The square ice is a two-dimensional spin liquid hosting a Coulomb phase physics. When constrained under specific boundary conditions, the so-called domain-wall boundary conditions, a phase separation occurs that leads to the formation of a spin liquid confined within a disk surrounded by magnetically ordered regions. Here, we numerically characterize the ground-state properties of this spin liquid, coined the arctic square ice in reference to a phenomenon known in statistical mechanics. Our results reveal that both the vertex distributions and the magnetic correlations are inhomogeneous within the liquid region, and they exhibit a radial dependence. If these properties resemble those of the conventional square ice close to the center of the disk, they evolve continuously as the disk perimeter is approached. There, the spin liquid orders. As a result, pinch points, signaling the presence of algebraic spin correlations, coexist with magnetic Bragg peaks in the magnetic structure factor computed within the disk. The arctic square ice thus appears as an unconventional Coulomb phase sharing common features with a fragmented spin liquid, albeit on a charge-neutral vacuum.

Three-dimensional Dirac semimetals (DSMs) have been shown to exhibit one-dimensional hinge modes which are termed the higher-order hinge Fermi-arc (HOFA) states. They are the topological consequences of Dirac points. Superconducting states from Dirac semimetals can inherit the Dirac points to form nodal Dirac superconducting states, raising a question of whether there exists a topological superconducting bulk-hinge correspondence similar to DSMs. In this work, we discuss the nodal superconducting states from half-filled DSMs respecting nonmagnetic (Type-II) Shubnikov space group (SSG) $P6/mmm{1}^{\prime }$. We find that the Bogoliubov–de Gennes (BdG) Dirac points can lead to higher-order topological Dirac superconducting (HOTDSC) states instead of the expected higher-order Majorana-arc states. The HOTDSC states can be regarded as a crossing between the HOFAs in normal states and the BdG shadow states. We demonstrate that HOTDSC states can be indicated by relative topologies of BdG Dirac points by utilizing the theory of magnetic topological quantum chemistry.

The ${\mathrm{LaH}}_{10}$ superconductor has attracted much attention due to its near-room-temperature superconducting transition temperature. However, ${\mathrm{LaH}}_{10}$ requires extremely high pressure, about 200 GPa, to maintain its stability, thereby limiting its potential for industrial applications. Here, we perform the high-throughput structure searches of ${\mathrm{LaH}}_{10}$-like boron-nitrogen clathrate superconductors at ambient pressure. The calculated results reveal that the stabilities of main-group and transition metal doped-boron-nitrogen clathrates are affected by both the valence electrons and atomic radius of the guest metals, and the boron-nitrogen cages tend to accommodate small-sized guest metals. The guest metals transfer charges to the boron-nitrogen caged frameworks, forming stronger anion-cation interactions, and the strong polar covalent bonds formed between B and N enhance the structural stabilities of these boron-nitrogen clathrates. Four stable $M{\left(\mathrm{BN}\right)}_5$ ($M=$ Na, Al, In, Tl) superconductors with $T_c$ values of 8, 22, 15, and 15 K, respectively, are uncovered. Our findings indicate that the $p$ orbitals of $p$-region metals and the $p$ orbitals of B and N atoms exhibit the high-occupancy rate at the Fermi level, increasing the electronic density of the states at the Fermi surface, facilitating the electron-phonon coupling, and enhancing the superconductivity. The present results enrich the database of boron-nitrogen based superconductors and provide a promising avenue for design and synthesis high-temperature superconductors at ambient pressure.

