We investigate the Hall conductivity in a Sierpiński carpet, a fractal of Hausdorff dimension $d_f=ln\left(8\right)/ln\left(3\right)\approx 1.893$, subject to a perpendicular magnetic field. We compute the Hall conductivity using linear response and the recursive Green function method. Our main finding is that edge modes, corresponding to a maximum Hall conductivity of at least ${\sigma }_{xy}=\pm \frac{e^2}{h}$, seem to be generically present for arbitrary finite field strength, no matter how one approaches the thermodynamic limit of the fractal. We discuss a simple counting rule to determine the maximal number of edge modes in terms of paths through the system with a fixed width. This quantized edge conductance, as in the case of the conventional Hofstadter problem, is stable with respect to disorder and thus a robust feature of the system.

Cold atomic gases in a hexagonal optical lattice is a highly effective quantum simulator for exploring graphenelike physics. In this paper, we propose a feasible scheme to simulate and detect the Majorana dynamics with cold atoms in a bilayer hexagonal lattice. We explore the dynamics of a general Majorana particle, in which three key observables featuring the Majorana dynamics are studied, which include the pseudoenergy, orthogonality, and the fidelity. The results reveal that the fidelity is a good observable to distinguish Majorana from Dirac or Weyl dynamics. Through the decomposition of the Majorana equation, we address the Majorana Zitterbewegung, which is indeed the addition of two Dirac Zitterbewegung. Finally, we present a method to detect the Majorana dynamics with the quantum-state tomography implemented with quenches. Our scheme may provide an avenue for observing the phenomena described by the Majorana equation through bilayer graphene lattices.

We show that attractive spinor Bose-Einstein condensates under the action of spin-orbit coupling (SOC) and Zeeman splitting form self-sustained stable two- and three-dimensional (2D and 3D) states in free space, even when SOC acts in a lower-dimensional form. We find that two-dimensional states are stabilized by one-dimensional (1D) SOC in a broad range of chemical potentials, for atom numbers (or norm of the spinor wave function) exceeding a threshold value, which strongly depends on the SOC strength and vanishes at a critical point. The zero-threshold point is a boundary between single-peaked and striped states, realizing hybrids combining 2D and 1D structural features. In the vicinity of such a point, an asymptotic equation describing the bifurcation of the solitons from linear modes is derived and investigated analytically. We show that striped 3D solitary states are as well stabilized by 2D SOC, albeit in a limited range of chemical potentials and norms.

Combining electron paramagnetic resonance (EPR) with scanning tunneling microscopy (STM) enables detailed insight into the interactions and magnetic properties of single atoms on surfaces. A requirement for EPR-STM is the efficient coupling of microwave excitations to the tunnel junction. Here, we achieve a coupling efficiency of the order of unity by using a radio-frequency antenna placed parallel to the STM tip, which we interpret using a simple capacitive-coupling model. We further demonstrate the possibility to perform EPR-STM routinely above 4 K using amplitude as well as frequency modulation of the radio-frequency excitation. We directly compare different acquisition modes on hydrogenated Ti atoms and highlight the advantages of frequency and magnetic-field sweeps as well as amplitude and frequency modulation in order to maximize the EPR signal. The possibility to tune the microwave-excitation scheme and to perform EPR-STM at relatively high temperature and high power opens this technique to a broad range of experiments, ranging from pulsed EPR spectroscopy to coherent spin manipulation of single-atom ensembles.

