We study how the shape of a periodic magnetic field affects the presence of Majorana bound states (MBS) in a nanowire-superconductor system. Motivated by the field configurations that can be produced by an array of nanomagnets, we consider spiral fields with an elliptic cross section and fields with two sinusoidal components. We show that MBS are robust to imperfect helical magnetic fields. In particular, if the amplitude of one component is tuned to the value determined by the superconducting order parameter in the wire, the MBS can exist even if the second component has a much smaller amplitude. We also explore the effect of the chemical potential on the phase diagram. Our analysis is both numerical and analytical, with good agreement between the two methods.

The conductivity of a two-dimensional HgTe quantum well with a width $\sim 6.3\mathrm{nm}$, close to the transition from ordinary to topological insulating phases, is studied. The Fermi level is supposed to get to the overall energy gap. The consideration is based on the percolation theory. We have found that the width fluctuations convert the system to a random mixture of domains with positive and negative energy gaps with internal edge states formed near zero gap lines. In the case with no potential fluctuations, the conductance of a finite sample is provided by a random edge states network. The zero-temperature conductivity of an infinite sample is determined by the free motion of electrons along the zero-gap lines and tunneling between them. The conductance of a single $p-n$ junction, which is crossed by the edge state, is found. The result is applied to the situation when potential fluctuations transform the system to a mixture of $p$- and $n$-domains. It is stated that the tunneling across $p-n$ junctions forbids the low-temperature conductivity of a random system, but the latter is restored due to the random edge states crossing the junctions.

Recently, first-principles calculations based on density functional theory have been widely used to predict the temperature-dependent infrared spectrum of polar materials, but the calculations are usually limited to the harmonic frequency (0 K) and three-phonon scattering damping for the zone-center infrared-active optical phonon modes, and fail to predict the high-temperature infrared optical properties of materials such as sapphire ($\alpha -{\text{Al}}_2{\text{O}}_3$), GaAs, $\text{Ti}{\text{O}}_2$, etc., due to the neglect of high-order phonon scattering damping and phonon frequency shift. In this work, we implemented first-principles calculations to predict the temperature-dependent infrared dielectric function of polar materials by including four-phonon scattering and phonon frequency shift. The temperature-dependent phonon damping by including three- and four-phonon scattering as well as the phonon frequency shift by including cubic and quartic anharmonicity and the thermal expansion effect are calculated based on anharmonic lattice dynamics method. The infrared dielectric function of $\alpha -{\text{Al}}_2{\text{O}}_3$ is parameterized, and then the temperature-dependent infrared optical reflectance is determined. We find that our predictions agree better with the experimental data than the previous density functional theory-based methods. This work will help to effectively predict the thermal radiative properties of polar materials at elevated temperature, which is generally difficult to measure, and will enable predictive design of new materials for radiative applications.

Localization of wave functions is arguably the most familiar effect of disorder in quantum systems. It has been recently argued [V. Khemani, R. Nandkishore, and S. L. Sondhi, Nat. Phys. 11, 560 (2015)] that, contrary to naive expectation, manipulation of a localized site in the disordered medium may produce a disturbance over a length scale much larger than the localization length, $\xi$. Here we report on the observation of this nonlocal phenomenon in electronic transport experiments. Being a wave property, visibility of this effect hinges upon quantum coherence, and its spatial scale may be ultimately limited by the phase-coherent length of the disordered insulator. Evidence for quantum coherence in the Anderson-insulating phase may be obtained from magnetoresistance measurements which, however, are useful mainly in thin films. The technique used in this work offers an empirical method to measure this fundamental aspect of Anderson insulators even in relatively thick samples.