We present an efficient criterion for doing fast estimations of the critical temperature of hydrogen-based superconductors. We start by expanding the applicability of three-dimensional descriptors of electron localization to superconducting states within the framework of superconducting density functional theory (DFT). We first apply this descriptor to a model system, the hydrogen chain, which allows one to prove two main concepts: (i) the electron localization changes very little when the transition from the normal to the superconducting state takes place, i.e., it can be described at the DFT level from the normal state; and (ii) the formation of molecules can be characterized within this theoretical framework, enabling one to quickly filter out systems with marked molecular character and hence with low potential to be good superconductors. These two ideas are then exploited in real binary and ternary systems, showing (i) that the bonding type can be characterized automatically and (ii) that this provides a different index which enables one to feed machine-learning algorithms for a better prediction of critical temperatures. Overall, this sets a grounded theoretical scenario for an automatic and efficient high-throughput screening of potential hydrogen-based superconductors.

We investigate superconducting gallium in its $\alpha$ phase using scanning tunneling microscopy and spectroscopy at temperatures down to about 100 mK. High-resolution tunneling spectroscopies using both superconducting and normal tips show that superconducting $\alpha$-Ga is accurately described by Bardeen-Cooper-Schrieffer theory, with a gap ${\mathrm{\Delta }}_{\mathrm{Ga}}=163\mu \mathrm{eV}$ on the $\alpha \text{−}\mathrm{Ga}\left(112\right)$ facet, with highly homogeneous spectra over the surface, including atomic defects and step edges. Using a superconducting Pb tip, we furthermore study the low-bias conductance features of the Josephson junction formed between the tip and sample. The features are accurately described by dynamical Coulomb blockade theory, highlighting $\alpha \text{−}\mathrm{Ga}$ as a possible platform for surface science studies of mesoscopic superconductivity.

We investigate the phase transitions in a one-dimensional system with colored noise. Previous studies indicated that the phase diagram of this system included extended and disorder-induced localized phases. However, by studying the properties of wave functions, we find that this phase diagram can be further refined, revealing the existence of a bound phase for the large potential amplitude $W$ and noise control parameter $\alpha$. In the bound phase, the wave function cannot extend throughout the entire chain, tails decay faster than exponentially, and its distribution expands as the system size increases. By adjusting the potential amplitude to induce a transition from the extended phase to the bound phase, we find that bound states coexist with extended states in the spectrum. In contrast, when the system transitions from the Anderson localized phase to the bound phase, we do not observe the obvious coexistence of Anderson localized and bound states. Finally, by performing the time evolution, we find that the dynamic transition point of the bound phase is inconsistent with the static one for large $\alpha$.

The influence of a rotating magnetic field (in the $ab$ plane) on the density of states has been investigated in the superconducting state of the nematic FeSe superconductor using high sensitivity specific heat measurements. As expected for (quasi-)nodal superconductors, oscillations in the specific heat $C$ associated with the Doppler energy shift of Cooper pairs with momenta close to the gap minima are observed. In the $T_c=9$ K crystal, $C(\varphi$) displays a twofold symmetry at low temperature and low magnetic field confirming the nematic character of FeSe from thermodynamical measurements. As expected, a $\pi /2$ phase shift is observed for increasing temperatures (at $H=1$ T) but our measurements suggest that the gap structure abruptly changes above $\approx 1$ K in this sample. At low temperature, the maxima observed for $H\left|\right|a$ axis at low $H$ split into lobes at $\pm {45}^{\circ }$ when the magnetic field is increased, which can be accounted for by assuming that the electron gap rapidly closes with field.

Motivated by the generation by optical pulses of nonthermal distributions of nuclear spins in quantum dots we investigate the effect of optical pulses applied to Bardeen-Cooper-Schrieffer (BCS) superconductors. Using time-dependent mean-field theory formulated with Anderson pseudospins, we study the electronic configurations and the energy deposited in the system by optical pulses. The pulses are included by Peierls substitution and we study short rectangular pulses as well as idealized $\delta$ pulses. Already a few and even a single pulse generates highly nontrivial distributions of electron expectation values which we simulate numerically and explain analytically based on the linearization of the equations of motion. These results suggest so far unexplored experimental possibilities for the optical control of superconducting states.

