Tensioned graphene membranes are of interest both for fundamental physics and for applications ranging from water filtration to nanomechanical resonators. It is generally assumed that these membranes have a stretching modulus of about 340 N/m and a negative, temperature-independent thermal expansion coefficient due to transverse phonon modes. In this paper, we study the two-dimensional Young's modulus and thermal expansion of graphene as functions of temperature by using laser interferometry to detect the static displacement of the membrane in a cryostat. Surprisingly, we find that the modulus decreases strongly with increasing temperature, which leads to a positive temperature-dependent thermal expansion coefficient. We show that the thermally rippled membrane theory is not consistent with our data, while the effects of surface contaminants typically present on these membranes may explain the observed behavior. Our experiments undermine long-standing assumptions about tensioned two-dimensional membranes, but are consistent with puzzling behavior observed in previous experiments on graphene resonators.

The Haldane model on a honeycomb lattice is a paradigmatic example of a system featuring quantized Hall conductivity in the absence of an external magnetic field, that is, a quantum anomalous Hall effect. Recent theoretical work predicted that the anomalous Hall conductivity of massive Dirac fermions can display Shubnikov–de Haas (SdH) oscillations, which could be observed in topological insulators and honeycomb layers with strong spin-orbit coupling. Here, we investigate the electronic transport properties of Chern insulators subject to high magnetic fields by means of accurate spectral expansions of lattice Green's functions. We find that the anomalous component of the Hall conductivity displays visible SdH oscillations at low temperature. The effect is shown to result from the modulation of the next-nearest-neighbor flux accumulation due to the Haldane term, which removes the electron-hole symmetry from the Landau spectrum. To support our numerical findings, we derive a long-wavelength description beyond the linear (“Dirac cone”) approximation. Finally, we discuss the dependence of the energy spectra shift for reversed magnetic fields with the topological gap and the lattice bandwidth.

Recent success in the experimental isolation and synthesis of highly stable atomically thin antimonene has triggered great interest into examining its potential role in nanoelectronic applications. In this work, we investigate the mechanical and electronic properties of monolayer antimonene in its most stable $\beta$-phase using first-principles calculations. The upper region of its valence band is found to solely consist of lone pair $p$-orbital states, which are by nature more delocalized than the $d$-orbital states in transition metal dichalcogenides, implying superior transport performance of antimonene. The Young's and shear moduli of $\beta$-antimonene are observed to be $\sim 25\%$ higher than those of bulk antimony, while the hexagonal lattice constant of the monolayer reduces significantly ($\sim 5\%$) from that in bulk, indicative of strong interlayer coupling. The ideal tensile test of $\beta$-antimonene under applied uniaxial strain highlights ideal strengths of 6 and 8 GPa, corresponding to critical strains of 15% and 17% in the zigzag and armchair directions, respectively. During the deformation process, the structural integrity of the material is shown to be better preserved, albeit moderately, in the armchair direction. Interestingly, the application of uniaxial strain in the zigzag and armchair directions unveil direction-dependent trends in the electronic band structure. We find that the nature of the band gap remains insensitive to strain in the zigzag direction, while strain in the armchair direction activates an indirect-direct band gap transition at a critical strain of 4%, owing to a band switching mechanism. The curvature of the conduction band minimum increases during the transition, which suggests a lighter effective mass of electrons in the direct-gap configuration than in the free-standing state of equilibrium. The work function of free-standing $\beta$-antimonene is 4.59 eV, and it attains a maximum value of 5.07 eV under an applied biaxial strain of 4%. The findings reported in this work provide fundamental insights into the mechanical behavior and strain-tunable nature of the electronic properties of monolayer $\beta$-antimonene, in support of its promising role for future nanoelectromechanical systems and optoelectronic applications.

