Near a quantum critical point in a metal, a strong fermion-fermion interaction, mediated by a soft boson, acts in two different directions: it destroys fermionic coherence and it gives rise to an attraction in one or more pairing channels. The two tendencies compete with each other. We analyze a class of quantum critical models, in which momentum integration and the selection of a particular pairing symmetry can be done explicitly, and the competition between non-Fermi liquid and pairing can be analyzed within an effective model with dynamical electron-electron interaction $V\left({\mathrm{\Omega }}_m\right)\propto 1/{\left|{\mathrm{\Omega }}_m\right|}^{\gamma }$ (the $\gamma$ model). In this paper, the first in the series, we consider the case $T=0$ and $0<\gamma <1$. We argue that tendency to pairing is stronger, and the ground state is a superconductor. We argue, however, that a superconducting state is highly nontrivial as there exists a discrete set of topologically distinct solutions for the pairing gap ${\mathrm{\Delta }}_n\left({\omega }_m\right)$ ($n=0,1,2,...,\infty$). All solutions have the same spatial pairing symmetry, but differ in the time domain: ${\mathrm{\Delta }}_n\left({\omega }_m\right)$ changes sign $n$ times as a function of Matsubara frequency ${\omega }_m$. The $n=0$ solution ${\mathrm{\Delta }}_0\left({\omega }_m\right)$ is sign preserving and tends to a finite value at ${\omega }_m=0$, like in BCS theory. The $n=\infty$ solution corresponds to an infinitesimally small $\mathrm{\Delta }\left({\omega }_m\right)$, which oscillates down to the lowest frequencies as $\mathrm{\Delta }\left({\omega }_m\right)\propto |{\omega }_m{|}^{\gamma /2}cos[2\beta log(|{\omega }_m|/{\omega }_0\left)\right]$, where $\beta =O\left(1\right)$ and ${\omega }_0$ is of order of fermion-boson coupling. As a proof, we obtain the exact solution of the linearized gap equation at $T=0$ on the entire frequency axis for all $0<\gamma <1$, and an approximate solution of the nonlinear gap equation. We argue that the presence of an infinite set of solutions opens up a new channel of gap fluctuations. We extend the analysis to the case where the pairing component of the interaction has additional factor $1/N$ and show that there exists a critical $N_{cr}>1$, above which superconductivity disappears, and the ground state becomes a non-Fermi liquid. We show that all solutions develop simultaneously once $N$ gets smaller than $N_{cr}$.

In this paper we continue the analysis of the interplay between non-Fermi liquid and superconductivity for quantum-critical systems, the low-energy physics of which is described by an effective model with dynamical electron-electron interaction $V\left({\mathrm{\Omega }}_m\right)\propto 1/{\left|{\mathrm{\Omega }}_m\right|}^{\gamma }$ (the $\gamma$ model). In paper I [A. Abanov and A. V. Chubukov, Phys. Rev. B 102, 024524 (2020)], two of us analyzed the $\gamma$ model at $T=0$ for $0<\gamma <1$ and argued that there exists a discrete, infinite set of topologically distinct solutions for the superconducting gap, all with the same spatial symmetry. The gap function ${\mathrm{\Delta }}_n\left({\omega }_m\right)$ for the $n\mathrm{th}$ solution changes sign $n$ times as the function of Matsubara frequency. In this paper we analyze the linearized gap equation at a finite $T$. We show that there exists an infinite set of pairing instability temperatures, $T_{p,n}$, and the eigenfunction ${\mathrm{\Delta }}_n\left({\omega }_m\right)$ changes sign $n$ times as a function of a Matsubara number $m$. We argue that ${\mathrm{\Delta }}_n\left({\omega }_m\right)$ retains its functional form below $T_{p,n}$ and at $T=0$ coincides with the $n\mathrm{th}$ solution of the nonlinear gap equation. Like in paper I, we extend the model to the case when the interaction in the pairing channel has an additional factor $1/N$ compared to that in the particle-hole channel. We show that $T_{p,0}$ remains finite at large $N$ due to special properties of fermions with Matsubara frequencies $\pm \pi T$, but all other $T_{p,n}$ terminate at $N_{\text{cr}}=O\left(1\right)$. The gap function vanishes at $T\to 0$ for $N>N_{\text{cr}}$ and remains finite for $N<N_{\text{cr}}$. This is consistent with the $T=0$ analysis.