Accurate determination of the bilayer structure of the recently discovered high transition temperature superconductor $\mathrm{L}{\mathrm{a}}_3\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_7$ under pressure is a prerequisite for understanding its electronic properties and revealing its dominant superconducting mechanism. Here we present the first systematic exploration of the structural evolution of $\mathrm{L}{\mathrm{a}}_3\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_7$ under different pressure schemes, with the long-range London dispersion force between neighboring bilayers taken into account explicitly. We find, within a broad pressure range of 10 to 35 GPa, that the structure is essentially always in-plane symmetric under hydrostatic pressure, in clear contradiction to the experimentally observed asymmetric structure. Nevertheless, when the applied pressure is anisotropic together with inclusion of a proper dispersion force, the asymmetric structure can be reproduced, accompanied by pronounced flat bands of $d_{z^2}$ orbitals around the Fermi level that in turn benefit superconductivity. These findings offer stringent constraints on developing mechanistic understanding of superconductivity of $\mathrm{L}{\mathrm{a}}_3\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_7$.

We consider the most energetically favorable symmetry-allowed spin-singlet and spin-triplet superconducting pairing symmetries in twisted bilayer graphene at the magic angle, whose normal state physics is described by a six-band effective tight-binding model. We compute the Chern number as a function of the superconducting order parameter strength and the chemical potential and we find a topological phase transition only for the chiral $p+i{p}^{\prime }$ superconducting state. Different from the regular graphene systems for which this happens at the van Hove singularity, for TBG the topological phase transition arises at the point where the Fermi surface becomes tangent to the boundary of the first Brillouin zone. For each pairing symmetry we study the formation of subgap impurity states for both scalar and magnetic impurities. We analyze the number of subgap states as well as their spin-polarized density of states that we find to exhibit peculiar properties that allows one to distinguish between spin-singlet and triplet pairing. Thus only triplet-paired states may exhibit opposite-energy impurity states with the same spin, same as for regular graphene systems; moreover, we find that this spin may flip at the twist-induced van Hove singularity.

The $\sqrt{13}\times \sqrt{13}$ charge density wave state of the $T$ polytype of ${MX}_2$ $(M=\mathrm{Nb}, \mathrm{Ta}, X=\mathrm{S}, \mathrm{Se})$ is known to host a half-filled flat band which electronic correlations drive into a Mott insulating state. When $T$ polytypes are coupled to strongly metallic $H$ polytypes, such as in $T/H$ bilayer heterostructures or the bulk $4H_b$ polytype, charge transfer can destabilize the Mott state, but quantifying its magnitude has been a source of controversy. In this work, we perform a systematic ab initio study of charge transfer for all experimentally relevant $T/H$ bilayers and bulk $4H_b$ structures. In all cases we find charge transfer from $T$ to $H$ layers which depends strongly on the interlayer distance but weakly on the Hubbard interaction. Additionally, Se compounds display smaller charge transfer than S compounds, and $4H_b$ bulk polytypes display more charge transfer than isolated bilayers. We rationalize these findings in terms of band structure properties and argue they might explain differences between compounds observed experimentally. Our work reveals the tendency to Mott insulation and the origin of superconductivity may vary significantly across the family of $T/H$ heterostructures.

The quantum geometric tensor (QGT) quantifies the distances and phases encoded in the wave function, thereby revealing the topological nature of quantum matter. Despite recent strides in researching QGT within various symmetry-broken environments, its meaning and origin remain obscure. Here, we show a cause of quantum geometry by revealing how real-space twists uniquely induce QGT in a chiral chain. From the real-space metric tensor of helical geometry, an effective gauge field appears as a generator of the screw rotation, intertwining the chain-directional and the chain-perpendicular motion of electrons. Consequently, a universal form of the interband QGT emerges with equivalent in-plane components of the quantum metric tensor and Berry curvature. This applies to any quantum entities residing in the chiral chain and gives rise to diverse nonlinear Hall transports. On top of offering an intuitive insight into quantum geometry, our paper introduces a control knob of QGT through real-space geometry.

