capacity measurements, we derived the normal and superconducting state electronic and thermodynamic properties of the pristine and doped samples. Substitution of Ir/Rh at the Ru site of $\mathrm{La}{\mathrm{Ru}}_3{\mathrm{Si}}_2$ resulted in a rather slow but linear suppression of superconducting transition temperature ($T_{\mathrm{c}}$), which may be related to the decrease in the density of states. As manifested by the estimated electron-phonon (el-ph) coupling constant (${\lambda }_{\mathrm{el}\text{−}\mathrm{ph}}\sim 0.58\text{–}0.66$) and the normalized specific heat jump at $T_{\mathrm{c}}$ ($\mathrm{\Delta }C/\gamma T_c\sim 1.5$), the observed superconductivity in $\mathrm{La}{\mathrm{Ru}}_3{\mathrm{Si}}_2$ and the doped variants is moderately coupled. We observed a nonmonotonous variation of the upper critical field $\left[{\mu }_0{H}_{c2}\left(0\right)\right]$ with respect to the doping concentration, as it is influenced by the effective SOC and the coherence length. Most strikingly, we found an enhancement of the superconducting gap parameter $({\mathrm{\Delta }}_0/k_{\mathrm{B}}{T}_{\mathrm{c}})$ with doping concentration even though ${\lambda }_{\mathrm{el}\text{−}\mathrm{ph}}$ remains essentially unchanged. Moreover, we also notice a nonzero residual electronic specific heat coefficient (${\gamma }_r$) in the limit $T$ →0 for all compositions. Interestingly, the evolution of the ${\gamma }_r$ with the magnetic field can be well described by a $\sqrt{H}$ dependence, which was attributed to multiband superconductivity.

${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ is a two-dimensional van der Waals bonded layered compound that shows high-temperature itinerant ferromagnetism. We study aspects of the scattering mechanism in the single crystal of high-$T_{\text{C}}{\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ via resistivity, magnetotransport, and Hall effect measurements. The quadratic temperature dependence of electrical resistivity below the $T_{\text{C}}$ (210 K) points towards the dominance of electron-magnon scattering. A nonsaturating positive magnetoresistance (MR) is observed at low temperatures when the magnetic field is applied parallel to the sample plane. The linear negative MR at high fields for $T<T_{\text{C}}$ corroborates to the suppression in the magnon population due to the damping of spin waves. In the high-temperature regime ($T>T_{\text{C}}$), MR can be described by the scattering from spin fluctuations using the Khosla and Fischer model. Isothermal Hall resistivity curves unveil the presence of anomalous Hall resistivity. The correlation between magnetoresistance and side jump mechanism further reveals that the electron-magnon scattering is responsible for the side jump contribution to the anomalous Hall effect. Our results provide a clear understanding of the role of electron-magnon scattering on the temperature-driven evolution of the anomalous Hall effect that rules out its origin to be the topological band structure.

We study electron correlations and their impact on magnetic properties of bcc vanadium by a combination of density functional and dynamical mean-field theory. The calculated uniform magnetic susceptibility in bcc structure is of Pauli type at low temperatures, while it obeys the Curie-Weiss law at higher temperatures. Thus, we qualitatively reproduce the experimental temperature dependence of magnetic susceptibility without introducing the martensitic phase transition. Our results for local spin-spin correlation function and local susceptibility reveal that the Curie-Weiss behavior appears due to partial formation of local magnetic moments, which originate from $t_{2g}$ states and occur due to local spin correlations caused by Hund's rule coupling. At the same time, the fermionic quasiparticles remain well defined, while the formation of local moments is accompanied by a deviation from the Fermi-liquid behavior. In particular, the self-energy of the $t_{2g}$ states shows the nonanalytic frequency dependence, which is a characteristic of the spin-freezing behavior, while the quasiparticle damping changes approximately linearly with temperature in the intermediate temperature range 200–700 K. By analyzing the momentum dependence of static magnetic susceptibility, we find incommensurate magnetic correlations, which may provide a mechanism for unconventional superconductivity at low temperatures.

Driven by various physical origins, the interesting reentrant phenomena in quantum Hall effect (QHE), quantum anomalous Hall effect (QAHE), and non-Hermitian systems have been discussed recently. Here, we present that the reentrant phenomena of the quantum spin Hall effect (QSHE) can be achieved by introducing a uniform exchange field into a topological insulator with a four-band model Hamiltonian. Furthermore, it is found that both time-reversal (TR) symmetry broken QSHE and spin-polarized QAHE can simultaneously be generated in the system with proper exchange field strength by inspecting the corresponding edge states. Through analyzing the energy-dependent spin-Chern number ${\nu }_s$ and transmission in the presence of random disorders, we verify the topological protection and the robustness of induced QSHE and QAHE. Finally, the theoretical realization of reentrant QSHE in a topolectrical circuit is demonstrated. Our work not only extends the reentrant phenomena into the QSHE but also stimulates interest in their realization in different systems.

This work demonstrates a first-principles-based approach to obtaining finite temperature thermal and electronic transport properties which can be employed to model and understand mesoscale structural evolution during electronic, magnetic, and structural phase transitions. A computationally tractable model was introduced to estimate electron relaxation time and its temperature dependence. The model is applied to ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ with a focus on understanding its electrical resistivity across the electronic phase transition at 48 K. A quasiharmonic phonon approach to the lattice vibrations was employed to account for thermal expansion while the Boltzmann transport theory including spin-orbit coupling was used to calculate the electron-transport properties, including the temperature dependence of electrical conductivity.