Topological insulator nanowires with uniform cross section, combined with a magnetic flux, can host both a perfectly transmitted mode and Majorana zero modes. Here we consider nanowires with rippled surfaces—specifically, wires with a circular cross section with a radius varying along its axis—and we calculate their transport properties. At zero doping, chiral symmetry places the clean wires (no impurities) in the AIII symmetry class, which results in a $\mathbb{Z}$ topological classification. A magnetic flux threading the wire tunes between the topologically distinct insulating phases, with perfect transmission obtained at the phase transition. We derive an analytical expression for the exact flux value at the transition. Both doping and disorder break the chiral symmetry and the perfect transmission. At finite doping, the interplay of surface ripples and disorder with the magnetic flux modifies quantum interference such that the amplitude of Aharonov-Bohm oscillations reduces with increasing flux, in contrast to wires with uniform surfaces where it is flux-independent.

The critical properties of the antiferromagnetic Heisenberg model on the three-dimensional stacked-triangular lattice are studied by means of a large-scale Monte Carlo simulation in order to get insight into the controversial issue of the criticality of the noncollinear magnets with the $O\left(3\right)\times O\left(2\right)$ symmetry. The maximum size studied is ${384}^3$, considerably larger than the sizes studied by the previous numerical works on the model. Availability of such large-size data enables us to examine the detailed critical properties including the effect of corrections to the leading scaling. Strong numerical evidence of the continuous nature of the transition is obtained. Our data indicate the existence of significant corrections to the leading scaling. Careful analysis by taking account of the possible corrections yields critical exponents estimates, $\alpha =0.44\left(3\right), \beta =0.26\left(2\right), \gamma =1.03\left(5\right), \nu =0.52\left(1\right), \eta =0.02\left(5\right)$, and the chirality exponents, ${\beta }_{\kappa }=0.40\left(3\right)$ and ${\gamma }_{\kappa }=0.77\left(6\right)$, supporting the existence of the $O\left(3\right)$ chiral [or $O\left(3\right)\times O\left(2\right)$] universality class governed by a “chiral” fixed point. We also obtain an indication that the underlying fixed point is of the focus type, characterized by the complex-valued correction-to-scaling exponent, $\omega =0.1_{-0.05}^{+0.4}+i0.7_{-0.4}^{+0.1}$. The focus-like nature of the chiral fixed point accompanied by the spiral-like renormalization-group (RG) flow is likely to be the origin of the apparently complicated critical behavior. The results are compared and discussed in conjunction with the results of other numerical simulations, several distinct types of RG calculations including the higher-order perturbative massive and massless RG calculations and the nonperturbative functional RG calculation, and the conformal-bootstrap program.

The tunability of the electronic topological transition is fundamentally important to unveil new quantum matters. Here, we report the observation of pressure-induced electronic anomaly below 12.0 GPa in $\mathrm{N}{\mathrm{b}}_{0.25}\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ using a combination of electrical transport, synchrotron x-ray diffraction, Raman-scattering spectroscopy measurements, and first-principles calculations. At ambient pressure, the band-structure calculations demonstrate the $\mathrm{N}{\mathrm{b}}_{0.25}\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ is a heavily electron-doped semiconductor with multiple band structure. With applying pressure, it is shown that the pressure can induce Fermi-surface reconstruction at a time-reversal invariant point. We further present evidence of multiband superconductivity characterized by an upward curvature in the upper critical field in the pressurized $\mathrm{N}{\mathrm{b}}_{0.25}\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ crystal. The superconducting critical parameters of pressurized $\mathrm{N}{\mathrm{b}}_{0.25}\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$ crystal are obtained. Furthermore, the superconducting phase diagram under high pressure is discussed within BCS theory. These findings highlight the critical role of the multiple-band structure induced by strong hybridization between the $\mathrm{Nb}-4d$ and $\mathrm{Bi}/\mathrm{Se}-p$ orbitals in accessing quantum states.

We consider a $(2+1)$-dimensional Wilson-Fisher boson coupled to a $(3+1)$-dimensional U(1) gauge field. This theory possesses a strong-weak duality in terms of the coupling constant $e$ and is self-dual at a particular value of $e$. We derive exact relations between transport coefficients for a $\nu =1$ quantum Hall state at the self-dual point. Using boson-fermion duality, we map the $\nu =1$ bosonic quantum Hall state to a Fermi sea of the dual fermion and observe that the exact relationships between transport coefficients at the bosonic self-dual point are reproduced by a simple random-phase approximation (RPA), coupled with a Drude formula, in the fermionic theory. We explain this success of the RPA by pointing out a cancellation of a parity-breaking term in the fermion theory which occurs only at the self-dual point, resulting in the fermion self-dual theory explored previously. In addition, we argue that the equivalence of the self-dual structure can be understood in terms of electromagnetic duality or modular invariance, and these features are not inherited by the nonrelativistic cousins of the present model.