Although Zitterbewegung—the jittery motion of relativistic particles—was known since 1930 and was predicted in solid-state systems long ago, it has been directly measured so far only in so-called quantum simulators, i.e., quantum systems under strong control, such as trapped ions and Bose-Einstein condensates. A reason for the lack of further experimental evidence is the transient nature of wave-packet Zitterbewegung. Here, we study how the jittery motion can be manipulated in Dirac systems via time-dependent potentials with the goal of slowing down/preventing its decay or of generating its revival. For the harmonic driving of a mass term, we find persistent Zitterbewegung modes in pristine, i.e., scattering free, systems. Furthermore, an effective time-reversal protocol—the “Dirac quantum time mirror”—is shown to retrieve Zitterbewegung through echoes.

We report on the magnetic and elastic properties of ${\mathrm{Er}}_3{\mathrm{Ru}}_4{\mathrm{Al}}_{12}$ in static and pulsed magnetic fields up to 58 T. From the ultrasound results, we obtain evidence for a phase transition at 2 K related to magnetic ordering. Furthermore, in the paramagnetic state, ${\mathrm{Er}}_3{\mathrm{Ru}}_4{\mathrm{Al}}_{12}$ shows pronounced anomalies in the magnetization and elastic moduli as a function of temperature and magnetic field. We explain our findings using a crystal-electric-field (CEF) model that includes quadrupolar interactions and propose a CEF level scheme for this material. However, the CEF effects cannot explain all field-induced anomalies, which indicates that refined models are needed for explaining these.

High-pressure synthesis techniques have allowed for the growth of ${\mathrm{Sn}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$ samples beyond the ambient In-saturation limit of $x=0.5$ ($T_c\sim 4.5$ K). In this study we present measurements of the temperature dependence of the London penetration depth $\mathrm{\Delta }\lambda \left(T\right)$ in this superconducting doped topological insulator for $x=0.7$, where $T_{c,\text{onset}}\approx 5$ K. The results indicate fully gapped BCS-like behavior, ruling out odd-parity $A_{2u}$ pairing; however, odd-parity $A_{1u}$ pairing is still possible. Critical field values measured below 1 K and other superconducting parameters are also presented.

We study the evolution of the magnetic phase diagram of ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Ge}$ alloys with concentration $x\left(0\le x\le 0.3\right)$ by small-angle neutron scattering. We unambiguously observe the absence of a skyrmion (Sk) lattice (or $A$ phase) in bulk MnGe and its onset under a small Mn/Fe substitution. The $A$ phase is there endowed with extremely small Sks, potentially resulting in a high density, and is stabilized within a very large temperature region and a field range which scales with the Fe concentration. Our findings highlight the possibility to fine tune the properties of skyrmion lattices by means of chemical doping.

The $\delta$ phase of ${\mathrm{Bi}}_2{\mathrm{O}}_3$ has the highest known value of oxide ion conductivity within the solid state and, therefore, remains a benchmark for the development of future generations of electrolyte materials to fuel-cell technologies. Conventionally, the high value of conductivity in $\delta \text{−}{\mathrm{Bi}}_2{\mathrm{O}}_3$ has been explained by a large concentration of inherent vacancies together with a strongly polarizable Bi-O bond. We show from ab initio molecular dynamics simulations that short “chains” of collective migrating oxygens also contribute strongly to the high value of conductivity with the single-particle Nernst-Einstein (N.E.) conductivity to collective (dc) conductivity ${\sigma }^{\mathrm{N}.\mathrm{E}.}/{\sigma }^{\mathrm{dc}}\sim 0.57\pm 0.05$ at 1033 K. The nature of collective events is investigated from a hopping model, the distinct part of the van Hove function and from the extent of dynamical heterogeneities in the superionc regime. Results from this analysis indicate that the main contribution to collective ionic diffusion in $\delta \text{−}{\mathrm{Bi}}_2{\mathrm{O}}_3$ involves short collinear chains of two or three oxygens. These chains are either initiated by an oxygen that jumps into an already occupied oxygen cavity (where they coexist for a very short time before the residential oxygen is kicked out of its cavity) or from a jump into a vacant cavity which triggers a next-nearest-neighboring oxygen to migrate. Since $\delta \text{−}{\mathrm{Bi}}_2{\mathrm{O}}_3$ is easily stabilized in a range of environments, the nature of these collective chains can give important insight into the design of $\delta \text{−}{\mathrm{Bi}}_2{\mathrm{O}}_3$-based fuel cells for the future.

