As the first intrinsic antiferromagnetic topological insulator, ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ has provided a material platform to realize various emergent phenomena arising from the interplay of magnetism and band topology. Here, by investigating (${\mathrm{Mn}}_{1-x}{\mathrm{Pb}}_x){\mathrm{Bi}}_2{\mathrm{Te}}_4(0\le x\le 0.82)$ single crystals via the x-ray, electrical transport, magnetometry and neutron measurements, chemical analysis, external pressure, and first-principles calculations, we reveal the magnetic dilution effect on the magnetism and band topology in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. With increasing $x$, both lattice parameters $a$ and $c$ expand linearly by around 2%. All samples undergo the paramagnetic to A-type antiferromagnetic transition with the $\mathrm{N}\acute{\text{e}}\mathrm{el}$ temperature decreasing lineally from 24 K at $x=0$ to 2 K at $x=0.82$. Our neutron data refinement of the $x=0.37$ sample indicates that the ordered moment is 4.3(1)${\mu }_B$/Mn at 4.85 K and the amount of the ${\mathrm{Mn}}_{\mathrm{Bi}}$ antisites is negligible within the error bars. Isothermal magnetization data reveal a slight decrease of the interlayer plane-plane antiferromagnetic exchange interaction and a monotonic decrease of the magnetic anisotropy due to diluting magnetic ions and enlarging the unit cell. For $x=0.37$, the application of external pressures enhances the interlayer antiferromagnetic coupling, boosting the $\mathrm{N}\acute{\text{e}}\mathrm{el}$ temperature at a rate of 1.4 K/GPa and the saturation field at a rate of 1.8 T/GPa. Furthermore, our first-principles calculations reveal that the band inversion in the two end materials, ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ and ${\mathrm{PbBi}}_2{\mathrm{Te}}_4$, occurs at the $\mathrm{\Gamma }$ and $Z$ point, respectively, while two gapless points appear at $x=$ 0.44 and $x=$ 0.66, suggesting possible topological phase transitions with doping.

We examine the transport properties of magnetically doped topological insulator (TI) thin films subject to correlated nonmagnetic disorder. For the disorder we choose a quasiperiodic potential with a random phase. We restrict the disorder to a central region, which is coupled to two leads in a clean quantum spin Hall insulator (QSHI) state and concentrate on different orientations of the quasiperiodicity in the two-dimensional central region. In the case of a diagonally oriented or purely longitudinal quasiperiodicity we find different topological Anderson insulator (TAI) phases, with a quantum anomalous Hall insulator (QAHI), a quantum spin Chern insulator (QSCI), or a QSHI phase being realized before the Anderson insulation takes over at large disorder strength. Quantized transport from extended bulk states is found for diagonal quasiperiodicity in addition to the above TAI phases that are also observed for the case of uncorrelated disorder. For a purely transverse orientation of the quasiperiodicity the emerging QSHI and QSCI phases persist to arbitrarily strong disorder potential. These topological phase transitions (except to the Anderson insulator phase) can be understood from a self consistent Born approximation.

The magnetic free energy is usually quadratic in the magnetic field and depends on the mutual orientation of the magnetic field and the crystalline axes. Tiny in magnitude, this magnetocrystalline anisotropy energy (MAE) is nevertheless indispensable for the existence of permanent magnets. Here, we show that in ${\mathrm{Mn}}_3\mathrm{Sn}$, a noncollinear antiferromagnet that has attracted much attention following the discovery of its large anomalous Hall effect, the free energy of the spins has superquadratic components, which drive the MAE. We experimentally demonstrate that the thermodynamic free energy includes terms odd in the magnetic field [$F\left(H^3\right)+F\left(H^5\right)$] and generating sixfold and 12-fold angular oscillations in the torque response. We show that they are quantitatively explained by theory, which can be used to quantify relevant energy scales (Heisenberg, Dzyaloshinskii-Moriya, Zeeman, and single-ion anisotropy) of the system. Based on the theory, we conclude that in contrast to common magnets, what drives the MAE in ${\mathrm{Mn}}_3\mathrm{Sn}$ is the field-induced deformation of the spin texture.

