Topological band theory strongly relies on prototypical lattice models with particular symmetries. We report here on a theoretical and experimental work on acoustic waveguides that are directly mapped to the one-dimensional Su-Schrieffer-Heeger model. Starting from the continuous two-dimensional wave equation, we use a combination of monomode approximation and the condition of equal-length tube segments to arrive at the wanted chiral symmetric discrete equations. It is shown that open or closed boundary conditions lead automatically to the existence of topological edge modes. We illustrate by graphical construction how the edge modes appear naturally owing to a quarter-wavelength condition and the conservation of flux. Furthermore, the transparent chirality of our system, which is ensured by simple geometrical constraints allows us to study chiral disorder numerically and experimentally. Our experimental results in the audible regime demonstrate the predicted robustness of the topological edge modes.

In this work, using first-principles calculation we investigate the magnetic anisotropy (MA) of single-atom iridium (Ir) on $\mathrm{Ta}{\mathrm{S}}_2$ substrate. We find that the strength and direction of MA in the Ir adatom can be tuned by strain. The MA arises from two sources, namely the spin-conservation term and the spin-flip term. The spin-conservation term is mainly generated by spin-orbit coupling (SOC) interaction on the $d_{xy}/d_{x^2\text{−}{y}^2}$ orbitals and is contributed to the out-of-plane MA. The spin-flip term is caused by SOC interaction on the $d_{xz}/d_{yz}$ and $p_x/p_y$ orbitals and is responsible for the in-plane MA. We further find that strain-tuned MA is mainly determined by exchange splitting and ligand-field splitting. Increase of strain will reduce the ligand-field splitting and enhance the exchange splitting, resulting in the enhancement of the out-of-plane MA from $d_{xy}/d_{x^2\text{−}{y}^2}$ orbitals and the reduction of the in-plane MA from $d_{xz}/d_{yz}$ and $p_x/p_y$ orbitals, hence leading to the change of the strength and direction of the total MA. Our study provides a way for tuning the MA of a single-atom magnet on 2D transition metal dichalcogenide substrate by control of the exchange splitting and the ligand-field splitting.

Skew scattering—an asymmetric scattering of electrons by impurities—is one of the major mechanisms causing anomalous/spin Hall effects. Although many microscopic mechanisms for skew scattering are known, the Hall angle of anomalous Hall effect by these mechanisms is often small, typically $\theta =0.1^{\circ }-1^{\circ }$. In this paper, we study the skew scattering by three-spin clusters focusing on the strong Kondo-coupling regime. Using a $T$-matrix formalism, we calculate the scattering probability for arbitrary strength of Kondo coupling, going beyond perturbation theory in previous studies. From a systematic analysis of the scattering probability for one-, two-, and three-spin clusters, we show that three spins are necessary for the skew scattering in the absence of spin-orbit interaction. The skew scattering by the three-spin cluster produces a skew angle on the order of $0.1\pi \mathrm{rad}(\sim {18}^{\circ })$ when the electron-spin coupling is comparable to the bandwidth. We also study the relationship between the anomalous/spin Hall effects and the spin chiralities and argue that the anomalous-(spin) Hall skew angle is approximately proportional to the scalar (net vector) spin chirality even for the strong-coupling cases. This mechanism is potentially relevant to anomalous/spin Hall effects in noncentrosymmetric and frustrated magnets.

Materials realization of chiral topological superconductivity is a crucial condition for observing and manipulating Majorana fermions in condensed matter physics. Here we develop a tight-binding description of ${\mathrm{Pb}}_3\mathrm{Bi}/\mathrm{Ge}\left(111\right)$, identified recently as an appealing candidate system for realizing chiral $p$-wave topological superconductivity [Nat. Phys. 15, 796 (2019)]. We first show that our phenomenological model can capture the two main features of the electronic band structures obtained from first-principles calculations, namely, the giant Rashba splitting and type-II van Hove singularity. Next, when the $s$-wave superconducting property of the parent Pb system is explicitly considered, we find the alloyed system can be tuned into a chiral topological superconductor with Chern number $\mathcal{C}=-2$, resulting from the synergistic effect of a sufficiently strong Zeeman field and the inherently large Rashba spin-orbit coupling. The nontrivial topology with $\mathcal{C}=-2$ is further shown to be detectable as two chiral Majorana edge modes propagating along the same direction of the system with proper boundaries. We finally discuss the physically realistic conditions to establish the predicted topological superconductivity and observe the corresponding Majorana edge modes, including the influence of the superconducting gap, Landé $g$ factor, and critical magnetic field. The present study provides useful guides in searching for effective $p$-wave superconductivity and Majorana fermions in two-dimensional or related interfacial systems.

