The waiting time distribution has, in recent years, proven to be a useful statistical tool for characterizing transport in nanoscale quantum transport. In particular, as opposed to moments of the distribution of transferred charge, which have historically been calculated in the long-time limit, waiting times are able to detect nonrenewal behavior in mesoscopic systems. They have failed, however, to correctly incorporate backtunneling events. Recently, a method has been developed that can describe unidirectional and bidirectional transport on an equal footing: the distribution of first-passage times. Rather than the time between successive electron tunnelings, the first passage refers to the first time the number of extra electrons in the drain reaches $+1$. Here, we demonstrate the differences between first-passage time statistics and waiting time statistics in transport scenarios where the waiting time either cannot correctly reproduce the higher-order current cumulants or cannot be calculated at all. To this end, we examine electron transport through a molecule coupled to two macroscopic metal electrodes. We model the molecule with strong electron-electron and electron-phonon interactions in three regimes: (i) sequential tunneling and cotunneling for a finite bias voltage through the Anderson model, (ii) sequential tunneling with no temperature gradient and a bias voltage through the Holstein model, and (iii) sequential tunneling at zero bias voltage and a temperature gradient through the Holstein model. We show that for each transport scenario, backtunneling events play a significant role; consequently, the waiting time statistics do not correctly predict the renewal and nonrenewal behavior, whereas the first-passage time distribution does.

Even though the integer quantum Hall transition has been investigated for nearly four decades its critical behavior remains a puzzle. The best theoretical and experimental results for the localization length exponent $\nu$ differ significantly from each other, casting doubt on our fundamental understanding. While this discrepancy is often attributed to long-range Coulomb interactions, Gruzberg et al. [Phys. Rev. B 95, 125414 (2017)] recently suggested that the semiclassical Chalker-Coddington model, widely employed in numerical simulations, is incomplete, questioning the established central theoretical results. To shed light on the controversy, we perform a high-accuracy study of the integer quantum Hall transition for a microscopic model of disordered electrons. We find a localization length exponent $\nu =2.58\left(3\right)$ validating the result of the Chalker-Coddington network.

We study gapped boundaries of Abelian type-I fracton systems in three spatial dimensions. Using the X-cube model as our motivating example, we give a conjecture, with partial proof, of the conditions for a boundary to be gapped. In order to state our conjecture, we use a precise definition of fracton braiding and show that bulk braiding of fractons has several features that make it insufficient to classify gapped boundaries. Most notable among these is that bulk braiding is sensitive to geometry and is “nonreciprocal”; that is, braiding an excitation $a$ around $b$ need not yield the same phase as braiding $b$ around $a$. Instead, we define fractonic “boundary braiding,” which resolves these difficulties in the presence of a boundary. We then conjecture that a boundary of an Abelian fracton system is gapped if and only if a “boundary Lagrangian subgroup” of excitations is condensed at the boundary; this is a generalization of the condition for a gapped boundary in two spatial dimensions, but it relies on boundary braiding instead of bulk braiding. We also discuss the distinctness of gapped boundaries and transitions between different topological orders on gapped boundaries.

Coherent excitation of materials via ultrafast laser pulses can have interesting, observable dynamics in time-resolved photoemission measurements. The broad spectral width of ultrafast pump pulses can coherently excite multiple exciton energy levels. When such coherently excited states are probed by means of photoemission spectroscopy, interference between the polarization of different exciton levels can lead to observable coherent exciton beats. Here, we present the theoretical formalism for evaluating the time- and angle-resolved photoemission spectra (tr-ARPES) arising from the coherently excited exciton states in the regime of zero overlap between the pump and probe pulses. We subsequently apply our formalism to a simple model example of hydrogenic exciton energy levels to identify the dependencies that control the quantum beats. Our findings indicate that the most pronounced effect of coherent quantum excitonic beats is seen midway between the excited exciton energy levels and the central energy of the pump pulse provides tunability of this effect.