Recent studies have shown that moiré flat bands in twisted bilayer graphene (TBG) can acquire nontrivial Berry curvatures when aligned with a hexagonal boron nitride substrate, which can be manifested as a correlated Chern insulator near the 3/4 filling. In this Letter, we show that the large Berry curvatures in the moiré bands lead to a strong nonlinear Hall (NLH) effect in strained TBG with general filling factors. Under a weak uniaxial strain $\sim 0.1\%$, the Berry curvature dipole which characterizes the nonlinear Hall response can be as large as $\sim 200\text{Å}$, exceeding the values of previously known nonlinear Hall materials by two orders of magnitude. The dependence of the giant NLH effect as a function of electric gating, strain, and twist angle is further investigated systematically. Importantly, we point out that the giant NLH effect appears generically for a twist angle near the magic angle due to the strong susceptibility of nearly flat moiré bands to symmetry breaking induced by strains, which can even induce a topological band inversion. Our results establish TBG as a promising platform for investigating nonlinear effects such as the NLH effect, the nonlinear Nernst effect, and the nonlinear thermal Hall effect due to its giant Berry curvature dipole.

We report studies of the Fermi surface (FS) of isotopically pure polycrystalline ${}^7\mathrm{Li}$ from ambient pressure to 4.7 GPa. Shubnikov–de Haas (SdH) oscillations at 300 mK in external magnetic fields up to 35 T are measured to map the spherical parts of the FS of lithium. Our ambient pressure data show that the principal SdH frequencies consist of three distinct peaks at $41.25\pm 0.05, 41.65\pm 0.05$, and $42.05\pm 0.05\mathrm{kT}$, which are theoretically consistent with the presence of two crystal structure domains exhibiting nearly spherical FS. The size of the spherical parts of the FS is compatible with bcc and fcc crystal structures. The measured frequencies at 41.25 and 42.65 kT present direct quantitative evidence for the spherical deformation of the FS in fcc Li. Our high-pressure data show that while the FS of Li deforms under compression, it remains mostly spherical up to 4.7 GPa and the pressure dependence of the SdH frequency is consistent with the theoretically calculated pressure dependence in the fcc structure. Finally, we find that the electron effective mass does not deviate under pressure significantly from its ambient pressure value.

In insulators, the longitudinal resistivity becomes infinitely large at zero temperature. For classical insulators, the Hall conductivity becomes zero at the same time. However, there are special systems, such as two-dimensional quantum Hall insulators, in which a more complex scenario is observed at high magnetic fields. Here, we report experimental evidence for a quasiquantized Hall insulator in the quantum limit of the three-dimensional compound $\mathrm{Sr}{\mathrm{Si}}_2$. Our measurements reveal a magnetic-field range, in which the longitudinal resistivity diverges with decreasing temperature, while the Hall conductivity approaches a quasiquantized value that is given only by the conductance quantum and the Fermi wave vector in the field direction. The quasiquantized Hall insulator appears in a magnetic field induced insulating ground state of three-dimensional materials and is deeply rooted in quantum Hall physics.

In this paper, we investigate the driven dynamics of the localization transition in the non-Hermitian Aubry-André model with the periodic boundary condition. Depending on the strength of the quasiperiodic potential $\lambda$, this model undergoes a localization-delocalization phase transition. We find that the localization length $\xi$ satisfies $\xi \sim {\varepsilon }^{-\nu }$ with $\varepsilon$ being the distance from the critical point and $\nu =1$ being a universal critical exponent independent of the non-Hermitian parameter. In addition, from the finite-size scaling of the energy gap between the ground state and the first excited state, we determine the dynamic exponent $z$ as $z=2$. The critical exponent of the inverse participation ratio for the $n\mathrm{th}$ eigenstate is also determined as $s=0.1197$. By changing $\varepsilon$ linearly to cross the critical point, we find that the driven dynamics can be described by the Kibble-Zurek scaling (KZS). Moreover, we show that the KZS with the same set of the exponents can be generalized to the localization phase transitions in the excited states.