We theoretically investigate dynamics of classical spins exchange coupled through an isotropic medium. The coupling is treated at the adiabatic level of the medium's response, which mediates a first order in frequency dissipative interaction along with an instantaneous Heisenberg exchange. The resultant damped spin precession yields exceptional points (EPs) in the coupled spin dynamics, which should be experimentally accessible with the existing magnetic heterostructures. In particular, we show that an EP is naturally approached in an antiferromagnetic dimer by controlling local damping, while the same is achieved by tuning the dissipative coupling between spins in the ferromagnetic case. Extending our treatment to one-dimensional spin chains, we show how EPs can emerge within the magnonic Brillouin zone by tuning the dissipative properties. The critical point, at which an EP pair emerges out of the Brillouin zone center, realizes a gapless Weyl point in the magnon spectrum. Tuning damping beyond this critical point produces synchronization (level attraction) of magnon modes over a finite range of momenta, both in ferromagnetic and antiferromagnetic cases. We thus establish that damped magnons can generically yield singular points in their band structure, close to which their kinematic properties, such as group velocity, become extremely sensitive to the control parameters.

We propose the ${\mathbb{Z}}_Q$ Berry phase as a topological invariant for higher-order symmetry-protected topological (HOSPT) phases for two- and three-dimensional systems. It is topologically stable for electron-electron interactions assuming the gap remains open. As a concrete example, we show that the Berry phase is quantized in ${\mathbb{Z}}_4$ and characterizes the HOSPT phase of the extended Benalcazar-Bernevig-Hughes (BBH) model, which contains the next-nearest-neighbor hopping and the intersite Coulomb interactions. In addition, we introduce the ${\mathbb{Z}}_4$ Berry phase for the spin-model analog of the BBH model. Furthermore, we demonstrate the Berry phase is quantized in ${\mathbb{Z}}_4$ for the three-dimensional version of the BBH model. We also confirm the bulk-corner correspondence between the ${\mathbb{Z}}_4$ Berry phase and the corner states in the HOSPT phases.

An external magnetic field is needed to drive a nanowire in proximity to an $s$-wave superconductor into a topological regime which supports Majorana end states. However, magnetic field generally suppresses the proximity superconducting gap induced on the nanowire. In recent experiments using InSb nanowires coupled to conventional superconductors such as Al and NbTiN, the induced proximity gap vanishes at magnetic fields $B\sim 1$ T. This results in a small superconducting gap on the wire and a narrow topological regime which is proportional to the strength of the magnetic field. In this work, we show that by placing nanowires in proximity to recently discovered Ising superconductors such as the atomically thin transition-metal dichalcogenide ${\mathrm{NbSe}}_2$, the topological superconducting gap on the wire can be maintained at a large magnetic field as strong as $B\sim 10$ T. This robust topological superconducting gap is induced by the unique equal-spin triplet Cooper pairs of the parent Ising superconductor. The strong magnetic field allows a topological regime ten times larger than those in InSb wires coupled to conventional superconductors. Our work establishes a realistic platform for building robust Majorana-based qubits.

Realization of an elemental solid-state quasicrystal has remained a distant dream so far in spite of extensive work in this direction for almost two decades. In the present work, we report the discovery of quasiperiodic ordering in a thick layer of elemental Sn grown on icosahedral $\left(i\right)$-Al-Pd-Mn. The scanning tunneling microscopy (STM) images and the low-energy electron diffraction patterns of the Sn layer show specific structural signatures that portray quasiperiodicity but are distinct from the substrate. Photoemission spectroscopy reveals the existence of the pseudogap around the Fermi energy up to the maximal Sn thickness. The structure of the Sn layer is modeled as a form of quasicrystalline clathrate on the basis of multiple supporting evidences: First, from ab initio total energy evaluation, the energy of bulk Sn clathrate quasicrystal is lower than the high-temperature metallic $\beta$-Sn phase, but higher than the low-temperature $\alpha$-Sn phase. A comparative study of the free slab energetics shows that surface energy favors clathrate over $\alpha$-Sn up to about 4-nm layer thickness and matches $\beta$-Sn for narrow window of slab thickness of 2–3 nm. Second, the bulk clathrate exhibits gap opening near Fermi energy, while the free slab form exhibits a pronounced pseudogap, which explains the pseudogap observed in photoemission. Third, the STM images exhibit good agreement with clathrate model. Finally, we establish the adlayer-substrate compatibility based on very similar (within 1%) the cage-cage separation in the Sn clathrate and the pseudo-Mackay cluster-cluster separation on the $i$-Al-Pd-Mn surface. Furthermore, the nucleation centers of the Sn adlayer on the substrate are identified and these are shown to be a valid part of the Sn clathrate structure. Thus, based on both experimental and ab initio density functional theory calculations, we propose that 4-nm-thick Sn adlayer deposited on fivefold surface of $i$-Al-Pd-Mn substrate is in fact a metastable realization of elemental, clathrate family quasicrystal.