We study the nonequilibrium evolution of a one-dimensional quantum Ising chain with spatially disordered, time-dependent, transverse fields characterized by white noise correlation dynamics. We establish prethermalization in this model, showing that the quench dynamics of the on-site transverse magnetization first approaches a metastable state unaffected by noise fluctuations, and then relaxes exponentially fast toward an infinite temperature state as a result of the noise. We also consider energy transport in the model, starting from an inhomogeneous state with two domain walls which separate regions characterized by spins with opposite transverse magnetization. We observe at intermediate timescales a phenomenology akin to Anderson localization: energy remains localized within the two domain walls, until the Markovian noise destroys coherence and, accordingly, disorder-induced localization, allowing the system to relax toward the late stages of its nonequilibrium dynamics. We compare our results with the simpler case of a noisy quantum Ising chain without disorder, and we find that the prethermal plateau is a generic property of spin chains with weak noise, while the phenomenon of prethermal Anderson localization is a specific feature arising from the competition of noise and disorder in the real-time transport properties of the system.

We report a detailed study of magnetic properties in double perovskite iridate ${\mathrm{La}}_2{\mathrm{ZnIrO}}_6$ single crystal, which exhibits an antiferromagnetic (AFM) ground state. The field- and angle-dependent magnetizations $\left[M\right(H)$ and $M\left(\phi \right)]$ suggest strong magnetic anisotropy in this system. The magnetization of ${\mathrm{La}}_2{\mathrm{ZnIrO}}_6$ is isotropic in the $ab$ plane, while it is much stronger than that along the $c$ axis. A field-induced magnetic transition from AFM to ferromagnetic (FM) state is found, which is of a first-order type. The critical behavior is investigated, where critical exponents $\beta =0.2317\left(1\right),\gamma =0.9783\left(2\right)$, and $\delta =5.0071\left(5\right)$ are obtained. The critical exponents belong to the universality class of the tricritical mean-field model, which indicates a field-induced tricritical phenomenon. Based on the scaling equations, we construct the $H\text{−}T$ phase diagram for ${\mathrm{La}}_2{\mathrm{ZnIrO}}_6$ single crystal with $H//b$. A tricritical point is revealed at the intersection point between the AFM, FM, and paramagnetic phases ($T_{tr}\approx 8$ K; $H_{tr}\approx 170$ Oe).

Ferromagnets in contact with a topological insulator have become appealing candidates for spintronics due to the presence of Dirac surface states with spin-momentum locking. Because of this, bilayer ${\mathrm{Bi}}_2{\mathrm{Se}}_3$-EuS structures, for instance, show a finite magnetization at the interface at temperatures well exceeding the Curie temperature of bulk EuS. Here, we determine theoretically the effective magnetic interactions at a topological insulator-ferromagnet interface above the magnetic ordering temperature. We show that by integrating out the Dirac fermion fluctuations an effective Dzyaloshinskii-Moriya interaction and magnetic charging interaction emerge. As a result, individual magnetic skyrmions and extended skyrmion lattices can form at the interfaces of ferromagnets and topological insulators, the first indications of which have been very recently observed experimentally.