Recently, the discovery of room-temperature superconductivity (SC) was experimentally realized in the fcc phase of ${\mathrm{LaH}}_{10}$ under megabar pressures. This SC of compressed ${\mathrm{LaH}}_{10}$ has been explained in terms of strong electron-phonon coupling (EPC), but the detailed nature of how the large EPC constant and high superconducting transition temperature $T_{\mathrm{c}}$ are attained has not yet been clearly identified. Based on the density-functional theory and the Migdal-Eliashberg formalism, we reveal the presence of two nodeless, anisotropic superconducting gaps on the Fermi surface (FS). Here, the small gap is mostly associated with the hybridized states of H $s$ and La $f$ orbitals on the three outer FS sheets, while the large gap arises mainly from the hybridized state of neighboring H $s$ or $p$ orbitals on the one inner FS sheet. Further, we find that compressed ${\mathrm{YH}}_{10}$ with the same sodalitelike clathrate structure has the two additional FS sheets, enhancing EPC constant and $T_{\mathrm{c}}$. It is thus demonstrated that the nature of room-temperature SC in compressed ${\mathrm{LaH}}_{10}$ and ${\mathrm{YH}}_{10}$ features the multiband pairing of hybridized electronic states with large EPC constants.

Since the discovery of two-gap superconductivity in bulk ${\mathrm{MgB}}_2$, many efforts have been devoted to searching for multigap superconductors. Recently, a monolayer of ${\mathrm{MgB}}_2$ and a trilayer film of ${\mathrm{AlB}}_4$ were predicted to be robust three-gap superconductors. Here we investigate using the fully anisotropic Migdal-Eliashberg theory the superconducting behaviors in a series of boron-based monolayers and trilayer films that are dynamically stable but not synthesized experimentally heretofore. Remarkably, we find that the trilayer film of ${\mathrm{MgB}}_4$ has an exciting four-gap superconducting nature with a high transition temperature $T_c\sim 52$ K. We demonstrate that this high-$T_c$ four-gap superconductivity is closely related to the Fermi surface exhibiting an unusually strong electron-phonon coupling with evident four-region distribution characteristics. The electron-lattice coupling is dominated by the acoustic modes of a softening kink and the high-energy optical phonons around the Brillouin-zone center, of which the former ones place the system on the verge of a latent charge density wave state. To our knowledge, no material with more than three superconducting gaps has been reported. At the same time, we also show that the ${\mathrm{GaB}}_4$ trilayer film has a robust three-gap nature with $T_c\sim 51$ K, and the trilayer films of ${\mathrm{BeB}}_4$ and ${\mathrm{LiB}}_4$ are two-gap superconductors with $T_c$'s of $\sim 39$ and 32 K, respectively.

Planar normal state resistivity data taken from three families of cuprate superconductors are compared with theoretical calculations from the recent extremely correlated Fermi liquid theory (ECFL) [B. S. Shastry, Phys. Rev. Lett. 107, 056403 (2011)]. The two hole-doped cuprate materials LSCO and BSLCO and the electron-doped material LCCO have yielded rich data sets at several densities $\delta$ and temperatures $T$, thereby enabling a systematic comparison with theory. The recent ECFL resistivity calculations for the highly correlated $t\text{−}{t}^{\prime }\text{−}J$ model by us give the resistivity for a wide set of model parameters [B. S. Shastry and P. Mai, New J. Phys. 20, 013027 (2018); P. Mai and B. S. Shastry, Phys. Rev. B 98, 205106 (2018)]. After using x-ray diffraction and angle-resolved photoemission data to fix parameters appearing in the theoretical resistivity, only one parameter, the magnitude of the hopping $t$, remains undetermined. For each data set, the slope of the experimental resistivity at a single temperature-density point is sufficient to determine $t$, and hence the resistivity on absolute scale at all remaining densities and temperatures. This procedure is shown to give a fair account of the entire data.