Rejuvenation of hydrodynamic transport in solids provides a new window to study the collective motion of electrons, where electrons behave like a viscous fluid akin to classical liquids. So far the discussion on the fate of hydrodynamic electronics in the presence of disorder scattering is largely phenomenological, and a systematical study is still lacking. Here we investigate the hydrodynamic properties of Dirac electron fluid in graphene from a microscopic viewpoint. We present strong evidence that, due to frequent electron-hole collisions, the shear viscosity can be enhanced by electron-disorder scattering in the low-energy region, which is in sharp contrast to the common sense of traditional Fermi liquids. Moreover, we clarify that the anomalous behavior of Dirac electron fluid can be also revealed by the dynamic and magneto-hydrodynamics. Therefore, our paper demonstrates the exotic landscape of hydrodynamic electronics in graphene, and presents experimentally relevant responses to quantify the effects of electronic viscosity.

We investigate the features arising from hydrodynamic effects in graphene and phosphorene devices with finite heat sources, using ab initio calculations to go beyond Callaway's model and inform a full linearized scattering operator, and solving the phonon Boltzmann transport equation through energy-based deviational Monte Carlo methods. We explain the mechanisms that create those hydrodynamic features, showing that boundary scattering and the relation of sample dimensions to the nonlocal length $\ell$ are the determinant factors, regardless of the relative importance of normal versus resistive scattering. From this point of view, the nonlocal length $\ell$ reflects the ability of scattering to randomize the heat flux, and we show that approximations made on the scattering operator may have, through the value of $\ell$, qualitative consequences on the signatures of hydrodynamic behavior.

A family of pentagonal quasicrystals can be defined by projecting a section of the five-dimensional cubic lattice to two dimensions. A single parameter, the sum of intercepts $\mathrm{\Gamma }={\sum }_j{\gamma }_j$, describes this family by defining the cut in the five-dimensional space. Each value of $0\le \mathrm{\Gamma }\le \frac{1}{2}$ defines a unique local isomorphism class for these quasicrystals, with $\mathrm{\Gamma }=0$ giving the Penrose lattice. Except for a few special values of $\mathrm{\Gamma }$, these lattices lack simple inflation-deflation rules making it hard to count how frequently a given local configuration is repeated. We consider the vertex-tight-binding model on these quasicrystals and investigate the strictly localized states (LS) for all values of $\mathrm{\Gamma }$. We count the frequency of localized states both by numerical exact diagonalization on lattices of ${10}^5$ sites and by identifying localized state types and calculating their perpendicular space images. While the imbalance between the number of sites forming the two sublattices of the bipartite quasicrystal grows monotonically with $\mathrm{\Gamma }$, we find that the localized state fraction first decreases and then increases as the distance from the Penrose lattice grows. The highest LS fraction of $10.17\%$ is attained at $\mathrm{\Gamma }=0.5$ while the minimum is $4.5\%$ at $\mathrm{\Gamma }\simeq 0.12$. The LS on the even sublattice are generally concentrated near sites with high symmetry, while the LS on the odd sublattice are more uniformly distributed. The odd sublattice has a higher LS fraction, having almost three times the LS frequency of the even sublattice at $\mathrm{\Gamma }=0.5$. We identify 20 LS types on the even sublattice, and their total frequency agrees well with the numerical exact diagonalization result for all values of $\mathrm{\Gamma }$. For the odd sublattice, we identify 45 LS types. However, their total frequency remains significantly below the numerical calculation, indicating the possibility of more independent LS types.

We propose a method to study nonequilibrium dynamics of scalar fields starting from non-Gaussian initial conditions using Keldysh field theory. We use it to study dynamics of phonons coupled to noninteracting bosonic and fermionic baths starting from initial Fock states. We find that in one dimension long-wavelength phonons coupled to fermionic baths do not thermalize at low and high bath-temperatures. At low temperature, constraints from energy-momentum conservation lead to a narrow bandwidth of particle-hole excitations and the phonons effectively do not see this bath. On the other hand, the strong band-edge divergence of the particle-hole density of states leads to an undamped polaritonlike mode of the dressed phonons above the band edge of the particle-hole excitations. These undamped modes contribute to the lack of thermalization of long wavelength phonons at high temperatures. In higher dimensions, these constraints and the divergence of density of states are weakened and lead to thermalization at all wavelengths.