We use the density matrix renormalization group (DMRG) to study the correlated electron states favored by the Coulomb interaction projected onto the narrow bands of twisted bilayer graphene within a spinless one-valley model. The Hilbert space of the narrow bands is constructed from a pair of hybrid Wannier states with opposite Chern numbers, maximally localized in one direction and Bloch extended in another direction. Depending on the parameters in the Bistritzer-Macdonald model, the DMRG in this basis determines the ground state at one particle per unit cell to be either the quantum anomalous Hall (QAH) state or a state with zero Hall conductivity which is nearly a product state. Based on this form, we then apply the variational method to study their competition, thus identifying three states: the QAH, a gapless $C_2\mathcal{T}$-symmetric nematic, and a gapped $C_2\mathcal{T}$-symmetric stripe. In the chiral limit, the energies of the two $C_2\mathcal{T}$-symmetric states are found to be significantly above the energy of the QAH. However, all three states are nearly degenerate at the realistic parameters of the Bistritzer-Macdonald model. The single-particle spectrum of the nematic contains either a quadratic node or two close Dirac nodes near $\mathrm{\Gamma }$. Motivated by the Landau level degeneracy found in this state, we propose it to be the state observed at the charge neutrality point once spin and valley degeneracies are restored. The optimal period for the $C_2\mathcal{T}$ stripe state is found to be two unit cells. In addition, using the fact that the topological charge of the nodes in the $C_2\mathcal{T}$-nematic phase is no longer described simply by their winding numbers once the translation symmetry is broken, but rather by certain elements of a non-Abelian group that was recently pointed out, we identify the mechanism of the gap opening within the $C_2\mathcal{T}$ stripe state. Although the nodes at the Fermi energy are locally stable, they can be annihilated after braiding with other nodes connecting them to adjacent (folded) bands. Therefore, if the translation symmetry is broken, the gap at one particle per unit cell can open even if the system preserves the $C_2\mathcal{T}$ and valley $\text{U}\left(1\right)$ symmetries, and the gap to remote bands remains open.

We evaluate the transient response of an optically tunable meta-atom composed of an electric inductor-capacitor resonator that is loaded with a piece of high-resistivity silicon and perform a proof-of-concept experiment to demonstrate the storage and release of electromagnetic waves using this meta-atom in the microwave region. The transient time of the meta-atom immediately after commencing laser light illumination of the silicon in the meta-atom is found to be inversely proportional to the incident laser power. The transmittance of the meta-atom at the resonance frequency increases to ten times that obtained without laser illumination at 5.2 ns after the start of laser illumination for a laser power of $1600\mathrm{mW}$, a laser spot size of $2\mathrm{mm}\times 1\mathrm{mm}$, and a laser wavelength of $447\mathrm{nm}$. In contrast, the transient time after turning the laser light off is dependent on the carrier lifetime of silicon and is measured to be several tens of microseconds. Based on the results of evaluation of the transient response of the meta-atom, we propose a method for the storage and release of electromagnetic waves using a Fabry-Perot resonator that includes the meta-atom as one of its mirrors. The electromagnetic wave that is stored in the Fabry-Perot resonator for a few tens of nanoseconds is then successfully released by illuminating the silicon in the meta-atom with the laser light. It is also possible to use this method in the higher-frequency region because metamaterials with semiconductor elements can even be used as active metamaterials in the optical region as long as their band gap energy is higher than the signal photon energy.

We propose theoretically how unconventional superconducting pairing in a repulsively interacting Hubbard ladder can be enhanced via the application of a Floquet driving. Initially the Hubbard ladder is prepared in its charge-density-wave dominated ground state. A periodic Floquet drive is applied that modulates the energy offset of the two legs and effectively reduces the tunneling along the rungs. This modulation of the energy offsets might be caused by the excitation of a suitable phononic mode in solids or a superlattice modulation in cold atomic gases. We use state-of-the-art matrix product state methods to monitor the resulting real-time dynamics of the system. We find an enormous enhancement of the unconventional superconducting pair correlations by approximately one order of magnitude.

We investigate the electronic and spin structure of Pb atomic chains on a $\mathrm{Si}\left(100\right)-2\times 1$ surface using first-principles calculations. We revealed that the electronic spectra of linear dimerized Pb chains with orientations perpendicular and parallel to the Si dimers are characterized by one-dimensional large Rashba spin splitting providing exclusive spin polarization of the carriers that makes these systems suitable for studying the spin-transport phenomena and realizing a tunable spin current. A buckled dimerized Pb chain with a parallel orientation was predicted to be an insulating Rashba system with a vortical spin texture and asymmetric charge distribution. In this paper we trace the origin of Rashba band anisotropy and its interplay with chain geometry. The Rashba parameters of the considered chains are compared with other well-known systems.