Magnetism, coupled with nontrivial band topology, can bring about many interesting and exotic phenomena, so that magnetic topological materials have attracted persistent research interest. However, compared with nonmagnetic topological materials (TMs), the magnetic TMs are less studied, since their magnetic structures and topological phase transitions are usually complex and the first-principles predictions are usually sensitive on the effect of Coulomb interaction. In this work we present a comprehensive investigation of $X{\mathrm{Fe}}_4{\mathrm{Ge}}_2(X=\text{Y},\text{Lu})$ and ${\mathrm{Mn}}_3\mathrm{Pt}$, and find these materials to be filling-enforced magnetic topological metals. Our first-principles calculations show that $X{\mathrm{Fe}}_4{\mathrm{Ge}}_2(X=\text{Y},\text{Lu})$ host Dirac points near the Fermi level at high symmetry point $S$. These Dirac points are protected by $P\mathcal{T}$ symmetry $(P$ and $\mathcal{T}$ are inversion and time-reversal transformations, respectively) and a twofold screw rotation symmetry. Moreover, through breaking $P\mathcal{T}$ symmetry, the Dirac points would split into Weyl nodes. ${\mathrm{Mn}}_3\mathrm{Pt}$ is found to host fourfold degenerate band crossings in the whole high symmetry path of $A–Z$. We also utilize the $\mathrm{GGA}+U$ scheme to take into account the effect of Coulomb repulsion and find that the filling-enforced topological properties are naturally insensitive on $U$.

We study the excitonic fine structure of CdSe nanocrystals (also known as quantum dots) using atomic effective pseudopotentials in combination with the screened configuration interaction method, and we obtain excellent agreement with experiment. The direct comparison between atomistic and effective mass results reveals qualitative differences that become apparent almost as soon as confinement effects start to play a role, i.e., for the experimentally most relevant sizes. We proceed with a comparison of the wurtzite and zinc-blende fine structure as a function of size and ellipticity. We show that the absorption of significantly oblate zinc-blende nanocrystals can be very similar to “spherical” wurtzite nanocrystals. On the other hand, if the nanocrystals have no ellipticity but different crystal structures, the fine structure differs significantly. Conversely, structures with high ellipticity, either oblate or prolate, with different crystal structures show similar fine structures.

We explore the dynamics of two-dimensional massless Dirac fermions within a quantum shutter approach, which involves the time evolution of an initial cutoff plane wave. We show that the probability density is governed by an interplay between diffraction in time and Zitterbewegung phenomena typical of relativistic quantum shutter systems with nonzero mass. The time diffraction appears as an oscillatory pattern in the probability density, similar to the effect predicted by Moshinsky in 1952 [Phys. Rev. 88, 625 (1952)] for Schrödinger free matter waves. The Zitterbewegung manifests itself as high-frequency oscillations embedded in the time-diffraction profile. We found that these two transient effects are induced by the transverse momentum component of the incident wave $k_y$ that acts as an effective mass of the system. Furthermore, this effective mass can be manipulated by tuning the incidence angle of the initial quantum state, which allows us to control the frequencies of the transients. In particular, we demonstrate that near a normal incidence condition, the Zitterbewegung appears as a series of quantum beats in the probability density, with a beating frequency $2k_y{v}_F$, where $v_F$ is the Fermi velocity.

