We consider two coupled time-reversal-invariant helical edge modes of the same helicity, such as would occur on two stacked quantum spin Hall insulators. In the presence of interaction, the low-energy physics is described by two collective modes, one corresponding to the total current flowing around the edge and the other one describing relative fluctuations between the two edges. We find that quite generically, the relative mode becomes gapped at low temperatures, but only when tunneling between the two helical modes is nonzero. There are two distinct possibilities for the gapped state depending on the relative size of different interactions. If the intraedge interaction is stronger than the interedge interaction, the state is characterized as a spin-nematic phase. However, in the opposite limit, when the interaction between the helical edge modes is strong compared to the interaction within each mode, a spin-density wave forms, with emergent topological properties. First, the gap protects the conducting phase against localization by weak nonmagnetic impurities; second, the protected phase hosts localized zero modes on the ends of the edge that may be created by sufficiently strong nonmagnetic impurities.

We study the infrared dynamics of low-energy atoms interacting with a sample of suspended graphene at finite temperature. The dynamics exhibits severe infrared divergences order by order in perturbation theory as a result of the singular nature of low-energy flexural phonon emission. Our model can be viewed as a two-channel generalization of the independent boson model with asymmetric atom-phonon coupling. This allows us to take advantage of the exact nonperturbative solution of the independent boson model in the stronger channel while treating the weaker one perturbatively. In the low-energy limit, the exact solution can be viewed as a resummation (exponentiation) of the most divergent diagrams in the perturbative expansion. As a result of this procedure, we obtain the atom's Green function which we use to calculate the atom damping rate, a quantity equal to the quantum sticking rate. A characteristic feature of our results is that the Green's function retains a weak, infrared cutoff dependence that reflects the reduced dimensionality of the problem. As a consequence, we predict a measurable dependence of the sticking rate on graphene sample size. We provide detailed predictions for the sticking rate of atomic hydrogen as a function of temperature and sample size. The resummation yields an enhanced sticking rate relative to the conventional Fermi golden rule result (equivalent to the one-loop atom self-energy), as higher-order processes increase damping at finite temperature.

We present evidence of strain-induced modulation of electron correlation effects and increased orbital anisotropy in the rutile phase of epitaxial ${\mathrm{VO}}_2\text{/}{\mathrm{TiO}}_2$ films from hard x-ray photoelectron spectroscopy and soft V L-edge x-ray absorption spectroscopy, respectively. By using the U(1) slave spin formalism, we further argue that the observed anisotropic correlation effects can be understood by a model of orbital selective Mott transition at a filling that is noninteger but close to the half filling. Because the overlaps of wave functions between $d$ orbitals are modified by the strain, orbital-dependent renormalizations of the bandwidths and the onsite energy occur. These renormalizations generally result in different occupation numbers in different orbitals. We find that if the system has a noninteger filling number near the half filling such as for ${\mathrm{VO}}_2$, certain orbitals could reach an occupation number closer to half filling under the strain, resulting in a strong reduction in the quasiparticle weight $Z_{\alpha }$ of that orbital. Our work demonstrates that such an orbital selective Mott transition, defined as the case with $Z_{\alpha }=0$ in some but not all orbitals, could be accessed by epitaxial-strain engineering of correlated electron systems.

Systems with spin-orbit coupling have the potential to realize exotic quantum states which are interesting both from fundamental and technological perspectives. We investigate the physics that arises when a correlated spin-$\frac{1}{2}$ quantum impurity hybridizes with a spin-orbit coupled Fermi system. The intriguing aspect uncovered is that, in contrast to unit local moments in conventional systems, the impurity here develops a fractional local moment of 2/3. The concomitant Kondo effect has a high Kondo temperature $\left(T_K\right)$. Our theory explains these features including the origins of the fractional local moment and provides a recipe to use spin-orbit coupling $\left(\lambda \right)$ to enhance the Kondo temperature $\left(T_K\sim {\lambda }^{4/3}\right)$. Even as our finding of such rich phenomena in a simple looking many-body system is of interest in itself, we also point out opportunities for systems with tunable spin-orbit coupling (such as cold atoms) to explore this physics.