Motivated by a recent discovery of correlated insulating and superconducting behavior in twisted bilayer graphene, we revisit graphene's honeycomb lattice doped close to the van Hove singularity, using the truncated unity functional renormalization group approach. We consider an extended Hubbard model on the honeycomb lattice including on-site and nearest-neighbor Coulomb repulsions, and nearest-neighbor ferromagnetic exchange and pair hopping interactions. By varying the strength of the nearest-neighbor exchange coupling and Coulomb repulsion as free parameters, we present rich ground-state phase diagrams which contain the spin-triplet $f$-wave and spin-singlet chiral $d$-wave superconducting phases, the commensurate and incommensurate spin- and charge-density-wave phases, and the ferromagnetic phase. In the absence of the exchange coupling and for the small value of the nearest-neighbor repulsion, the four-sublattice spin-density-wave phase is generated right around the van Hove filling, while the chiral $d$-wave superconductivity emerges slightly away from it. Surprisingly, the chiral $d$-wave superconductivity is strongly suppressed by a weak nearest-neighbor exchange coupling in our calculations. We argue that this suppression might be one of the reasons why the chiral superconductivity proposed for doped graphene has not yet been observed experimentally.

In a time-reversal invariant system, while the anomalous Hall effect identically vanishes in the linear response regime due to the constraint of time-reversal symmetry on the distribution of Berry curvature, a nonlinear Hall effect can emerge in the second-order response regime if the inversion symmetry is broken to allow a nonzero Berry curvature dipole (BCD) on the Fermi surface. In this work, we study the nonlinear Hall effect of the BCD origin in two-dimensional doped insulators and semimetals belonging to the symmetry class AI which has spinless time-reversal symmetry. Despite the fact that the class AI does not host any strong topological insulator phase in two dimensions, we find that they can still be classified as topologically obstructed insulators and trivial insulators if putting certain constraint on the Hamiltonians. When the insulator gets closer to the phase boundary of the two distinct phases, we find that the BCDs will become more prominent if the doping level is located near the band edge. Moreover, when the insulator undergoes a phase transition between the two distinct phases, we find that the BCDs will dramatically change their signs. For the semimetals without inversion symmetry, we find that the BCDs will sharply reverse their signs when the doping level crosses the Dirac points. With the shift of the locations of Dirac points in energy, the critical doping level at which the BCDs sharply reverse their signs will accordingly change. Our study reveals that class-AI materials can also have interesting geometrical and topological properties, and remarkable nonlinear Hall effect can also appear in this class of materials even though the spin-orbit coupling is negligible. Our findings broaden the scope of materials to study the nonlinear Hall effect and provide perspectives for the application of this effect.

Recent observations of nonlocal transport in ultraclean two-dimensional materials raised the tantalizing possibility of accessing hydrodynamic correlated transport of a many-electron state. However, it has been pointed out that nonlocal transport can also arise from impurity scattering rather than interaction. At the crux of the ambiguity is the focus on linear effects, i.e., Ohm's law, which cannot easily differentiate among different modes of transport. Here we propose experiments that can reveal rich hydrodynamic features in the system by tapping into the nonlinearity of the Navier-Stokes equation. Three experiments we propose will each manifest a unique phenomenon that is well known in classical fluids: the Bernoulli effect, Eckart streaming, and Rayleigh streaming. Analysis of known parameters confirms that the proposed experiments are feasible and the hydrodynamic signatures are within reach of graphene-based devices. Experimental realization of any one of the three phenomena will provide a stepping stone to formulating and exploring the notions of nonlinear electron fluid dynamics with an eye to celebrated examples from classical nonlaminar flows, e.g., pattern formation and turbulence.

The introduction of non-Hermiticity has greatly enriched the research field of traditional condensed matter physics and eventually led to a series of discoveries of exotic phenomena. We investigate the effect of non-Hermitian imaginary hoppings on the Hubbard model. The exact bound-pair solution shows that the electron-electron correlation suppresses the non-Hermiticity, resulting in off-diagonal long-range order (ODLRO) ground state in the attractive Hubbard model. In a large $U$ limit, such non-Hermiticity contributes an extra minus sign in the virtual exchange of the particles. As a consequence, the energy of the effective spin model describing the behavior of the ground state and low energy excitations will be reversed. The corresponding ground state experiences a transition from antiferromagnetism to ferromagnetism characterized by the appearance of a non-decaying correlation function. The numerical result indicates that the $\eta$-pairing ground state exits in 1D and 2D systems and is insensitive to the disorder. We further propose a protocol to adiabatically generate the $\eta$-pairing state. Our results provide a promising approach for the non-Hermitian strongly correlated system.