Out-of-time-order correlators (OTOCs), vigorously being explored as a measure of quantum chaos and information scrambling, is studied here in the natural and simplest multiparticle context of bipartite systems. We show that two strongly chaotic and weakly interacting subsystems display two distinct regimes in the growth of OTOCs. The first is dominated by intrasubsystem scrambling, when an exponential growth with a positive Lyapunov exponent is observed until the Ehrenfest time. This regime is essentially independent of the interaction, while the second one is an interaction dominated exponential approach to saturation that is universal and described by a random matrix model. This simple random matrix model of weakly interacting strongly chaotic bipartite systems, previously employed for studying entanglement and spectral transitions, is approximately analytically solvable for its OTOC. The example of two coupled kicked rotors is used to demonstrate the different regimes, and the extent to which the random matrix model is applicable. We remark that the second regime implies an emergent invariance of the OTOC under local unitary transformations suggesting that the rate of relaxation is connected to the entangling power of the interaction. That the two regimes correspond to delocalization in the subsystems followed by intersubsystem mixing is seen via the participation ratio in phase space. We also point out that the second, universal, regime alone exists when the observables are in a sense locally prescrambled.

We combine first-principles density functional calculations with empirical relationships for the Coulomb interactions in the monomer model of $\kappa -{(\mathrm{BEDT}-\mathrm{TTF})}_{2}X$. This enables us to calculate the parameters for the model of coupled dipolar and spin degrees of freedom proposed by Hotta [Phys. Rev. B 82, 241104 (2010)], and Naka and Ishihara [J. Phys. Soc. Jpn. 79, 063707 (2010)]. In all materials studied, retaining only the largest interactions leads to a transverse-field Ising model of the dipoles. This quantifies, justifies, and confirms recent claims that the dipoles are of crucial importance for understanding these materials. We show that the competition between two effects are responsible for a range of behaviors found in the dipoles in different $\kappa -{(\mathrm{BEDT}-\mathrm{TTF})}_{2}X$ salts. (i) The intradimer hopping, $t_{b1}$, which gives rise to the transverse field in the Ising model for the dipoles ($H^T=2t_{b1}$), is between a third and a tenth smaller in the mercuric materials than for the mercury-free salts. (ii) The Ising model of dipoles is in the quasi-one-dimensional limit for the mercuric salts, but quasi-two-dimensional (between the square and isotropic triangular limits) for the mercury-free materials. Thus, the dimensionless critical fields will be quite different in the two sets of materials. Effect (ii) is much larger than effect (i). Simple explanations of both effects based on the band structures of the different salts are given. We show that dipolar order and even short-range dipolar correlations have a profound impact on the nature of the interdimer magnetic (superexchange) interactions. For example, dipole crystallization drives the materials toward quasi-one-dimensional magnetic interactions, which could be important for understanding the spin liquids found in some of these materials.

We theoretically study magnon-phonon hybrid excitations in a square lattice ferromagnet subjected to a magnetic field by varying the field direction. The bulk bands of hybrid excitations, which are referred to as magnon-polarons, are investigated by considering all three phonon modes: Vertical phonon, transverse phonon, and longitudinal phonon. We show that the topological properties of three hybridizations are different in terms of the Berry curvature and the Chern numbers. We also find that the topological properties of the bands can be controlled by changing the direction of the magnetic field, exhibiting one or more topological phase transitions. The dependence of thermal Hall conductivity as a function of magnetic field direction is proposed as an experimental probe of our theoretical results.

Topological phases of matter are the center of much current interest, with promising potential applications in, e.g., topologically protected transport and quantum computing. Traditionally such states are prepared by tuning the system Hamiltonian while coupling it to a generic bath at very low temperatures. However, this approach is often ineffective, especially in cold-atom systems. It was recently shown that topological phases can emerge much more efficiently even in the absence of a Hamiltonian, by properly engineering the interaction of the system with its environment, to directly drive the system into the desired state. Here we concentrate on dissipatively induced two-dimensional Chern insulator (lattice quantum Hall) states. We employ open quantum systems tools to explore their transport properties, such as persistent currents and the conductance in the steady state, in the presence of various Hamiltonians. We find that, in contrast with equilibrium systems, the usual confinement of currents to the edge, as well as the usual relation between the Chern topological number and the Hall conductance, could be broken. We explore the intriguing edge behaviors and elucidate under which conditions the Hall conductance is quantized.