The quasiskutterudite superconductor ${\mathrm{La}}_3{\mathrm{Co}}_4{\mathrm{Sn}}_{13}$ undergoes a phase transition at $T^{*}=152$ K. By measuring the temperature dependence of heat capacity, electrical resistivity, and the superlattice reflection intensity using x rays, we explore the character of the phase transition at $T^{*}$. Our lattice dynamic calculations found imaginary phonon frequencies around the $M$ point when the high-temperature structure is used in the calculations, indicating that the structure is unstable at the zero-temperature limit. The combined experimental and computational results establish that $T^{*}$ is associated with a second-order structural transition with $\mathit{q}=(0.5,0.5,0)$ (or the $M$ point). Further electronic band structure calculations reveal Fermi surface sheets with low-curvature segments, which allow us to draw qualitative comparison with both ${\mathrm{Sr}}_3{\mathrm{Ir}}_4{\mathrm{Sn}}_{13}$ and ${\mathrm{Sr}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ in which similar physics has been discussed recently.

We study the effect of the long-range Coulomb interaction in $j=3/2$ Dirac electrons in cubic crystals with the $O_h$ symmetry, which serves as an effective model for antiperovskite topological crystalline insulators. The renormalization group analysis reveals three fixed points that are Lorentz invariant, rotationally invariant, and $O_h$ invariant. Among them, the Lorentz- and $O_h$-invariant fixed points are stable in the low-energy limit, while the rotationally invariant fixed point is unstable. The existence of a stable $O_h$-invariant fixed point of Dirac fermions with finite velocity anisotropy presents an interesting counterexample to emergent Lorentz invariance in solids.

We investigate the charge excitations of a Weyl semimetal in the axionic charge density wave (axionic CDW) state. While it has been shown that the topological response (anomalous Hall conductivity) is protected against the CDW state, we find that the long-wavelength plasmon excitation is radically influenced by the dynamics of the CDW order parameter. In the normal state, we show that an undamped collective mode should exist at $\vec{q}\approx {\vec{Q}}_{\text{CDW}}$ if there is an attractive interaction favoring the formation of the CDW state. The undamped nature of this collective mode is attributed to a gaplike feature in the particle-hole continuum at $\vec{q}\approx {\vec{Q}}_{\text{CDW}}$ due to the chirality of the Weyl nodes, which is not seen in other materials with CDW instability. In the CDW state, the long-wavelength plasmon excitations become more dispersive due to the additional interband scattering not allowed in the normal state. Moreover, because the translational symmetry is spontaneously broken, umklapp scattering, the process conserving the total momentum only up to $n{\vec{Q}}_{\text{CDW}}$, with $n$ an integer and ${\vec{Q}}_{\text{CDW}}$ the ordering wave vector, emerges in the CDW state. We find that the plasmon excitation couples to the phonon mode of the CDW order via the umklapp scattering, leading to two branches of resonant collective modes observable in the density-density correlation function at $\vec{q}\approx 0$ and $\vec{q}\approx {\vec{Q}}_{\text{CDW}}$. Based on our analysis, we propose that measuring these resonant plasmon-axion excitations around $\vec{q}\approx 0$ and $\vec{q}\approx {\vec{Q}}_{\text{CDW}}$ by momentum-resolved electron energy loss spectroscopy could serve as a reliable way to detect the axionic CDW state in Weyl semimetals.

Starting from a Su-Schrieffer-Heeger-like model inferred from first-principles simulations, we show that the metal-insulator transition in In/Si(111) is a first-order grand canonical Peierls transition in which the substrate acts as an electron reservoir for the wires. This model explains naturally the existence of a metastable metallic phase over a wide temperature range below the critical temperature and the sensitivity of the transition to doping. Raman scattering experiments corroborate the softening of the two Peierls deformation modes close to the transition.