Traditional approaches to controlling single spins in quantum dots require the generation of large electromagnetic fields to drive many Rabi oscillations within the spin coherence time. We demonstrate “flopping-mode” electric dipole spin resonance, where an electron is electrically driven in a Si/SiGe double quantum dot in the presence of a large magnetic field gradient. At zero detuning, charge delocalization across the double quantum dot enhances coupling to the drive field and enables low-power electric dipole spin resonance. Through dispersive measurements of the single-electron spin state, we demonstrate a nearly three order of magnitude improvement in driving efficiency using flopping-mode resonance, which should facilitate low-power spin control in quantum dot arrays.

We study the effect of local projective measurements on the quantum quench dynamics. As a concrete example, a one-dimensional Bose-Hubbard model is simulated by the matrix product state and time-evolving block decimation. We map out a global phase diagram in terms of the measurement rate in spatial space and time domain, which demonstrates a volume-to-area law entanglement phase transition. When the measurement rate reaches the critical value, we observe a logarithmic growth of entanglement entropy as the subsystem size or evolved time increases. Moreover, we find that the probability distribution of the single-site entanglement entropy distinguishes the volume and area law phases, similar to the case of disorder-induced many-body localization. We also investigate the scaling behavior of entanglement entropy and mutual information between two separated sites, which is indicative of a single universality class and thus suggests a possible unified description of this transition.

We consider the electronic spectrum near $M=(\pi ,\pi )$ in the nematic phase of FeSe $(T<T_{\mathrm{nem}})$ and make a detailed comparison with recent ARPES and STM experiments. Our main focus is the unexpected temperature dependence of the excitations at the $M$ point. These have been identified as having $xz$ and $yz$ orbital character well below $T_{\mathrm{nem}}$, but remain split at $T>T_{\mathrm{nem}}$, in apparent contradiction to the fact that in the tetragonal phase the $xz$ and $yz$ orbitals are degenerate. Here we present two scenarios which can describe the data. In both scenarios, hybridization terms present in the tetragonal phase leads to an orbital transmutation, a change in the dominant orbital character of some of the bands, between $T>T_{\mathrm{nem}}$ and $T\ll T_{\mathrm{nem}}$. The first scenario relies on the spin-orbit coupling at the $M$ point. We show that a finite spin-orbit coupling gives rise to orbital transmutation, in which one of the modes, identified as $xz$ ($yz)$ at $T\ll T_{\mathrm{nem}}$, becomes predominantly $xy$ at $T>T_{\mathrm{nem}}$ and hence does not merge with the predominantly $yz$ ($xz$) mode. The second scenario, complementary to the first, takes into consideration the fact that both ARPES and STM are surface probes. In the bulk, a direct hybridization between the $xz$ and $yz$ orbitals is not allowed at the $M$ point, however, it is permitted on the surface. In the presence of a direct $xz/yz$ hybridization, the orbital character of the $xz/yz$ modes changes from pure $xz$ and pure $yz$ at $T\ll T_{\mathrm{nem}}$ to $xz\pm yz$ at $T>T_{\mathrm{nem}}$, i.e., the two modes again have mono-orbital character at low $T$, but do not merge at $T_{\mathrm{nem}}$. We discuss how these scenarios can be distinguished in polarized ARPES experiments.