We theoretically investigate the decay constant of surface plasmon polaritons in a Weyl semimetal and propose an experimental method for detecting Weyl semimetals. It is revealed that the surface plasmon polariton in a Weyl semimetal exhibits various characteristics depending on the plasmon wave vector. It can be a pure surface wave, a pseudosurface wave that couples with a bulk plasmon, or a generalized surface wave with complex decay constants. Such diverse surface plasmon characteristics are peculiar to Weyl semimetals that obey axion electrodynamics. The results suggest that the measurement of the decay length, the inverse of the decay constant, can be a powerful experimental probe for identifying Weyl semimetals.

Magnetic materials with high mobilities are intriguing subjects of research from both fundamental and application perspectives. Based on first-principle calculations, we investigate the physical properties of the already synthesized $A\mathrm{MnBi}$ ($A=\mathrm{K}$, Rb, Cs) family materials. We show that these materials are antiferromagnetic (AFM), with Néel temperatures above 300 K. They contain AFM ordered Mn layers, while the interlayer coupling changes from ferromagnetic (FM) for KMnBi to AFM for RbMnBi and CsMnBi. We find that these materials are narrow gap semiconductors. Owing to the small effective mass, the electron carrier mobility can be very high, reaching up to ${10}^5{\mathrm{cm}}^2/(\mathrm{V}\mathrm{s}$) for KMnBi. In contrast, the hole mobility is much suppressed, typically lower by two orders of magnitude. We further study their two-dimensional (2D) single layer structures, which are found to be AFM with fairly high mobility $\sim {10}^3{\mathrm{cm}}^2/\left(\mathrm{V}\mathrm{s}\right)$. Their Néel temperatures can still reach room temperature. Interesting, we find that the magnetic phase transition is also accompanied by a metal-insulator phase transition, with the paramagnetic metal phase possessing a pair of nonsymmorphic-symmetry-protected 2D spin-orbit Dirac points. Furthermore, the magnetism can be effectively controlled by the applied strain. When the magnetic ordering is turned into FM, the system can become a quantum anomalous Hall insulator with gapless chiral edge states.

A detailed study of the structural and magnetic properties of inverse spinel $\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$ nanoparticles and nanostructured $\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$ microgranules is made by the first-principles calculations. We have estimated the relative strengths of crystal fields, exchange fields, and magnetic exchange interactions using the electronic structure calculations and electron density maps. We find that the electron-electron correlation plays a significant role in obtaining the correct ground-state structure. A significant local structural distortion at the octahedral site and “inverted” sublattice occupancy in $\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$ affects the magnetic exchange interactions substantially. The trends in magnetic exchange interactions are analyzed in terms of structural parameters and the features of their electronic structures and magnetic properties. We find that Fe states in $\mathrm{Co}{\mathrm{Fe}}_2{\mathrm{O}}_4$ are extremely localized, irrespective of the symmetry of the site. Also, Co and Fe ions prefer their high-spin configurations with higher spin moments at octahedral sites.

We study the sub-band-gap high harmonic generation (HHG) in a methylammonium lead trichloride single crystal. Anisotropy in the crystal orientation dependence of the high harmonic yield is observed, and the yield varies substantially with the electric field strength of the midinfrared laser pulse used for excitation. Our real-time ab initio simulations reproduce the experimental results well and also show that the HHG is independent of the interband decoherence time. Based on a microscopic analysis of the intraband current, we reveal that the orientation dependence of the HHG in this perovskite semiconductor is governed by the virtual band population, rather than the anharmonicity of the electronic band structure.

We study higher order topology in the presence of strong interactions in a two-dimensional, experimentally accessible superlattice Bose-Hubbard model with alternating hoppings and strong on-site repulsion. We evaluate the phase diagram of the model around half-filling using the density renormalization group ansatz and find two gapped phases separated by a gapless superfluid region. We demonstrate that the gapped states realize two distinct higher order symmetry protected topological phases, which are protected by a combination of charge conservation and $C_4$ lattice symmetry. The phases are distinguished in terms of a many-body topological invariant and a quantized, experimentally accessible fractional corner charge that is robust against arbitrary, symmetry preserving edge manipulations. We support our claims by numerically studying the full counting statistics of the corner charge, finding a sharp distribution peaked around the quantized values. Our results allow for a direct comparison with experiments and represent a confirmation of theoretically predicted higher order topology in a strongly interacting system. Experimentally, the fractional corner charge can be observed in ultracold atomic settings using state of the art quantum gas microscopy.