Double perovskites exhibit a variety of interesting phenomena due to numerous combinations of cation orderings and distortions. $\mathrm{CaMnT}{\mathrm{i}}_2{\mathrm{O}}_6$ and $\mathrm{CaFeT}{\mathrm{i}}_2{\mathrm{O}}_6$ are the only two discovered double perovskites that have the columnar type A-site ordering associated with the $a^{+}{a}^{+}{c}^{-}$ titling system. The former perovskite, synthesized recently, has a polar structure below $T_c$ and shows an unusual ferroelectricity. The latter, while synthesized decades ago, received less investigation. Here, we have synthesized $\mathrm{CaFeT}{\mathrm{i}}_2{\mathrm{O}}_6$ under high pressure and carried out thorough characterizations through measurements of x-ray powder diffraction (XRD), second harmonic generation (SHG), dc and ac magnetization, Mössbauer spectra, resistivity, thermoelectric power, and specific heat. Although the structural refinement of the XRD pattern cannot distinguish two possible tetragonal phases, SHG measurements help to rule out the possibility of a polar structure observed in $\mathrm{CaMnT}{\mathrm{i}}_2{\mathrm{O}}_6$. Fitting the paramagnetic susceptibility to a Curie-Weiss law gives a negligible Weiss constant. The weak exchange interaction gives way to a dipole-dipole interaction and single-ion anisotropy. An anomaly at 1.2 K in the specific heat is too broad for a magnetic transition, but suggestive of a spin-ice-like state as in the pyrochlores. Mössbauer spectroscopy shows two distinct iron sites, as expected for the crystal structure. Both sites are occupied by high-spin $\mathrm{F}{\mathrm{e}}^{2+}$ as indicated by the isomer shift. The sharply different temperature dependence of the quadrupole splitting at the two iron sites can be well explained based on the local structural distortions from the refinement of XRD patterns. The line broadening associated with long spin-relaxation times is observed at 6 K as the spin freezing transition is approached from high temperatures.

Although ferromagnetism is in general a long-range collective phenomenon, it is possible to induce local spatial variations of magnetic properties in ferromagnetic materials. For example, systematic variation of the exchange coupling strength can be used to create systems that behave as if they are composed of virtually independent segments that exhibit “local” Curie temperatures. Such localization of thermodynamic behavior leads to boundaries between strongly and weakly magnetized regions that can be controllably moved within the material with temperature. The utility of this interesting functionality is largely dependent on the inherent spatial resolution of magnetic properties, specifically the distance over which the exchange strength and corresponding properties behave locally. To test the degree to which this type of localization can be realized in materials, we have fabricated epitaxial films of ${\mathrm{Co}}_{1-x}{\mathrm{Ru}}_x$ alloy featuring a nanometer-scale triangular wavelike concentration depth profile. Continuous nanoscale modulation of the local Curie temperature was observed using polarized neutron reflectometry. These results are consistent with mean-field simulations of spin systems that encompass the possibility of delocalized exchange coupling and show that composition grading can be used to localize magnetic properties in films down to the nanometer level. Since this is demonstrated here for an itinerant metal, we assert that for virtually any modulated magnetic material system, collective effects can be suppressed to length scales smaller than about 3 nm, so that magnetic behavior overall can be well described in terms of local material properties.

We theoretically study the magnetic phase diagram of a three-dimensional topological Kondo insulator by means of real-space dynamical mean-field theory. We find that ferromagnetically ordered states become stable upon hole doping. Besides a wide ferromagnetic phase, we observe surface magnetism close to half-filling, which corresponds to an A-type antiferromagnetic state. We further study the impact of the magnetism on the symmetry protected surface states and find that depending on the surface and the magnetization direction, surface states are still protected by reflection symmetry present in our model. The symmetry protected surface states are shifted away by the magnetization from their original high-symmetry momenta in the Brillouin zone. Remarkably, due to the magnetization, the surface states are deformed, resulting in the appearance of arcs in the momentum resolved spectrum.

We present a formal derivation of the many-body perturbation theory for a system of electrons and bosons subject to a nonlinear electron-boson coupling. The interaction is treated at an arbitrary high order of bosons scattered. The considered Hamiltonian includes the well-known linear coupling as a special limit. This is the case, for example, of the Holstein and Fröhlich Hamiltonians. Indeed, whereas linear coupling has been extensively studied, the scattering processes of electrons with multiple bosonic quasiparticles are largely unexplored. We focus here on a self-consistent theory in terms of dressed propagators and generalize the Hedin's equations using the Schwinger technique of functional derivatives. The method leads to an exact derivation of the electronic and bosonic self-energies, expressed in terms of a new family of vertex functions, high-order correlators, and bosonic and electronic mean-field potentials. In the electronic case we prove that the mean-field potential is the $n\mathrm{th}$-order extension of the well-known Debye-Waller potential. We also introduce a bosonic mean-field potential entirely dictated by nonlinear electron-boson effects. The present scheme, treating electrons and bosons on an equal footing, demonstrates the full symmetry of the problem. The vertex functions are shown to have purely electronic and bosonic character as well as a mixed electron-boson one. These four vertex functions are shown to satisfy a generalized Bethe-Salpeter equation. Multibosons response functions are also studied and explicit expressions for the two and the three bosons case are given.