The propagation of waves through transmission eigenchannels in complex media is emerging as a new frontier of condensed matter and wave physics. A crucial step towards constructing a complete theory of eigenchannels is to demonstrate their spatial structure in any dimension and their wave-coherence nature. Here we show a surprising result in this direction. Specifically, we find that as the width of diffusive samples increases transforming from quasi-one-dimensional (1D) to two-dimensional (2D) geometry, notwithstanding the dramatic changes in the transverse (with respect to the direction of propagation) intensity distribution of waves propagating in such channels, the dependence of intensity on the longitudinal coordinate does not change and is given by the same analytical expression as that for quasi-1D. Furthermore, with a minimal modification, the expression describes also the spatial structures of localized resonances in strictly 1D random systems. It is thus suggested that the key ingredients of eigenchannels are not only universal with respect to the disorder ensemble and the dimension, but also of 1D nature and closely related to the resonances. Our findings open up a way to tailor the spatial energy density distribution in opaque materials.

The Aubry-André one-dimensional lattice model describes a particle hopping in a pseudorandom potential. Depending on its strength $\lambda$, all eigenstates are either localized $\left(\lambda >1\right)$ or delocalized $\left(\lambda <1\right)$. Near the transition, the localization length diverges like $\xi \sim {(\lambda -1)}^{-\nu }$ with $\nu =1$. We show that when the particle is initially prepared in a localized ground state and the potential strength is slowly ramped down across the transition, then—in analogy with the Kibble-Zurek mechanism—it enters the delocalized phase having finite localization length $\widehat{\xi }\sim {\tau }_Q^{\nu /(1+z\nu )}$. Here ${\tau }_Q$ is the ramp/quench time and $z$ is a dynamical exponent. At $\lambda =1$ we determine $z\simeq 2.37$ from the power-law scaling of an energy gap with a lattice size $L$. Even though for infinite $L$ the model is gapless, we show that the gap that is relevant for excitation during the ramp remains finite. Close to the critical point it scales like ${\xi }^{-z}$ with the value of $z$ determined by the finite-size scaling. It is the gap between the ground state and the lowest of those excited states that overlaps with the ground state enough to be accessible for excitation. We propose an experiment with a noninteracting BEC to test our prediction. Our hypothesis is further supported by considering a generalized version of the Aubry-André model possessing an energy-dependent mobility edge.

We have studied the low-temperature electrical transport properties of ${\mathrm{Pb}}_x{\left({\mathrm{SiO}}_2\right)}_{1-x}$ ($x$ being the Pb volume fraction) nanogranular films with thicknesses of $\sim 1000$ nm and $x$ spanning the dielectric, transitional, and metallic regions. It is found that the percolation threshold $x_c$ lies between 0.57 and 0.60. For films with $x\lesssim 0.50$, the resistivities $\rho$ as functions of temperature $T$ obey a $\rho \propto exp(\mathrm{\Delta }/k_{B}T)$ relation ($\mathrm{\Delta }$ being the local superconducting gap and $k_B$ the Boltzmann constant) below the superconducting transition temperature $T_c$ ($\sim 7$ K) of Pb granules. The value of the gap obtained via this expression is almost identical to that by single electron tunneling spectra measurement. The magnetoresistance is negative below $T_c$ and its absolute value is far larger than that above $T_c$ at a certain field. These observations indicate that single electron hopping (or tunneling), rather than Cooper pair hopping (or tunneling), governs the transport processes below $T_c$. The temperature dependence of resistivities shows reentrant behavior for the $0.50<x<0.57$ films. This effect is a consequence of the competition between resistance decrease due to the occurrence of superconductivity on isolated Pb grains and the enhancement of excitation resistance due to the opening of the energy gap on the grains. For the $0.60\lesssim x\lesssim 0.72$ films, the resistivities sharply decrease with decreasing temperature just below $T_c$, and then show a dissipation effect with further decreasing temperature. Treating the conducting paths composed of Pb particles as nanowires, we have found that the $R\left(T\right)$ data below $T_c$ can be well explained by a model that includes both thermally activated phase slips and quantum phase slips.