We present Floquet theory based predictions and electrically detected magnetic resonance (EDMR) experiments to elucidate the nature of multiphoton magnetic resonance shifts of charge-carrier spin states in films of the perdeuterated π-conjugated polymer poly[2-(2-ethylhexyloxy-${\mathrm{d}}_{17}$)-5-methoxy-${\mathrm{d}}_3$-1,4-phenylenevinylene-${\mathrm{d}}_4]$ (d-MEH-PPV) under strong magnetic resonant drive conditions (radiation amplitude $B_1$ comparable to Zeeman field $B_0$). Room-temperature, continuous-wave EDMR experiments on d-MEH-PPV-based, electroluminescent, bipolar-injection diodes [i.e., organic light-emitting diodes (OLEDs)] confirm the ability of a nonperturbative numerical method to make quantitative predictions of two-photon resonance shifts in such devices. Additional numerical simulations show that the two-photon resonance shift with increasing power is nearly the same under both linearly and circularly polarized drive, in contrast to the one-photon shift, which only occurs under conditions of noncircularly polarized drive. We therefore treat the Floquet Hamiltonian analytically using arbitrary amplitudes of the co- and counterrotating components of the radiation field to gain insight into the nature of the polarization dependence of multiphoton resonance shifts. The results show that multiphoton resonance shifts depend on both the co- and counterrotating components of an arbitrarily polarized drive field, whereas the one-photon shift depends only on the counterrotating component.

The ${\mathrm{G}}_0{\mathrm{W}}_0$ spectra of quasiholes/quasielectrons in electrostatically and potassium doped graphene is studied and compared with previous experimental and theoretical results. The appearance of plasmarons, the renormalization of group $v_{\pi }$, $v_{{\pi }^{*}}$ and Fermi $v_{\text{F}}$ velocities, decay widths $\mathrm{\Gamma }\left(E\right)$ and kinks at Fermi $\left(E_{\text{F}}\right)$ and Dirac $\left(E_{\text{D}}\right)$ energy for different graphene dopings $\rho$ have been discussed. In contrast to previous investigations, our spectra do not show diamond shaped patterns and the plasmaron is well defined only in the energy range $E_{\text{D}}<E<E_{\text{F}}$. Relative plasmaron binding energy ${\mathrm{\Delta }}_{\text{DPS}}/E_{\text{F}}$ converges to a value of 0.5, as determined experimentally. In pristine graphene, group velocity $v_{\pi }$ overestimates, while $v_{{\pi }^{*}}$ underestimates the DFT value. A band gap opening or kink at Dirac point is not visible, in contradiction to previous theoretical results. The renormalized group velocity $v_{\pi }=1.06\times {10}^6\text{m/s}$ agrees well with the experimental result of $1.1\times {10}^6\text{m/s}$. Quasiparticle spectra show a kink at $E_{\text{F}}$, and sudden increase of spectral width $\mathrm{\Gamma }\left(E\right)$ below $E_{\text{D}}$. This is a cause of another kink (observed experimentally), for which has been proven that it arises from a hole decay due to the Dirac plasmon emission. Quasiparticle spectral width (around $E_{\text{F}}$) exhibits behavior $\mathrm{\Gamma }\sim {\left|E\right|}^{3/2}$, as also experimentally predicted.