Tight-binding (TB) models exploited in calculating band structure of monolayer transition-metal dichalcogenides (TMDCs), namely ${MX}_2$ ($M=$ Mo and W; $X=$ S, Se and Te), can be divided into two groups: one is based on group theory and the other uses Slater-Koster (SK) method. The former in general is lack of flexibility to be extended to confined finite systems with lower symmetry, e.g., nanoribbons (NRs) and quantum dots. Unlike ubiquitous TB models, here we present an improved scheme of the flexible SK TB method in which the second-nearest-neighbor $M\text{−}M$ and $X\text{−}X$ hopping terms are included. Its improvement, being of comparable accuracy to first-principles calculations, is clearly elucidated through a comprehensive comparison between our results and those produced by widely accepted TB models in literature for monolayer ${\mathrm{MoS}}_2$. Besides, its high flexibility allows us to successfully extend our TB model from monolayer TMDCs to the $\mathrm{Mo}{X}_2$ ($X=$ S, Se, and Te) and $\mathrm{W}{X}_2$ ($X=$ S and Se) NRs of both zigzag and armchair types. We find that the zigzag NR could be either metallic or semiconducting, depending on the spin-orbit strength and band gap of its parent two-dimensional bulk TMDC, which is in contradiction to the usual consensus concerning TMDC NRs which exhibit the metallic behavior only. For a certain Fermi level, remarkably, we discovered that the ${\mathrm{MoS}}_2$ NRs demonstrate quantum valley Hall effect, while others only present topological insulator phase.

We construct explicit lowest-Landau-level wave functions for the composite-fermion Fermi sea and its low-energy excitations following a recently developed approach [Pu, Wu, and Jain, Phys. Rev. B 96, 195302 (2017)] and demonstrate them to be very accurate representations of the Coulomb eigenstates. We further ask how the Berry phase associated with a closed loop around the Fermi circle, predicted to be $\pi$ in a Dirac composite fermion theory satisfying particle-hole symmetry [D. T. Son, Phys. Rev. X 5, 031027 (2015)], is affected by Landau-level mixing. For this purpose, we consider a simple model wherein we determine the variational ground state as a function of Landau-level mixing within the space spanned by two basis functions: the lowest-Landau-level projected and the unprojected composite-fermion Fermi sea wave functions. We evaluate Berry phase for a path around the Fermi circle within this model following a recent prescription, and find that it rotates rapidly as a function of Landau-level mixing. We also consider the effect of a particle-hole symmetry-breaking three-body interaction on the Berry phase while confining the Hilbert space to the lowest Landau level. Our study deepens the connection between the $\pi$ Berry phase and the exact particle-hole symmetry in the lowest Landau level.

One-dimensional (1D) edge states formed at the boundaries of 2D normal and topological insulators have shown intriguing quantum phases such as charge density wave and quantum spin Hall effect. Based on first-principles density-functional theory calculations including spin-orbit coupling (SOC), we show that the edge states of zigzag Sb(111) and Bi(111) nanoribbons drastically change the stability of their edge structures. For zigzag Sb(111) nanoribbon, the Peierls-distorted or reconstructed edge structure is stabilized by a band-gap opening. However, for zigzag Bi(111) nanoribbons, such insulating structures are destabilized due to the presence of topologically protected gapless edge states, resulting in the stabilization of a metallic, shear-distorted edge structure. We also show that the edge states of the Bi(111) nanoribbon exhibit a larger Rashba-type spin splitting at the boundary of Brillouin zone compared to those of the Sb(111) nanoribbon. Interestingly, the spin textures of edge states in the Peierls-distorted Sb edge structure and the shear-distorted Bi edge structure have all three spin components perpendicular and parallel to the edges due to their broken mirror-plane symmetry. The present findings demonstrate that the topologically trivial and nontrivial edge states play crucial roles in determining the edge structures of normal and topological insulators.