There has been a great interest in magnetic field induced quantum spin liquids in Kitaev magnets after the discovery of neutron scattering continuum and half-quantized thermal Hall conductivity in the material $\alpha \text{−}{\mathrm{RuCl}}_3$. In this work, we provide a semiclassical analysis of the relevant theoretical models, which enable us to treat large system sizes approximating the thermodynamic limit. We find a series of competing magnetic orders with fairly large unit cells at intermediate magnetic fields, which are mostly missed by previous studies. We show that quantum fluctuations are typically strong in these large unit cell orders, while the magnetic excitations, magnons, have a dispersion that resembles a scattering continuum. The huge quantity of magnon bands with finite Chern numbers also gives rise to an unusually large thermal Hall conductivity. Given the highly frustrated nature of the spin model, the large unit cell orders are likely to melt into the putative spin liquid in the quantum limit. Our work provides an important basis for a thorough investigation of emergent spin liquids and competing phases in Kitaev magnets.

We show that homogeneous lattice gauge theories can realize nonequilibrium quantum phases with long-range spatiotemporal order protected by gauge invariance instead of disorder. We study a kicked ${\mathbb{Z}}_2$-Higgs gauge theory and find that it breaks the discrete temporal symmetry by a period doubling. In a limit solvable by Jordan-Wigner analysis we extensively study the time-crystal properties for large systems and further find that the spatiotemporal order is robust under the addition of a solvability-breaking perturbation preserving the ${\mathbb{Z}}_2$ gauge symmetry. The protecting mechanism for the nonequilibrium order relies on the Hilbert space structure of lattice gauge theories, so that our results can be directly extended to other models with discrete gauge symmetries.

We construct the effective field theory for time-reversal symmetry-breaking multi-Weyl semimetals (MWSMs), composed of a single pair of Weyl nodes of (anti)monopole charge $n$, with $n=1,2,3$ in crystalline environment. From both the continuum and lattice models, we show that a MWSM with $n>1$ can be constructed by placing $n$ flavors of linearly dispersing simple Weyl fermions (with $n=1$) in a bath of an $\text{SU}\left(2\right)$ non-Abelian static background gauge field. Such an $\text{SU}\left(2\right)$ field preserves certain crystalline symmetry (fourfold rotational or $C_4$ in our construction), but breaks the Lorentz symmetry, resulting in nonlinear band spectra, namely, $E\sim {(p_x^2+p_y^2)}^{n/2}$, but $E\sim |p_z|$, for example, where momenta $\mathbf{p}$ is measured from the Weyl nodes. Consequently, the effective field theory displays $\text{U}\left(1\right)\times \text{SU}\left(2\right)$ non-Abelian anomalies, yielding the anomalous Hall effect, its non-Abelian generalization, and various chiral conductivities. The anomalous violation of conservation laws is determined by the monopole charge $n$ and a specific algebraic property of the $\text{SU}\left(2\right)$ Lie group, which we further substantiate by numerically computing the regular and isospin densities from the lattice models of MWSMs. These predictions are also supported from a strongly coupled (holographic) description of MWSMs. Altogether our findings unify the field-theoretic descriptions of MWSMs of arbitrary monopole charge $n$ (featuring $n$ copies of the Fermi arc surface states), predict signatures of non-Abelian anomaly in table-top experiments, and pave the way to explore the structure of anomalies for multifold fermions, transforming under arbitrary half-integer or integer spin representations.

Quantum impurity models are prevalent throughout many body physics, providing some prime examples of strongly correlated systems. Aside from being of great interest in themselves, they can provide deep insight into the effects of strong correlations in general. The classic example is the Kondo model wherein a magnetic impurity is screened at low energies by a noninteracting metallic bath. Here we consider a magnetic impurity coupled to a quantum wire with pairing interaction which dynamically generates a mass gap. Using Bethe ansatz, we solve the system exactly finding that it exhibits both screened and unscreened phases for an antiferromagnetic impurity. We determine the ground-state density of states and magnetization in both phases as well as the excitations. In contrast to the well studied case of magnetic impurities in superconductors, we find that there are no intragap bound states in the spectrum. The phase transition is not associated to a level crossing but with quantum fluctuations.