As a prototypical one-dimensional electron system, self-assembled indium (In) nanowires on the Si(111) surface have been believed to drive a metal-insulator transition by a charge-density-wave (CDW) formation due to Fermi surface nesting. Here, our first-principles calculations demonstrate that the structural phase transition from the high-temperature $4\times 1$ phase to the low-temperature $8\times 2$ phase occurs through an exothermic reaction with the consecutive bond-breaking and bond-making processes, giving rise to an energy barrier between the two phases as well as a gap opening. This atomistic picture for the phase transition not only identifies its first-order nature but also solves a long-standing puzzle of the origin of the metal-insulator transition in terms of the $\times 2$ periodic lattice reconstruction of In hexagons via bond breakage and new bond formation, not by the Peierls-instability-driven CDW formation.

We consider a topological insulator (TI) of spherical geometry and numerically investigate the influence of disorder on the density of surface states. The energy spectrum of the spherical TI surface is discrete, for a sphere of finite radius, and can be truncated by imposing a high-energy cutoff at the scale of the bulk band gap. To this clean system we add a surface disorder potential of the most general Hermitian form, $V=V^0(\theta ,\varphi )\mathbb{1}+\mathbf{V}(\theta ,\varphi )·\sigma$, where $V^0$ describes the spin-independent part of the disorder and the three components of $\mathbf{V}$ describe the spin-dependent part. We expand these four disorder functions in spherical harmonics and draw the expansion coefficients randomly from a four-dimensional, zero-mean Gaussian distribution. Different strengths and classes of disorder are realized by specifying the $4\times 4$ covariance matrix. For each instantiation of the disorder, we solve for the energy spectrum via exact diagonalization. Then we compute the disorder-averaged density of states, $\rho \left(E\right)$, by averaging over $200000$ different instantiations. Disorder broadens the Landau-level delta functions of the clean density of states into peaks that decay and merge together. If the spin-dependent term is dominant, these peaks split due to the breaking of the degeneracy between time-reversed partner states. Increasing disorder strength pushes states closer and closer to zero energy (the Dirac point), resulting in a low-energy density of states that becomes nonzero for sufficient disorder, typically approaching an energy-independent saturation value, for most classes of disorder. But for purely spin-dependent disorder with $\mathbf{V}$ either entirely out-of-surface or entirely in-surface, we identify intriguing disorder-induced features in the vicinity of the Dirac point. In the out-of-surface case, a new peak emerges at zero energy. In the in-surface case, we see a symmetry-protected zero at zero energy, with $\rho \left(E\right)$ increasing linearly toward nonzero-energy peaks. These striking features are explained in terms of the breaking (or not) of two chiral symmetries of the clean Hamiltonian.

The propagation of a surface plasmon polariton along a stack of doped graphene sheets is considered. This auxiliary problem is used to discuss: (i) the scattering of such a mode at an interface between the stack and the vacuum, and (ii) the scattering at an interface where there is a sudden change of the electronic doping. The formalism is then extended to the barrier problem. In this system rich physics is found for the plasmonic mode, showing total reflection, total transmission, Fabry-Pérot oscillations, and coupling to photonic modes.

Among the novel two-dimensional (2D) materials, silicene and germanene, which are two honeycomb crystal structures composed of a monolayer of Si and Ge, respectively, have attracted the attention of material scientists because they combine the advantages of the new 2D ultimate-scaled electronics with their compatibility with industrial processes presently based on Si and Ge. We envisage pseudomorphic lateral heterostructures based on ribbons of silicene and germanene, which are the 2D analogs of conventional 3D Si/Ge superlattices and quantum wells. In spite of the considerable lattice mismatch ($\sim 4\%$) between free-standing silicene and germanene, our ab initio simulations predict that, considering striped 2D lateral heterostructures made by alternating silicene and germanene ribbons of constant width, the silicene/germanene junction remains pseudomorphic—i.e., it maintains lattice-matched edges—up to critical ribbon widths that can reach some tens of nanometers. Such critical widths are one order of magnitude larger than the critical thickness measured in 3D pseudomorphic Si/Ge heterostructures and the resolution of state-of-the-art lithography, thus enabling the possibility of lithography patterned silicene/germanene junctions. We computed how the strain produced by the pseudomorphic growth modifies the crystal structure and electronic bands of the ribbons, providing a mechanism for band-structure engineering. Our results pave the way for lithography patterned lateral heterostructures that can serve as the building blocks of novel 2D electronics.