Majorana billiards are finitely sized, arbitrarily shaped superconducting islands that host Majorana bound states. We study the fermion-parity switches of the ground state of Majorana billiards. In particular, we study the density and statistics of these fermion-parity switches as a function of applied magnetic field and chemical potential. We derive formulas that specify how the average density of fermion-parity switches depends on the geometrical shape of the billiard. Moreover, we show how oscillations around this average value are determined by the classical periodic orbits of the billiard. Finally, we find that the statistics of the spacings of these fermion-parity switches are universal and are described by a random matrix ensemble, the choice of which depends on the antiunitary symmetries of the system in its normal state. We thus demonstrate that “one can hear (information about) the shape of a Majorana billiard” by investigating its “fermion-parity switch spectrum.”

We predict three full Heusler compounds $X{\mathrm{InPd}}_2$ ($X$ = Zr, Hf, and Ti) to be potential candidates for type-II Dirac semimetals. The crystal symmetry of these compounds have appropriate chemical environment with a unique interplay of inversion, time-reversal, and mirror symmetries. These symmetries help to give six pairs of type-II Dirac nodes on the ${\mathrm{C}}_4$-rotation axis, closely located at/near the Fermi level. Using first-principles calculations, symmetry arguments, and crystal-field splitting analysis, we illustrate the occurrence of such Dirac nodes in these compounds. Bulk Fermi surfaces have been studied to understand the Lorentz symmetry breaking and Lifshitz transition (LT) of Fermi surfaces. Bulk nodes are projected on the (001) and (111) surfaces, which form the surface Fermi arcs, that can further be detected by probes such as angle resolved photo-emission and scanning tunneling spectroscopy. By analyzing the evolution of arcs with changing chemical potential, we prove the fragile nature and the absence of topological protection of the Dirac arcs. Our predicted compounds overcome the limitations of the previously reported ${\mathrm{PtTe}}_2$ class of compounds.

We extend random matrix theory to consider randomly interacting spin systems with spatial locality. We develop several methods by which arbitrary correlators may be systematically evaluated in a limit where the local Hilbert space dimension $N$ is large. First, the correlators are given by sums over stacked planar diagrams which are completely determined by the spectra of the individual interactions and a dependency graph encoding the locality in the system. We then introduce heap freeness as a generalization of free independence, leading to a second practical method to evaluate the correlators. Finally, we generalize the cumulant expansion to a sum over dependency partitions, providing the third and most succinct of our methods. Our results provide tools to study dynamics and correlations within extended quantum many-body systems which conserve energy. We further apply the formalism to show that quantum satisfiability at large $N$ is determined by the evaluation of the independence polynomial on a wide class of graphs.

The harmonic Hall measurement is widely used to determine the equivalent field of current-induced spin-orbit torque in ferromagnet/normal metal bilayers. We report that this method suffers from various thermoelectric artifacts that have not been considered. We propose and experimentally demonstrate how to eliminate major thermoelectric artifacts using, namely, the four-direction (4-D) methods interchanging current and field polarities, which allow us to determine the magnitudes and angular dependences of spin-orbit torques more accurately than a conventional method. The proposed 4-D method will be useful for searching suitable materials for device applications operated by spin-orbit torques.

In this article we present the fabrication of freestanding thin-film nanobridges of Ir. We perform magnetoconductance (MC) measurements of atomic contacts and monoatomic chains of Ir, realized by the mechanically controlled break-junction method. We observe continuous changes of the MC on the field scale of several tesla, as observed earlier for atomic-size contacts of two other strong paramagnets, Pd and Pt. The amplitude and the shape of the MC depend on the orientation of the magnetic field as well as on subtle details of the atomic arrangement, as confirmed by stretching studies of the contacts. Both positive dominant MC and negative dominant MC occur and are attributed to collinear or noncollinear alignment of the magnetic moments of the electrodes, respectively. By careful manipulation of the chain geometry we are able to study the transition between these two cases, which is hallmarked by a complex MC behavior. For special arrangements the MC almost vanishes. Our findings are in agreement with recent calculations of the geometry dependence of the magnetic anisotropy energy and open a route to tailor the MC behavior as required for particular applications.

Using a prototype model for proximity-induced superconductivity on a bilayer square lattice, we show that interlayer tunneling can drive change in topology of the Bogoliubov quasiparticle bands. Starting with topologically trivial superconductors, transitions to a nontrivial $p_x+i{p}_y$ state and back to another trivial state are discovered. We characterize these phases in terms of edge-state spectra and Chern indices. We show that these transitions can also be controlled by experimentally viable control parameters, the bandwidth of the metallic layer, and the gate potential. Insights from our results on a simple model for proximity-induced superconductivity may open up a new route to discover topological superconductors.