We predict a spin pure dephasing channel in electron relaxation between states with unequal Zeeman splittings, exemplified by a spin-preserving electron tunneling between quantum dots in a magnetic field. The dephasing is caused by a mismatch in electron $g$ factors in the dots leading to distinguishability of phonons emitted during tunneling with opposite spins. Combining multiband $\mathit{k}·\mathit{p}$ modeling and dynamical simulations via a master equation, we show that this fundamental effect of spin measurement effected by the phonon bath may be widely controlled by the size and composition of the dots or on demand via tuning of external fields. By comparing the numerically simulated degree of dephasing with the predictions of general theory based on distinguishability of environment states, we show that the proposed mechanism is the dominant phonon-related spin dephasing channel and may limit spin coherence time in tunnel-coupled structures at cryogenic temperatures.

We investigate correlated insulating states in magic-angle twisted bilayer graphene (TBG) by the exact diagonalization method applied to the extended Hubbard model with interaction parameters recently evaluated in the realistic effective model. Our model can handle the competing interactions among Wannier orbitals owing to their significant overlap, which is a crucial but overlooked aspect of the magic-angle TBG. We propose two candidates for the correlated insulating states: spin- and valley-ferromagnetic band insulator and the Dirac semimetallic state for two flavors with peculiar renormalization, where a flavor denotes a combined degree of freedom with spin and valley. One of the important consequences for the latter candidate is that it allows van Hove singularity near half-filling of the whole band structure (i.e., near the Dirac points) to play some role in superconductivity. The consistency between the two flavor degrees of freedom for the Dirac semimetallic state and the twofold degeneracy of the Landau level observed in the experiment is also noteworthy.

The study of electronic properties in topological systems is one of the most fascinating topics in condensed-matter physics, which has generated enormous interests in recent times. New materials are frequently being proposed and investigated to identify their nontrivial band structure. While sophisticated techniques such as angle-resolved photoemission spectroscopy have become popular to map the energy-momentum relation, the transport experiments lack any direct confirmation of Dirac and Weyl fermions in a system. From band-structure calculations, ${\mathrm{VAl}}_3$ has been proposed to be a type-II topological Dirac semimetal. This material represents a large family of isostructural compounds, all having similar electronic band structure and is an ideal system to explore the rich physics of Lorentz symmetry violating Dirac fermions. In this work, we present a detailed analysis on the magnetotransport properties of ${\mathrm{VAl}}_3$. A large, nonsaturating magnetoresistance has been observed. Hall resistivity reveals the presence of two types of charge carriers with high mobility. Our measurements show a large planar Hall effect in this material, which is robust and can be easily detectable up to high temperature. This phenomenon originates from the relativistic chiral anomaly and nontrivial Berry curvature, which validates the theoretical prediction of the Dirac semimetal phase in ${\mathrm{VAl}}_3$.