We report our numerical results for the effect of magnetic anisotropy on a skyrmion crystal with a high topological number of two, which was recently discovered in an itinerant electron model [R. Ozawa, S. Hayami, and Y. Motome, Phys. Rev. Lett. 118, 147205 (2017)]. By performing numerical simulations based on the kernel polynomial method and the Langevin dynamics for the Kondo lattice model on a triangular lattice, we find that the topological property remains robust against single-ion anisotropy, while the magnetic texture is deformed continuously. The resultant spin structure is characterized by three wave numbers (triple-$Q$ state), in which the $xy$ component of the spins forms a magnetic vortex crystal and the $z$ component of the spins behaves as a sinusoidal wave. For a larger anisotropy, we show that the system exhibits a phase transition from a skyrmion crystal to topologically trivial phases with vanishing scalar chirality: a single-$Q$ collinear state and double-$Q$ noncoplanar states for the easy-axis and easy-plane anisotropy, respectively. We also examine the effect of single-ion anisotropy in an external magnetic field, and find that the field range of the skyrmion crystal is rather insensitive to the anisotropy, in contrast to another skyrmion crystal with a topological number of one whose field range is considerably extended (reduced) by the easy-axis (easy-plane) anisotropy.

Polarization-analyzed small-angle neutron-scattering methods are used to determine the spin arrangements and experimental length scales of magnetic correlations in ordered three-dimensional assemblies of $\sim 7.4$-nm-diam core-shell ${\mathrm{Fe}}_3{\mathrm{O}}_4/{\mathrm{Mn}}_x{\mathrm{Fe}}_{3-x}{\mathrm{O}}_4$ nanoparticles. In moderate to high magnetic fields, the assemblies display a canted magnetic structure where the canting direction is coherent from nanoparticle to nanoparticle, in contrast to the less extended, more single-particle-like behavior for similar ferrite assemblies. The observed magnetic scattering is modeled by assuming that the interparticle dipolar coupling combined with Zeeman effects in a field leads to nanoparticle domains with preferred net spin alignments relative to packing symmetry axes. Over a range of fields and temperatures, the model qualitatively explains the observed scattering anomalies in terms of clusters that vary in area and thickness, highlighting the complex structures adopted in real, dense nanoparticle systems. The clusters often have a strong two-dimensional magnetic character which is attributed to structural stacking faults and the resulting influence of interparticle dipolar interactions for these magnetically soft nanoparticles.

$\mathrm{Li}{\mathbf{Sr}}_2\left[{\mathrm{CoN}}_2\right]$ single crystals were successfully grown out of Li-rich flux. Temperature- and field-dependent measurements of the magnetization in the range of $T=2–300\mathrm{K}$ and up to ${\mu }_0\mathit{H}=7\mathrm{T}$ as well as measurements of the heat capacity are presented. Ferromagnetic ordering emerges below $T_C=44\mathrm{K}$ and comparatively large coercivity fields of ${\mu }_{0}H=0.3\mathrm{T}$ as well as pronounced anisotropy are observed upon cooling. Polycrystalline samples of the Ca analog $\mathrm{Li}{\mathbf{Ca}}_2\left[{\mathrm{CoN}}_2\right]$ were obtained and investigated in a similar way. In both compounds Co manifests orbital contributions to the magnetic moment and large single-ion anisotropy caused by second-order spin-orbit couplings. Quantum chemistry calculations reveal a magnetic anisotropy energy of 7 meV, twice as large as the values reported for similar Co $d^8$ systems.