Recently, detailed real-space imaging using scanning tunneling spectroscopy of the vortex lattice in a weakly pinned $a$-MoGe thin film revealed that the vortex lattice melts in two steps with temperature or magnetic field, going first from a vortex solid to a hexatic vortex fluid and then from a hexatic vortex fluid to an isotropic vortex liquid. In this paper, we show that the resistance in the hexatic vortex fluid state is extremely sensitive to radio-frequency electromagnetic perturbation. In the presence of very low-amplitude excitation above few kilohertz, the resistance increases by several orders of magnitude. On the other hand, when the superconductor is well shielded from external electromagnetic radiation, the dissipation in the sample is very small and the resistance is below our detection limit.

There is growing experimental evidence that indicates discrete symmetry-breaking-like time-reversal ($\mathcal{T}$), parity ($\mathcal{P}$), and $C_4$ lattice rotation in the pseudogap state of underdoped copper-oxide-based (cuprate) superconductors. The discrete symmetry breaking manifests a true phase transition to an ordered state. A detailed thermodynamic understanding of these orders can answer various puzzles related to the nature of the transition at the pseudogap temperature $T^{*}$. In this work, we investigate the thermodynamic signature of $\mathcal{T}\mathcal{\text{−}}\mathcal{P}$ symmetry breaking considering superconductivity (SC) and bond-density wave (BDW) as two primary orders. The BDW can generate both modulating charge and current densities. This framework takes into account an intricate competition between the ubiquitous charge density wave and SC, which is prominent in various cuprates in the underdoped regime. We demonstrate that within the mean-field approach of competing BDW and SC orders, a $\mathcal{T}\mathcal{\text{−}}\mathcal{P}$ breaking ground state of coexisting BDW and SC can be stabilized, provided the BDW itself breaks $\mathcal{T}\text{−}\mathcal{P}$. But this ground state ceases to occur at higher temperatures. However, we show that fluctuations in SC and BDW can bring about the emergence of an unusual translational symmetry preserving order due to a preemptive phase transition by spontaneously breaking $\mathcal{T}\mathcal{\text{−}}\mathcal{P}$ at a higher temperature before the primary orders set in. We refer to this order as magnetoelectric loop current (MELC) order. We present the possible nature of the phase transition for this incipient MELC order and discuss some experimental relevance.

We investigated the temperature dependence of the saturation magnetization $M_S\left(T\right)$ and magnetic anisotropy constant $K_u\left(T\right)$ of ${\mathrm{CoMnO}}_3$ with an ilmenite structure, which is known as an orbital ferrimagnet. Because of strong antiferromagnetic coupling between the ${\mathrm{Co}}^{2+}$ spin $(d^7\text{:}S=3/2)$ and ${\mathrm{Mn}}^{4+}$ spin $(d^3\text{:}S=3/2)$ in ${\mathrm{CoMnO}}_3$, the net magnetic moment is considered to originate only from the orbital angular momentum [(OAM); $\langle L\rangle \approx 1]$ of ${\mathrm{Co}}^{2+}$. Experimental results for ${\mathrm{CoMnO}}_3$ epitaxial films clearly show that $K_u\left(T\right)$ is proportional to $M_S\left(T\right)$ for a wide temperature range up to the transition temperature, suggesting that $K_u\left(T\right)$ is proportional to $\langle L\rangle$. An electron theory based on the cluster model for $K_u$ and the OAM of ${\mathrm{Co}}^{2+}$ at 0 K also indicates that $K_u$ is proportional to the OAM and to the orbital angular anisotropy of ${\mathrm{Co}}^{2+}$.

Clusters of single spins form the relevant spin entities in the formation of long-range magnetic order in spin cluster Mott insulators. Such type of spin order bears resemblance to molecular crystals, and we therefore may expect a prototypical spin wave spectrum which can be divided into low-energy external and high-energy internal cluster spin wave modes. Here, we study high-energy spin cluster excitations in the spin cluster Mott insulator ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ by means of spontaneous Raman scattering. Multiple high-energy optical magnon modes are observed, of which the Raman activity is shown to originate in the Elliot-Loudon scattering mechanism. Upon crossing the long-range ordering transition temperature the magnetic modes significantly broaden, corresponding to scattering from localized spin excitations within the spin clusters. Different optical phonon modes show a strong temperature dependence, evidencing a strong magnetoelectric coupling between optical phonons and the high-energy spin cluster excitations. Our results support the picture that ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ can be regarded as a solid-state molecular crystal of spin nature.