Motivated by near-term experiments with ultracold alkaline-earth atoms confined to optical lattices, we establish numerically and analytically the phase diagram of two-leg $\mathrm{SU}\left(N\right)$ spin ladders. Two-leg ladders provide a rich and highly nontrivial extension of the single chain case on the way towards the relatively little explored two-dimensional situation. Focusing on the experimentally relevant limit of one fermion per site, antiferromagnetic exchange interactions, and $2\le N\le 6$, we show that the phase diagrams as a function of the interchain (rung) to intrachain (leg) coupling ratio, $J_{\perp }/J_{\parallel }$, strongly differ for even versus odd $N$. For even $N=4$ and 6, we demonstrate that the phase diagram consists of a single valence bond crystal (VBC) with a spatial period of $N/2$ rungs. For odd $N=3$ and 5, we find surprisingly rich phase diagrams exhibiting three distinct phases. For weak rung coupling, we obtain a VBC with a spatial period of $N$ rungs, whereas for strong coupling we obtain a critical phase related to the case of a single chain. In addition, we encounter intermediate phases for odd $N$, albeit of a different nature for $N=3$ as compared to $N=5$. For $N=3$, we find a novel gapless intermediate phase with $J_{\perp }$-dependent incommensurate spatial fluctuations in a sizeable region of the phase diagram. For $N=5$, there are strong indications for a narrow potentially gapped intermediate phase, whose nature is not entirely clear. Our results are based on (i) field theoretical techniques, (ii) qualitative symmetry considerations, and (iii) large-scale density matrix renormalization group (DMRG) simulations keeping beyond a million of states by fully exploiting and thus preserving the $\mathrm{SU}\left(N\right)$ symmetry.

We calculate the uniaxial and dilatation acoustic deformation potentials ${\mathrm{\Xi }}_u^{\text{L}}$ and ${\mathrm{\Xi }}_d^{\text{L}}$ of the conduction band L valleys of PbTe from first principles, using the local density approximation (LDA) and hybrid functional (HSE03) exchange-correlation functionals. We find that the choice of a functional does not substantially affect the effective band masses and deformation potentials as long as a physically correct representation of the conduction band states near the band gap has been obtained. Fitting of the electron-phonon matrix elements obtained in density functional perturbation theory (DFPT) with the LDA excluding spin-orbit interaction (SOI) gives ${\mathrm{\Xi }}_u^{\text{L}}=7.0$ eV and ${\mathrm{\Xi }}_d^{\text{L}}=0.4$ eV. Computing the relative shifts of the L valleys induced by strain with the HSE03 functional including SOI gives ${\mathrm{\Xi }}_u^{\text{L}}=5.5$ eV and ${\mathrm{\Xi }}_d^{\text{L}}=0.8$ eV, in good agreement with the DFPT values. Our calculated values of ${\mathrm{\Xi }}_u^{\text{L}}$ agree fairly well with experiment ($\sim 3–4.5$ eV). The computed values of ${\mathrm{\Xi }}_d^{\text{L}}$ are substantially smaller than those obtained by fitting electronic transport measurements ($\sim 17–22$ eV), indicating that intravalley acoustic phonon scattering in PbTe is much weaker than previously thought.

We study the Raman spectrum of ${\mathrm{CrI}}_3$, a material that exhibits magnetism in a single layer. We employ first-principles calculations within density functional theory to determine the effects of polarization, strain, and incident angle on the phonon spectra of the three-dimensional bulk and the single-layer two-dimensional structure, for both the high- and low-temperature crystal structures. Our results are in good agreement with existing experimental measurements and serve as a guide for additional investigations to elucidate the physics of this interesting material.

We study the low-energy physics of a one-dimensional array of superconducting quantum dots realized by proximity coupling a semiconductor nanowire to multiple superconducting islands separated by narrow uncovered regions. The effective electrostatic potential inside the quantum dots and the uncovered regions can be controlled using potential gates. By performing detailed numerical calculations based on effective tight-binding models, we find that multiple low-energy subgap states consisting of partially overlapping Majorana bound states emerge generically in the vicinity of the uncovered regions. Explicit differential conductance calculations show that a robust zero-bias conductance peak is not inconsistent with the presence of such states localized throughout the system, hence, the observation of such a peak does not demonstrate the realization of well-separated Majorana zero modes. However, we find that creating effective potential wells in the uncovered regions traps pairs of nearby partially overlapping Majorana bound states, which become less separated and acquire a finite gap that protects the pair of Majorana zero modes localized at the ends of the system. This behavior persists over a significant parameter range, suggesting that proximitized quantum dot arrays could provide a platform for highly controllable Majorana devices.