Collective hybridized plasmon modes, which enable strong magnetooptical coupling and consequent enhanced Faraday effect in three-dimensional periodic assemblies of magnetic dielectric nanoparticles coated with a noble-metal shell, are studied by means of rigorous full electrodynamic calculations using an extension of the layer-multiple-scattering method, in conjunction with the effective-medium approximation. A thorough analysis of relevant photonic dispersion diagrams and transmission spectra provides a consistent explanation of the underlying physical mechanisms to a degree that goes beyond existing interpretation. It is shown that properly designed structures of such composite magnetoplasmonic nanoparticles offer a versatile platform for engineering increased and broadband Faraday rotation.

Despite the intensive studies for decades, it is still not well understood how qualitatively different magnetic behaviors can occur in a narrow composition range for the Fe-rich Fe-transition metal (TM) amorphous alloys. In this study of amorphous $\mathrm{F}{\mathrm{e}}_{100-x}\mathrm{Z}{\mathrm{r}}_x$ ($x=7$, 9, 12) metallic glasses, normal ferromagnetism (FM) is found at 12 % Zr where only the FM-paramagnetic (PM) transition is observed at the Curie temperature, $T_C$. In contrast, spin-glass (SG)-PM transition at a temperature, $T_g$, called SG temperature, is only observed at 7 % Zr, while in the transient re-entrant composition range $\left(x=8-11\right)$, an SG-FM transition at a temperature, $T_f$, called spin-freezing temperature, is also observed at low temperature besides the normal FM-PM transition at $T_C$. In order to understand this unusual behavior, a detailed characterization of pressure (atomic volume), composition, and temperature dependence of the magnetic properties is coupled with high pressure synchrotron x-ray diffraction determination of the pressure dependence of the atomic volume. The results on $\mathrm{F}{\mathrm{e}}_{100-x}\mathrm{Z}{\mathrm{r}}_x$ ($x=7$, 9, 12) are compared to those obtained for the FM $\mathrm{C}{\mathrm{o}}_{91}\mathrm{Z}{\mathrm{r}}_9$ metallic glass not showing any kind of anomalous magnetic properties. It is confirmed that the unusual behavior is caused by a granularlike magnetic structure where weakly coupled magnetic clusters are embedded into a FM bulk matrix. Since the mechanism of the magnetization reversal was found to be of the curling type rather than homogeneous rotation, the energy barrier determining the blocking temperature of the clusters is calculated as AR, where A is the exchange constant and R is the cluster size, in contrast to the usual characterization of the energy barrier by KV where K is the anisotropy energy and V is the cluster volume. The volume fraction of the FM part is a fast changing function of the bulk composition: Almost 100% FM fraction is found at 12 % of Zr while no trace of real FM is observed at 7 at % Zr. The driving force of this surprising magnetic character is the atomic volume: The lower the Zr content, the higher is the fraction of Fe atoms with compressed atomic volume having low magnetic moment. The percolation of their network separates the clusters from the FM bulk. The complex magnetic behavior of the Fe-rich Fe-Zr amorphous system at low temperatures can thus be interpreted with the only assumption of a cluster-size distribution and a weak coupling of the clusters to the FM matrix. The introduction of this coupling is able to explain the opposite pressure dependence of $T_g$ and $T_f$. The threshold atomic volume in the low magnetic moment regions is found to be comparable to the atomic volume characteristic to the low-spin limit of the face-centered-cubic Fe alloys. The extensive literature results on the anomalous magnetism for various Fe-rich Fe-TM amorphous alloys and especially for the Fe-rich Fe-Zr glassy system are also found to be in agreement with this granular magnetic behavior.