We demonstrate the emergence and dynamics of intraparticle entanglement in massless Dirac fermions. This entanglement, generated by spin-orbit coupling, arises between the spin and sublattice pseudospin of electrons in graphene. The entanglement is a complex dynamic quantity but is generally large, independent of the initial state. Its time dependence implies a dynamical violation of a Bell inequality, while its magnitude indicates that large intraparticle entanglement is a general feature of graphene on a substrate. These features are also expected to impact entanglement between pairs of particles, and may be detectable in experiments that combine Cooper pair splitting with nonlocal measurements of spin-spin correlation in mesoscopic devices based on Dirac materials.

A kagome lattice is composed of corner-sharing triangles arranged on a honeycomb lattice such that each honeycomb bond hosts a kagome site while each kagome triangle encloses a honeycomb site. Such close relation implies that the two lattices share common features. We predict here that a kagome crystal, similar to the honeycomb lattice graphene, reacts to elastic strain in a unique way that the bulk electronic states in the vicinity of Dirac points are reorganized by the strain-induced pseudomagnetic field into pseudo-Landau levels, while the degenerate edge states in the undeformed crystal become separated in the energy dimension. When the strain is tuned continuously, the resulting scanning pseudomagnetic field gives rise to quantum oscillations in both the density of states and the electrical conductivity.

A Josephson junction in a topological superconductor can inject a charge $e/2$ into a normal-metal contact, carried by chiral Majorana edge modes. Here, we address the question whether this half-integer charge is a sharp observable, without quantum fluctuations. Because the Majorana modes are gapless, they support charge fluctuations in equilibrium at zero temperature. But we find that the excess noise introduced out of equilibrium by the $e/2$ charge transfer vanishes. We discuss a strategy to reduce the equilibrium fluctuations, by means of a heavy-tailed time-dependent detection efficiency, to achieve a nearly noiseless half-integer charge transfer.

Measurements and first-principles calculations probe the temperature-dependent thermal conductivity $\left(k\right)$ of GaN films with large densities of highly oriented dislocations. We demonstrate that phonon-dislocation scattering is weaker than suggested by previous measurements, likely due to sample and experiment size effects. Nonetheless, dislocation-limited $k$ is observed in samples with large dislocation densities and at lower temperatures where $k$ anisotropy is also observed. Combination of experiment and theory give insights into the interplay of thermal resistance mechanisms limiting GaN functionalities and suggest pathways for tuning $k$ via defect engineering.

Optical pump-terahertz probe measurements are performed to study the photoexcited carrier dynamics of the In-rich two-dimensional InSe multilayer, which is a promising candidate for future high performance electronic and photoelectronic applications. According to the transient terahertz measurements, the intraband and interband relaxation processes can be clearly identified from different carrier relaxation lifetimes. The intraband relaxation consists of an ultrafast ($\sim 2$ ps) carrier-optical phonon scattering and relatively slower ($\sim 10$ ps) anharmonic scattering of hot optical phonon. The subsequent interband recombination is dominated by a Shockley-Read-Hall recombination with lifetime on order of 100 ps. Because the grown polytype In-rich InSe multilayer has a high defect density, the primary recombination channel is through the defects in the surface, but the bulk recombination increases rapidly with temperature and can catch up the contribution of the surface recombination at high temperature.

Nonreciprocal spin waves have a chiral asymmetry so that their energy is different for two opposite wave vectors. They are found in atomically thin ferromagnetic overlayers with in-plane magnetization and are linked to the antisymmetric Dzyaloshinskii-Moriya surface exchange. We use an itinerant fermion theory based on first-principles calculations to predict that nonreciprocal magnons can occur in $\mathrm{Fe}{}_3\mathrm{GeTe}{}_2$, the first stand-alone metallic two-dimensional crystal with out-of-plane magnetization. We find that both the energy and lifetime of magnons are nonreciprocal, and we predict that acoustic magnons can have lifetimes up to hundreds of picoseconds, orders of magnitude larger than in other conducting magnets.