We introduce valence bond fluctuations, or bipartite fluctuations associated to bond-bond correlation functions, to characterize quantum spin liquids and the entanglement properties of them. Using analytical and numerical approaches, we find an identical scaling law between valence bond fluctuations and entanglement entropy in the two-dimensional Kitaev spin model and in one-dimensional chain analogs. We also show how these valence bond fluctuations can locate, via the linear scaling prefactor, the quantum phase transitions between the three gapped and the gapless Majorana semimetal phases in the honeycomb model. We then study the effect of a uniform magnetic field along the [111] direction opening a gap in the intermediate phase which becomes topological. We still obtain a robust signal to characterize the transitions toward the three gapped phases. The area-law behavior of such bipartite fluctuations in two dimensions is also distinguishable from the one in the Néel magnetic state that follows a volume square growth.

We propose two-dimensional (2D) Ising-type ferromagnetic semiconductors ${\mathrm{TcSiTe}}_3, {\mathrm{TcGeSe}}_3$, and ${\mathrm{TcGeTe}}_3$ with high Curie temperatures around 200–500 K. Owing to large spin-orbit couplings, the large magnetocrystalline anisotropy energy (MAE), large anomalous Hall conductivity, and large magneto-optical Kerr effect were discovered in these intriguing 2D materials. By comparing all possible 2D $M{\text{GeTe}}_3$ materials ($M=3d,4d,5d$ transition metals), we found a large orbital moment around $0.5{\mu }_B$ per atom and a large MAE for ${\mathrm{TcGeTe}}_3$. The large orbital moments are revealed to be from the comparable crystal fields and electron correlations in these Tc-based 2D materials. The microscopic mechanism of the high Curie temperature is also addressed. Our findings reveal the unique magnetic behaviors of 2D Tc-based materials and present a family of 2D ferromagnetic semiconductors with large MAE and Kerr rotation angles that would have wide applications in designing spintronic devices.

Bloch-Boltzmann transport theory fails to describe the carrier diffusion in current crystalline organic semiconductors, where the presence of large-amplitude thermal molecular motions causes substantial dynamical disorder. The charge transport mechanism in this original situation is now understood in terms of a transient localization of the carriers' wave functions, whose applicability is, however, limited to the strong disorder regime. To deal with the ever-improving performances of new materials, we develop here a unified theoretical framework that includes transient localization theory as a limiting case and smoothly connects with the standard band description when molecular disorder is weak. The theory, which specifically addresses the emergence of dynamical localization corrections to semiclassical transport, is used to determine a “transport phase diagram” of high-mobility organic semiconductors.

We use spatially resolved magneto-optical Kerr microscopy to track the complete microstates of arrays of perpendicular anisotropy nanomagnets during magnetization hysteresis cycles. These measurements, along with our statistical methodology, allow us to disentangle the intertwined effects of nearest-neighbor interactions, disorder, and stochasticity on magnetization switching. We find that the nearest-neighbor correlations depend on both interaction strength and disorder. We also find that although the global characteristics of the hysteretic switching are repeatable, the exact microstate sampled is stochastic with the behavior of individual islands varying between nominally identical runs. These protocols provide another way of understanding the relationship between macrohistory and microhistory in artificial magnetic arrays.

Majorana bound states are zero-energy excitations of topological superconductors that obey non-Abelian exchange statistics and are basic building blocks for topological quantum computation. To observe and exploit their extraordinary properties, we need to be able to properly manipulate them, for instance by braiding a couple of them in real space. We propose a setup based on the helical edges of two-dimensional topological insulators (2DTIs) that allows for a high degree of tunability by only controlling a handful of superconducting phases. In particular, our setup allows us to move the Majoranas along a single edge and to move them across two different edges coupled by a quantum point contact. Robustness against nonoptimal control of the phases is also discussed. This proposal constitutes an essential step forward toward realizing 2DTI-based architectures capable of performing braiding of Majoranas in a feasible way.