${\mathrm{Fe}}_{3-x}{\mathrm{GeTe}}_2$ is an itinerant ferromagnet composed of two-dimensional layers weakly connected by van der Waals bonding that shows a variety of intriguing phenomena. Inelastic neutron scattering measurements on bulk single crystals of ${\mathrm{Fe}}_{2.75}{\mathrm{GeTe}}_2$ were performed to quantify the magnetic exchange interaction energies and anisotropy. The observed inelastic excitations, which extend to a maximum energy of $\sim 75$ meV, are indicative of dominant in-plane correlations with negligible magnetic interactions between the layers. A spin gap of 3.7 meV is observed, allowing a measure of the magnetic anisotropy. The excitations are damped, reflective of both the magnetic site occupancy reduction of 25% on one Fe sublattice and the itinerant interactions. A minimal model is employed to describe the excitation spectra and extract magnetic exchange interaction values. The temperature evolution of the excitations are probed and correlations shown to persist above $T_c$, further supporting the low-dimensional nature of the magnetism.

We study theoretically the spectral and transport properties of a superconducting wire with a magnetic defect. We start by modeling the system as a one-dimensional magnetic Josephson junction and derive the equation determining the full subgap spectrum in terms of the normal-state transfer matrix for arbitrary length and exchange field of the magnetic region. We demonstrate that the quantum phase transition predicted for a short-range magnetic impurity, and associated with a change of the total spin of the system, also occurs in junctions of finite length. Specifically, we find that the total spin changes discontinuously by integer jumps when bound states cross the Fermi level. The spin can be calculated by using a generalization of the Friedel sum rule for the superconducting state, which we also derive. With these tools, we analyze the subgap spectrum of a junction with the length of the magnetic region smaller than the superconducting coherence length and demonstrate how phase transitions also manifest as a change of sign of the supercurrent.

In this work we study a molecular graphene model on the top of a superconductor in the presence of pseudomagnetic fields induced by coplanar strain fields. With the pseudomagnetic fields and the attractive interaction induced from the substrate, a flat-band superconductor can be achieved according to mean field analysis on the effective Hamiltonian. Based on a semiclassical approximation, we first show that the orbital limit is hugely enhanced by the pseudomagnetic fields. The physical reason is that the orbital angular momenta locking at $K$ and $K^{\prime }$ valleys due to the pseudomagnetic fields suppress the orbital magnetization from external magnetic fields. Considering the vanishing bandwidth in this system, we then study the effects of Gaussian fluctuations in both Hartree and pairing channels. We show that in the dilute limit, the phase transition is dominated by collective modes with critical temperatures much lower than the mean field results. At half-filling, our method gives no corrections to the mean field critical temperatures.

We analyze the electric current and magnetic field driven domain-wall motion in perpendicularly magnetized ultrathin ferromagnetic films in the presence of interfacial Dzyaloshinskii-Moriya interaction and both out-of-plane and in-plane uniaxial anisotropies. We obtain exact analytical Walker-type solutions in the form of one-dimensional domain walls moving with constant velocity due to both spin-transfer torques and out-of-plane magnetic field. These solutions are embedded into a larger family of propagating solutions found numerically. Within the considered model, we find the dependencies of the domain-wall velocity on the material parameters and demonstrate that adding in-plane anisotropy may produce domain walls moving with velocities in excess of 500 m/s in realistic materials under moderate fields and currents.

The kagome bands hosting exotic quantum phases generally and understandably pertain only to a kagome lattice. This has severely hampered the research of kagome physics due to the lack of real kagome-lattice materials. Interestingly, we discover that a coloring-triangle (CT) lattice, named after color-triangle tiling, also hosts kagome bands. We demonstrate first theoretically the equivalency between the kagome and CT lattices, and then computationally in photonic (waveguide lattice) and electronic (Au overlayer on electride $\mathrm{C}{\mathrm{a}}_2\mathrm{N}$ surface) systems by first-principles calculations. The theory can be generalized to even distorted kagome and CT lattices to exhibit ideal kagome bands. Our findings open an avenue to explore the alluding kagome physics.