We resolve several puzzles related to the electromagnetic response of topological superconductors in 3+1 dimensions. In particular we show by an analytical calculation that the interface between a topological and normal superconductor does not exhibit any quantum Hall effect as long as time reversal invariance is preserved. We contrast this with the analogous case of a topological insulator to normal insulator interface. The difference is that in the topological insulator the electromagnetic vector potential couples to a vector current in a theory with a Dirac mass, while in the superconductor a pair of Weyl fermions is gapped by Majorana masses and the electromagnetic vector potential couples to its axial currents.

We derive the disorder vs doping phase diagram of the doped Hubbard model via dynamical mean-field theory combined with typical medium theory, which allows the description of both Mott (correlation driven) and Anderson (disorder driven) metal-insulator transitions. We observe a transition from a metal to an Anderson-Mott insulator for increasing disorder strength at all interactions. In the weak correlation regime and rather small doping, the Anderson-Mott insulator displays properties which are similar to the ones found at half filling. In particular, this phase is characterized by the presence of empty sites. If we further increase either the doping or the correlation, however, an Anderson-Mott phase of a different kind arises for sharply weaker disorder strength. This phase occupies the largest part of the phase diagram in the strong-correlation regime and is characterized by the absence of the empty sites.

The quantum-critical properties of the transverse-field Ising model with algebraically decaying interactions are investigated by means of stochastic series expansion quantum Monte Carlo, on both the one-dimensional linear chain and the two-dimensional square lattice. We extract the critical exponents $\nu$ and $\beta$ as a function of the decay exponent of the long-range interactions. For ferromagnetic Ising interactions, we resolve the limiting regimes known from field theory, ranging from the nearest-neighbor Ising to the long-range Gaussian universality classes, as well as the intermediate regime with continuously varying critical exponents. In the long-range Gaussian regime, we treat the effect of dangerous irrelevant variables on finite-size scaling forms. For antiferromagnetic and therefore competing Ising interactions, the stochastic series expansion algorithm displays growing autocorrelation times leading to a reduced performance. Nevertheless, our results are consistent with the nearest-neighbor Ising universality for all investigated interaction ranges both on the linear chain and the square lattice.

The Andreev spectrum of a quantum dot embedded in a hybrid semiconductor-superconductor interferometer can be modulated by electrostatic gating, magnetic flux through the interferometer, and Zeeman splitting from an in-plane magnetic field. We demonstrate parity transitions in the embedded quantum dot system and show that the Zeeman-driven transition is accompanied by a 0-$\pi$ transition in the superconducting phase across the dot. We further demonstrate that flux through the interferometer modulates both dot parity and 0-$\pi$ transitions.

We report phase-resolved microwave magnetotransport measurements of a Coulomb-coupled quantum point contact in the edge state regime. We show that the inductive admittance is manifestly asymmetric under reversal of magnetic field, whereas the field-symmetric conductance is observed. Furthermore, the asymmetry is found to exhibit pronounced fluctuations as a function of magnetic field and transmission. This constitutes direct evidence that kinetic effects associated with the nonequilibrium polarization charge contribute to dynamical magnetoasymmetry in phase-coherent mesoscopic conductors. In addition, we find a striking magnetoasymmetry in the electronic transit time, providing important information about Coulomb coupling effects on quantum dynamics of electrons.

We have studied the commensurate-incommensurate phase transition, rotation epitaxy, and strain relief patterns in ${\mathrm{C}}_{60}$ overlayers grown on Cd(0001) with a low-temperature scanning tunneling microscopy. When deposited at low temperature (∼200 K), ${\mathrm{C}}_{60}$ molecules form the 10×10 high-order commensurate (HOC) phase with two different half-unit cells, resembling the $\mathrm{Si}\left(111\right)\text{−}7\times 7$ surface. Postannealing at room temperature (RT) results in the transition from HOC phase to incommensurate phase, in which strain relaxation takes place in the form of periodic vacancies and ${\mathrm{C}}_{60}$ heptamer arrays. In the case of RT deposition, parallel stripe domain walls appeared in the commensurate $2\sqrt{3}\times 2\sqrt{3}$ R30° phase. These results provide essential information for understanding the strain relaxation mechanism, and the role of substrate temperatures in the process of ${\mathrm{C}}_{60}$ thin films growth.