We study the Heisenberg-Kitaev spin chain in order to uncover the interplay between two qualitatively different integrable points in the physics of heat transport in one dimension. Focusing on high temperatures and using analytical as well as numerical approaches within linear response theory, we explore several directions in parameter space including exchange-coupling ratios, anisotropies, and external magnetic fields. We show the emergence of purely ballistic energy transport at all integrable points, manifest in pronounced Drude weights and low-frequency suppression of regular-conductivity contributions. Moreover, off integrability, we find extended quantum chaotic regions with vanishing Drude weights and well-defined dc conductivities. In the vicinity of the Kitaev point, we observe clear signatures of the topological gap in the response function. This gap coexists with a nonzero Drude weight in the Kitaev chain.

Unconventional superconductivity has been predicted to arise in the topologically nontrivial Fermi surface of doped inversion-symmetric Weyl semimetals (WSMs). In particular, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and nodal BCS states are theoretically predicted to be possible superconductor pairing states in inversion-symmetric doped WSMs. In an effort to resolve the preferred pairing state, we theoretically study two separate four-terminal quantum transport methods that each exhibit a unique electrical signature in the presence of FFLO and nodal BCS states in doped WSMs. We first introduce a Josephson junction that consists of a doped WSM and an $s$-wave superconductor in which we show that the application of a transverse uniform current in $s$-wave superconductors effectively cancels the momentum carried by FFLO states in doped WSMs. From our numerical analysis, we find a peak in Josephson current amplitude at finite uniform current in $s$-wave superconductors that serves as an indicator of FFLO states in doped WSMs. Furthermore, we show using a four-terminal measurement configuration that the nodal points may be shifted by an application of transverse uniform current in doped WSMs. We analyze the topological phase transitions induced by nodal pair annihilation in nonequilibrium by constructing the phase diagram and we find a characteristic decrease in the density of states that serves as a signature of the quantum critical point in the topological phase transition, thereby identifying nodal BCS states in doped WSMs.

We investigate the origin of a resonant period drop of a torsional oscillator (TO) containing solid ${}^4\mathrm{He}$ by inspecting its relation to a change in elastic modulus. To understand this relationship directly, we measure both phenomena simultaneously using a TO with a pair of concentric piezoelectric transducers inserted in its annulus. We confirm experimentally that both anomalies are directly related. Although the temperature, ${}^3\mathrm{He}$ concentration, and frequency dependence are essentially the same, a marked discrepancy in the drive amplitude dependence is observed. We find that this discrepancy originates from the anisotropic response of polycrystalline solid ${}^4\mathrm{He}$ connected with low-angle grain boundaries by studying the shear modulus parallel to and perpendicular to the driving direction.

Several recent experiments on three-dimensional topological insulators claim to observe a large charge current-induced nonequilibrium ensemble spin polarization of electrons in the helical surface state. We present a comprehensive criticism of such claims, using both theory and experiment: First, we clarify the interpretation of quantities extracted from these measurements by deriving standard expressions from a Boltzmann transport equation approach in the relaxation-time approximation at zero and finite temperature to emphasize our assertion that, despite high in-plane spin projection, obtainable current-induced ensemble spin polarization is minuscule. Second, we use a simple experiment to demonstrate that magnetic field-dependent open-circuit voltage hysteresis (identical to those attributed to current-induced spin polarization in topological insulator surface states) can be generated in analogous devices where current is driven through thin films of a topologically trivial metal. This result ipso facto discredits the naive interpretation of previous experiments with TIs, which were used to claim observation of helicity, i.e., spin-momentum locking in the topologically protected surface state.