We present a method for calculation of charge carrier mobility in systems with local electron-phonon interaction. The method is based on unitary transformation of the Hamiltonian to the form where the nondiagonal part can be treated perturbatively. The Green's functions of the transformed Hamiltonian were then evaluated using the Matsubara Green's functions technique. The mobility at low carrier concentration was subsequently evaluated from Kubo's linear response formula. The methodology was applied to investigate the carrier mobility within the one-dimensional Holstein model for a wide range of electron-phonon coupling strengths and temperatures. The results indicated that for low electron-phonon coupling strengths the mobility decreases with increasing temperature, while for large electron-phonon coupling the temperature dependence can exhibit one or two extremal points, depending on the phonon energy. Analytical formulas that describe such behavior were derived. Within a single framework, our approach correctly reproduces the results for mobility in known limiting cases, such as band transport at low temperatures and weak electron-phonon coupling and hopping at high temperatures and strong electron-phonon coupling.

First-principles calculations, in combination with the four-state energy mapping method, are performed to extract the magnetic interaction parameters of multiferroic ${\mathrm{BiFeO}}_3$. Such parameters include the symmetric exchange (SE) couplings and the Dzyaloshinskii-Moriya (DM) interactions up to second-nearest neighbors, as well as the single-ion anisotropy (SIA). All magnetic parameters are obtained not only for the $R3c$ structural ground state, but also for the $R3m$ and $R\overline{3}c$ phases in order to determine the effects of ferroelectricity and antiferrodistortion distortions, respectively, on these magnetic parameters. In particular, two different second-nearest-neighbor couplings are identified and their origins are discussed in details. Moreover, Monte Carlo (MC) simulations using a magnetic Hamiltonian incorporating these first-principles-derived interaction parameters are further performed. They result (i) not only in the accurate prediction of the spin-canted G-type antiferromagnetic structure and of the known magnetic cycloid propagating along a $\langle 1\overline{1}0\rangle$ direction, as well as their unusual characteristics (such as a weak magnetization and spin-density-waves, respectively), (ii) but also in the finding of another cycloidal state of low-energy and that awaits to be experimentally confirmed. Turning on and off the different magnetic interaction parameters in the MC simulations also reveal the precise role of each of them on magnetism.

We present an experimental study of a zero-phonon line (ZPL) in the absorption spectrum of Dy atoms solvated in superfluid He. The dopants reside in nanometer-sized spherical cavities known as atomic bubbles. We observe a temperature-dependent broadening of ZPL in the absorption spectrum. The effect is attributed to the scattering of thermal phonons on the atomic bubble that leads to the dephasing of the Dy transition dipole. The extrapolated ZPL intrinsic spectral width at zero temperature is 2300 times larger than the natural linewidth in a free atom. This can be assigned to a fast radiationless quenching of the upper state of the studied transition.

Superfluid ${}^3\mathrm{He}\text{−}B$ possesses three locally stable vortices known as a normal-core vortex $(o$ vortex), an $A$-phase-core vortex $(v$ vortex), and a double-core vortex $(d$ vortex). In this work, we study the effects of a magnetic field $(\lesssim 0.1$ T) parallel or perpendicular to the vortex axis on these structures by solving the two-dimensional Ginzburg-Landau equation for two different sets of strong coupling correction. The energies of the $v$ and $d$ vortices have nontrivial dependence on the magnetic field. As the parallel magnetic field increases, the $v$ vortex is energetically unstable even at high pressures and the $d$ vortex becomes energetically most stable at all possible pressures. In perpendicular magnetic field, the energy of the $v$ vortex is lower than that of the $d$ vortex in the high pressure regime. In addition, the orientation of the double cores in the $d$ vortex prefers to be parallel to the magnetic field at low pressures, while the $d$ vortex with the double cores perpendicular to the magnetic field is allowed to continuously deform into the $v$ vortex with increasing pressure.

In this work, we show that the checkerboard model exhibits the phenomenon of foliated fracton order. We introduce a renormalization-group transformation for the model that utilizes toric code bilayers as an entanglement resource and show how to extend the model to general three-dimensional manifolds. Furthermore, we use universal properties distilled from the structure of fractional excitations and ground-state entanglement to characterize the foliated fracton phase and find that it is the same as two copies of the X-cube model. Indeed, we demonstrate that the checkerboard model can be transformed into two copies of the X-cube model via an adiabatic deformation.