Persistent currents (PCs) in mesoscopic rings have been a subject of intense investigation since their proposal by Büttiker, Landauer, and Imry in 1983 [Phys. Lett. A 96, 365 (1983).]. In this paper, we explore the behavior of PC in spin-orbit coupled rings under the influence of a Zeeman field (without a need for a flux threading the ring), contrasting it with traditional PC observed in rings threaded by magnetic flux. Our study reveals that the emergence of PC in our setup crucially depends on nonzero values of spin-orbit coupling and the Zeeman field. Through theoretical analysis and numerical calculations, we uncover several intriguing phenomena. Specifically, in ballistic rings, we observe an inverse proportionality between PC and system size, with PC being zero at half filling for even numbers of sites. Additionally, the introduction of on-site disorder leads to the suppression of PC, with exponential decay observed for large disorder strengths and quadratic decay for smaller disorder strengths. Notably, disorder can enhance PC in individual samples, albeit with a configuration-averaged PC of zero. Furthermore, we find that the standard deviation of PC increases with disorder strength, reaching a maximum before decreasing to zero at high disorder strengths. We study the case of PC when the Zeeman field and the spin-orbit field are noncollinear. We also study persistent spin current, which shows behavior similar to that of PC except that at half filling, it is not zero. Our findings shed light on the intricate interplay between spin-orbit coupling, Zeeman fields, and disorder in mesoscopic quantum systems, offering different avenues for theoretical exploration and experimental verification.

We have investigated the structures and electronic properties of ultrathin Bi(110) films grown on an $s$-wave superconductor substrate using low-temperature scanning tunneling microscopy and spectroscopy. Remarkably, our experimental results validate the theoretical predictions that the manipulation of Bi(110) surface atom buckling can control the topological phase transition. Notably, we have observed robust unreconstructed edge states at the edges of both three- and four-bilayer Bi(110) films, with the four-bilayer film displaying stronger edge state intensity and a smaller degree of atomic buckling. First-principles calculations further substantiate these findings, demonstrating a gradual reduction in buckling as the film thickness increases, with average height differences between two Bi atoms of approximately 0.19, 0.10, 0.05, and 0.00 Å for the one-, two-, three-, and four-bilayer Bi(110) films, respectively. When Bi films are larger than two layers, the system changes from a trivial to a nontrivial phase. This research sets the stage for the controlled realization of topological superconductors through the superconducting proximity effect, providing a significant platform for investigating Majorana zero modes and fabricating quantum devices.

Ferroelectricity in lead halide perovskites has attracted tremendous interest due to its promising applications in high-performance optoelectronic devices. At present, ferroelectricity has been reported in some inorganic lead halide perovskite bulks, but whether it can exist in their ultra-thin films or even in the two-dimensional (2D) limit remains an unresolved issue. Here, we investigate ferroelectricity in lead halide perovskite monolayer films ${\mathrm{Cs}}_2\mathrm{Pb}{X}_4$ ($X$ = F, Cl, Br, I) using first-principles calculations, and demonstrate that the intrinsic ferroelectricity driven by the lone-pair electron effect of ${\mathrm{Pb}}^{2+}$ ions can exist in both freestanding and epitaxial strained ${\mathrm{Cs}}_2{\mathrm{PbF}}_4$ monolayer. Epitaxial strain maintains the polar ground-state phase established by octahedral rotation plus ferroelectric distortion in the ${\mathrm{Cs}}_2{\mathrm{PbF}}_4$ monolayer, whereas it does not induce ferroelectricity in the other monolayers. All the monolayers behave as semiconductors with a direct band gap that decrease with increasing anion radius. This work develops 2D ferroelectric semiconductors based on all-inorganic halide perovskites.

We compute the current and the noise power matrix in a quantum dot connected to two metallic reservoirs by using the Keldysh field theory approach, a nonequilibrium quantum field theory language in the functional integral formalism. We first show how this technique allows one to recover rapidly and straightforwardly well-known results in the literature, such as the Meir-Wingreen formula for the average current, which is extremely effective in dealing with the quantum transport problem. We then discuss in detail the electric and thermoelectric properties due to transport of electrons in the case of a single-level and two-level noninteracting quantum dot. In particular, we derive the optimal conditions for maximizing the thermoelectric current, finding an upper limit for the thermoelectric coefficient. Moreover, in the two-level system we show that the zero-temperature linear conductance drops rapidly to zero through a symmetrical removal of the degeneracy at the Fermi energy.