We perform systematic first-principles calculations to investigate the spin-phonon coupling (SPC) of $\mathrm{C}{\mathrm{r}}_2\mathrm{G}{\mathrm{e}}_2\mathrm{T}{\mathrm{e}}_6$ (CGT) monolayer (ML). It is found that the $E_{\mathrm{g}}$ phonon mode at $211.8\mathrm{c}{\mathrm{m}}^{-1}$ may have a SPC as large as $3.19\mathrm{c}{\mathrm{m}}^{-1}$, as it alters the direct exchange interaction across Cr-Cr pairs. The strength of SPC of the CGT ML can be decreased by an in-plane lattice stretch. These results provide useful insights for the understanding of SPC in two-dimensional magnetic semiconductors and may guide the design of spintronic and spin Seebeck materials and devices.

One-dimensional planar magnonic crystals are usually fabricated as a sequence of stripes intentionally or accidentally separated by nonmagnetic spacers. The influence of spacers on shaping the spin-wave spectra is complex and still not completely clarified. We perform detailed numerical studies of the one-dimensional single- and bicomponent magnonic crystals comprised of a periodic array of thin ferromagnetic stripes separated by nonmagnetic spacers. We show that the dynamic dipolar interactions between the stripes, mediated even by ultranarrow nonmagnetic spacers, lead to a significant increase in the frequency of the ferromagnetic resonance mode, while simultaneously reducing the spin-wave group velocity. We attribute these spectral deformations to the modifications of dipolar pinning and shape anisotropy, both of which are dependent on the width of the spacers and the thickness of the stripes, as well as changes with the dynamical magnetic volume charges formed due to inhomogeneous spin-wave amplitude.

Among the recently widely studied van der Waals layered magnets $\mathrm{Cr}{X}_3$ ($X=\mathrm{Cl}$, Br, I), $\mathrm{CrC}{\mathrm{l}}_3$ monolayer (ML) is particularly puzzling: it is shown by experiments to have only an in-plane magnetic easy axis and, furthermore, all previous first-principles calculation results contradict this. Through systematic first-principles calculations, we unveil that the in-plane shape anisotropy that dominates over the weak perpendicular magnetocrystalline anisotropy is responsible for the in-plane magnetic easy axis of $\mathrm{CrC}{\mathrm{l}}_3$ ML. To tune the in-plane ferromagnetism of $\mathrm{CrC}{\mathrm{l}}_3$ ML into the desirable perpendicular one, we propose substituting Cr with isovalent tungsten (W). We find that $\mathrm{CrWC}{\mathrm{l}}_6$ has a strong perpendicular magnetic anisotropy and a high Curie temperature up to 76 K. Our work not only gives insight into understanding the two-dimensional ferromagnetism of van der Waals MLs but also sheds new light on engineering their performances for nanodevices.

Many key features of the higher-dimensional Sachdev-Ye-Kitaev (SYK) model at finite $N$ remain unknown. Here we study the SYK chain consisting of $N\left(N\ge 2\right)$ fermions per site with random interactions and hoppings between neighboring sites. In the limit of vanishing SYK interactions, from both supersymmetric field theory analysis and numerical calculations we find that the random hopping model exhibits Anderson localization at finite $N$, irrespective of the parity of $N$. Moreover, the localization length scales linearly with $N$, implying no Anderson localization only at $N=\infty$. For finite SYK interaction $J$, from the exact diagonalization we show that there is a dynamic phase transition between many-body localization and thermal diffusion as $J$ exceeds a critical value $J_c$. In addition, we find that the critical value $J_c$ decreases with the increase of $N$, qualitatively consistent with the analytical result of $J_c/t\propto \frac{1}{N^{5/2}logN}$ derived from the weakly interacting limit.

We report the appearance of multiple numbers of completely flat band states in an extended Lieb lattice model in two dimensions with five atomic sites per unit cell. We also show that this edge-centered square lattice can host intriguing topologically nontrivial phases when intrinsic spin-orbit (ISO) coupling is introduced in the microscopic description of the corresponding tight-binding Hamiltonian of the system. This ISO coupling strength acts like a complex next-nearest-neighbor hopping term for this model and can be, in principle, tuned in a real-life experimental setup. In the presence of this ISO coupling, the band spectrum of the system gets gapped out, leading to nonzero integer values of the spin Chern number for different bands, indicating the nontrivial topological properties of the system. Furthermore, we show that for certain values of the ISO coupling, nearly flat bands with nonzero Chern numbers emerge in this lattice model. This opens up the possibility of realizing interesting fractional quantum spin Hall physics in this model when interaction is taken into account. This study might be very useful in an analogous optical lattice experimental setup. A possible application of our results can also be anticipated in the field of photonics using single-mode photonic waveguide networks.