We experimentally demonstrate the reversible motion of skyrmions driven by the controlled thermal fluctuations in a chiral magnet FeGe. A temperature gradient applied to the chiral magnet not only induces a flow of electrons but also excites a flow of magnons. Consequently, it is found that the skyrmion shows directional thermal diffusion toward two opposite directions along the gradient of temperature. We show that the skyrmions driven by the temperature gradient move from the cold terminal to the hot terminal due to the effect of magnon current induced by the temperature gradient. An obvious transverse shift of skyrmions is observed, which indicates the thermal-induced skyrmion Hall effect. Moreover, the thermal diffusion of skyrmions from the hot terminal to the cold terminal with a Hall motion as a result of competition of the magnon current, entropic force, and the spin-transfer torques induced by the thermally excited electron flow is also observed when the temperature at the hot terminal is high enough. Our results demonstrate an efficient manipulation of skyrmion dynamics by a controllable temperature gradient, which may provide a promising way for the realization of caloritronic applications based on topological spin textures.

We study the quantum dynamics of Josephson-junction arrays. We find isolated groups of low-entanglement eigenstates that persist even when the Josephson interaction is strong enough to destroy the overall organization of the spectrum in multiplets, and a perturbative description is no longer possible. These eigenstates lie in the inner part of the spectrum, far from the spectral edge, and provide a weak ergodicity breaking, reminiscent of the quantum scars. Due to the presence of these eigenstates, initializing with a charge-density-wave state, the system does not thermalize and the charge-density-wave order persists for long times. Considering global ergodicity probes, we find that the system tends toward more ergodicity for increasing system size: The parameter range where the bulk of the eigenstates look nonergodic shrinks for increasing system size. We study two geometries, a one-dimensional chain and a two-leg ladder. In the latter case, adding a magnetic flux makes the system more ergodic.

We performed scanning tunneling microscopy and spectroscopy (STM/STS) measurements to investigate the Zintl phase ${\mathrm{Eu}}_5{\mathrm{In}}_2{\mathrm{Sb}}_6$, a nonsymmorphic antiferromagnet. The theoretical prediction of a nontrivial Fermi surface topology stabilized by the nonsymmorphic symmetry motivated our research. On the cleaved (010) plane, we obtained striped patterns that can be correlated to the stacking of the [${\mathrm{In}}_2{\mathrm{Sb}}_6{]}^{10-}$ double chains along the crystallographic $c$ axis. The attempted cleavage along the $a$ axis revealed a more complex pattern. We combined the STS measurement on nonreconstructed (010) and (081) surfaces with DFT calculations to further elucidate the electronic structure of ${\mathrm{Eu}}_5{\mathrm{In}}_2{\mathrm{Sb}}_6$. From our investigations so far, direct experimental evidence of the predicted topological surface states remains elusive.

Strong light-matter interactions in van der Waals heterostructures (vdWHs) made of two-dimensional (2D) transition metal dichalcogenides (TMDs) provide a fertile ground for optoelectronic applications. Of particular interest are photoexcited interlayer electron-hole pairs, where electrons and holes are localized in different monolayers. Here, we present an ab initio quantum transport framework relying on maximally localized Wannier functions and the nonequilibrium Green's functions to explore light-matter interactions and charge transport in 2D vdWHs from first principles. Electron-photon scattering is accurately taken into account through dedicated self-energies. As testbed, the behavior of a ${\mathrm{MoSe}}_2\text{−}{\mathrm{WSe}}_2$ PIN photodiode is investigated under the influence of a monochromatic electromagnetic signal. Interlayer electron-hole pair generations are observed even in the absence of phonon-assisted processes. The origin of this phenomenon is identified as the delocalization of one valence band state over both monolayers composing the vdWH.