We demonstrate theoretically that an off-resonant circularly polarized electromagnetic field can induce a persistent current in carbon nanotubes, which corresponds to electron rotation about the nanotube axis. As a consequence, the nanotubes acquire magnetic moment along the axis, which depends on their crystal structure and can be detected in state-of-the-art measurements. This effect and related phenomena are analyzed within the developed Floquet theory describing the electronic properties of the nanotubes irradiated by the field.

We study the quantum ground-state phases of the one-dimensional disordered Bose-Hubbard model with attractive interactions, realized by a chain of superconducting transmon qubits or cold atoms. We map the phase diagram using perturbation theory and exact diagonalization. Compared to the repulsive Bose-Hubbard model, the quantum ground-state behavior is dramatically different. At strong disorder of the on-site energies, all the bosons localize into the vicinity of a single site, contrary to the Bose glass behavior of the repulsive model. At weak disorder, depending on hopping, the ground state is either superfluid or a $W$ state, which is a multisite and multiparticle entangled superposition of states where all the bosons occupy a single site. We show that the robustness of the $W$ phase against disorder diminishes as the total number of bosons increases.

The kagome metal ${\mathrm{KV}}_3{\mathrm{Sb}}_5$ hosts charge order, topologically nontrivial Dirac band crossings, and a superconducting ground state with unconventional characteristics, providing an ideal platform to investigate the interplay between different electronic states on the kagome lattice. Here we study the evolution of charge order and superconductivity in ${\mathrm{KV}}_3{\mathrm{Sb}}_5$ under hydrostatic pressure using electrical resistivity measurements. With the application of pressure, the superconducting transition temperature $T_{\mathrm{c}}=0.9$ K under ambient pressure quickly increases to 3.1 K at $p=0.4$ GPa, as charge order progressively weakens. Upon further increasing pressure, signatures of charge order disappear at $p_{\mathrm{c}1}\approx 0.5$ GPa and $T_{\mathrm{c}}$ is gradually suppressed, forming a superconducting dome that terminates at $p\approx 10$ GPa. Beyond $p\approx 10$ GPa, a second superconducting dome emerges with maximum $T_{\mathrm{c}}\approx 1.0$ K at $p_{\mathrm{c}2}\approx 22$ GPa, which becomes fully suppressed at $p\approx 28$ GPa. The suppression of superconductivity for the second superconducting dome is associated with the appearance of a unique high-pressure phase, possibly a distinct charge order.

Strong spin-orbital-coupling magnetic systems with the honeycomb structure can provide bond-directional interactions which may result in Kitaev quantum spin liquids and exotic anyonic excitations. However, one of the key ingredients in real materials—disorders—has been much less studied in Kitaev systems. Here we synthesized a trigonal ${\mathrm{SrIr}}_2{\mathrm{O}}_{6-\delta }$ with $\delta \approx 0.25$, which consists of two-dimensional honeycomb Ir planes with edge-sharing ${\mathrm{IrO}}_6$ octahedra. First-principles computation and experimental measurements suggest that the electronic system is gapped, and there should be no magnetic moment as the ${\mathrm{Ir}}^{5+}$ ion has no unpaired electrons. However, significant magnetism has been observed in the material, and it can be attributed to disorders that are most likely from oxygen vacancies. No magnetic order is found down to 0.05 K, and the low-temperature magnetic properties exhibit power-law behaviors in magnetic susceptibility and zero-field specific heat, and a single-parameter scaling of the specific heat under magnetic fields. These results provide strong evidence for the existence of the random singlet phase in ${\mathrm{SrIr}}_2{\mathrm{O}}_{6-\delta }$, which offers a different member to the family of spin-orbital entangled iridates and Kitaev materials.

The emergence of higher-order topological states is always considered to be determined by nontrivial topology of the bulk bands, and such the topological invariants strongly depend on specific symmetry of the bulk lattice. However, for real-physical systems, the intrinsic chiral-symmetry breaking can hinder the measurement of these states, and a spectrally isolated topological state always requires compensation to the on-site energy on the boundary sites. In this work, we reveal that in acoustic systems, the compensation is intensively determined by the surface impedance. Based on a regular Su-Schrieffer-Heeger (SSH) topological chain, we derive the analytical solutions of the topological states in acoustic systems and show that generalized chiral symmetry requires acoustic soft-wall boundary condition. Further, we propose a SSH-like chain and show that the surface impedance also crucially impacts the bulk topology. Finally, we extend our results to two-dimensional condition and demonstrate the consistency of the results. Our results provide new insights into the origin of the acoustic topological phenomena, which in turn offers a platform to design topological materials with desired topological properties.