Atomic sandwiches consisting of In layers with coverages ranging from $\sim 0.5$ to $\sim 2.5$ monolayers atop a single-atomic-layer ${\mathrm{NiSi}}_2$ have been grown on Si(111) and have been explored using a set of experimental techniques, i.e., scanning tunneling microscopy, angle-resolved photoelectron spectroscopy, and in situ low-temperature transport measurements, accompanied by the density functional theory calculations. It has been found that each of the three In phases forming on the ${\mathrm{NiSi}}_2/\mathrm{Si}\left(111\right)$ substrate has its definite counterpart among the In phases forming on the bare Si(111) surface. Structural, electronic, and transport properties of the single- and double-atomic In layers have been elucidated in detail.

The electronic states in ternary compound ${\mathrm{SnSb}}_2{\mathrm{Te}}_4$ wwere studied by first-principles and tight-binding calculations, and two pairs of topological Shockley surface bands below its Fermi energy were revealed theoretically. One shows the Rashba-type structure and the other shows a more complicated $\omega$-shaped bending structure. Combined with spin- and angle-resolved photoemission spectroscopy measurements, the existence of the predicted topological surface states was confirmed. Our theoretical and experimental investigations reveal the complex topological structures in ternary topological insulators, providing a new platform for studying novel topological properties in materials.

Materials with zero energy band gap display intriguing properties including high sensitivity of the electronic band structure to external stimulus such as pressure or magnetic field. An interesting candidate for zero energy band gap is Weyl nodes at the Fermi level $E_{\mathrm{F}}$. A prerequisite for the existence of Weyl nodes is to either have inversion or time reversal symmetry broken. Weyl nodes in systems with broken time reversal symmetry are ideal to realize the tunability of the electronic band structure by magnetic field. Theoretically, it has been shown that in ferromagnetic Weyl materials, the band structure is dependent upon the magnetization direction and thus the electronic bands can be tuned by controlling the magnetization direction. Here we demonstrate, by analysis of the Hall resistivity, tuning of the band structure in a kagome Weyl ferromagnetic metal ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$ with magnetization and magnetic field. Owing to spin-orbit coupling, we observe changes in the band structure depending on the magnetization direction that amount to a decrease in the net carrier density by a factor of 4 when the magnetization lies in the kagome plane as compared to when the magnetization is along the $c$ axis. Our discovery opens the way for tuning the carrier density in ferromagnetic materials.

The accuracy of effective masses predicted by density functional theory depends on the exchange-correlation functional employed, with nonlocal hybrid functionals giving more accurate results than semilocal functionals. In this article, we benchmark the performance of the Perdew-Burke-Ernzerhof (PBE), Tran-Blaha modified Becke-Johnson (TB-mBJ), and the hybrid Heyd-Scuseria-Ernzerhof (HSE06) exchange-correlation functionals and potentials for the calculation of effective masses with perturbation theory. We introduce the mstar60 dataset, which contains 60 effective masses derived from 18 semiconductors. The ratio between experimental and calculated effective masses is $1.70\pm 0.20$ for PBE, $0.76\pm 0.04$ for TB-mBJ, and $0.99\pm 0.04$ for HSE06. We reveal that the nonlocal exchange in HSE06 enlarges the optical transition matrix elements leading to the superior accuracy of the hybrid functional in the calculation of effective masses. The omission of nonlocal exchange in the transition operator for HSE leads to serious errors. For the semilocal PBE functional, the errors in the band gap and the optical transition matrix elements partially cancel out in the calculation of effective masses. The TB-mBJ functional yields PBE-like matrix elements paired with realistic band gaps leading to a consistent overestimation of effective masses. However, if only limited computational resources are available, experimental masses can be estimated by multiplying TB-mBJ masses by a factor of 0.76. We then compare effective masses of transition metal dichalcogenide bulk and monolayer materials: we show that changes in the matrix elements are important in understanding the layer-dependent effective mass renormalization.