Quantum spin liquids are topological states of matter that arise in frustrated quantum magnets at low temperatures. At low energies, such states exhibit emergent gauge fields and fractionalized quasiparticles and can also possess enhanced global symmetries compared to their parent microscopic Hamiltonians. We study the consequences of this emergent gauge and symmetry structure for the hydrodynamics of quantum spin liquids. Specifically, we analyze two cases, the $U\left(1\right)$ spin liquid with a Fermi surface and the $SU\left(4\right)$-symmetric “algebraic” spin liquid. We show that the emergent degrees of freedom in the spin liquid phase lead to a variety of additional hydrodynamic modes compared to the high-temperature paramagnetic phase. We identify a hydrodynamic regime for the internal $U\left(1\right)$ gauge field common to both states, characterized by slow diffusion of the internal transverse photon.

By using grazing incidence x-ray diffraction and scanning tunneling microscopy experiments, we determine the interface structure of a ${\mathrm{C}}_{60}$ layer deposited on a Co(0001) surface. The room temperature deposition gives rise to a ($4\times 4$) molecular structure with a 10% vertical relaxation of the underneath Co atoms. When annealed around 550 K, the interface undergoes a structural change with most of the buckyballs sitting in a seven Co vacancies nanohole. Ab initio calculations show that this interface reconstruction is stabilized by a strong C-Co hybridization and has a significant impact both on the interfacial magnetic anisotropy that is decreased and on the molecular spin polarization that it increased.

Particle-hole (PH) Pfaffian topological phases may exist in a uniform system due to strong Landau level (LL) mixing according to theoretical predictions based on the Son-Dirac composite fermion theory. Numerical investigations in the presence of large LL mixing are limited due to numerical complexities, when taking into account at least one more LL. Because of this, we apply the same field theoretical approach to the quantum Hall bilayer at total filling factor equal to one, for which many numerical studies exist. The most advanced in Zhu et al. [Zheng Zhu, Liang Fu, D. N. Sheng, Phys. Rev. Lett. 119, 177601 (2017)] predicts an intermediate phase (for intermediate distances between layers) with an even-odd effect. According to our approach, the intermediate phase represents a mixed negative-flux $p$-wave pairing i.e., coexisting intra (PH Pfaffian in each layer) and inter (a la PH Pfaffian) pairing correlations. This again underlines a necessity for strong entanglement with additional degrees of freedom, i.e., at least one more (additional) LL in the search for a stable PH Pfaffian phase in a single layer. Based on the analogy with the bilayer physics, we propose a PH Pfaffian wave function that resides in two LLs.

Quantum anomalous Hall (QAH) effect in topological insulators (TIs) is known to have involved energy bands with Chern numbers $C=\pm 1$. The QAH edge current would be electrically more accessible if one suppressed the edge-channel resistance, $h/C{e}^2$. That is why topological states $\left|C\right|>1$ are preferable for connecting them to an external circuit in device applications. The search for topological systems with a high Chern number is ongoing. This paper points to a semiconductor material system well developed for optoelectronic applications––III-nitrides. Polarization field in a compressed InN quantum well (QW) has two effects: it inverts conduction and valence energy bands, thus creating a prerequisite for topological insulator (TI), and generates Rashba spin splitting in conduction and valence bands. We calculate topological indexes in GaN/InN/GaN QW. In the QAH setting, value $\left|C\right|>1$ follows from the phase structure of interband coupling in III–V materials, providing Rashba and Zeeman fields act simultaneously. In nonmagnetic samples, explicitly calculated topological index $Z_2=1$ manifests the quantum spin Hall state.

In the present paper, we investigated the electron transport properties of molecular junctions with anharmonic vibrations described by double-well potentials in the sequential tunneling regime. It was found that the suppression of the low-bias current caused by strong electron-vibration couplings under harmonic approximation, i.e., the Franck-Condon blockade effect, could be lifted in the case of symmetric double-well potentials. The removal of the Franck-Condon blockade effect is a result of the distribution of the ground vibrational wave function in the two wells. Such a feature also enables the Franck-Condon blockade effect to be restored by breaking the symmetry of the double-well potential. We further demonstrated that the special vibrational transition properties of asymmetric double-well potentials could enable the effective modulation of the charge transport properties of such molecular junctions in the Franck-Condon blockade region by inducing population in excited vibrational levels with external fields such as infrared excitation.

We discuss novel transverse plasmon polaritons that are hosted by AA- and AB-stacked bilayer graphene due to perfect nesting. They are composed of oscillating counterflow currents in between the layers, giving a clear interpretation of these collective modes as magnetic excitations carrying magnetic moments parallel to the planes. For AA-stacked bilayer graphene, these modes can reach zero frequency at the neutrality point and we thus predict a symmetry-broken ground state leading to in-plane orbital ferromagnetism. Even though it could be hard to detect them in real solid-state devices, these novel magnetic plasmons should be observable in artificial setups such as optical lattices. Also, our results might be relevant for magic angle twisted bilayer graphene samples, as their electronic properties are mostly determined by confined AA-stacked regions.

We study the electronic phase diagram of the excitonic insulator candidates ${\mathrm{Ta}}_2\mathrm{Ni}{\left({\mathrm{Se}}_{1-x}{\mathrm{S}}_x\right)}_5$ $(x=0,\cdots ,1)$ using polarization resolved Raman spectroscopy. Critical excitonic fluctuations are observed that diminish with $x$ and ultimately shift to high energies, characteristic of a quantum phase transition. Nonetheless, a symmetry-breaking transition at finite temperatures is detected for all $x$, exposing a cooperating lattice instability that takes over for large $x$. Our study reveals a failed excitonic quantum phase transition, masked by a preemptive structural order.

Embedding a monolayer of a transition metal dichalcogenide in a high-$Q$ optical cavity results in the formation of distinct exciton polariton modes. The polaritons are affected by the strong exciton-phonon interaction in the monolayer. We use a time convolutionless master equation to calculate the phonon influence on the spectra of the polaritons. We discuss the nontrivial dependence of the line shapes of both branches on temperature and detuning. The peculiar polariton dispersion relation results in a linewidth of the lower polariton being largely independent of the coupling to acoustic phonons. For the upper polariton, acoustic phonons lead to a low-energy shoulder of the resonance in the linear response. Furthermore, we analyze the influence of inhomogeneous broadening being the dominant contribution to the lower polariton linewidth at low temperatures. Our results point towards interesting phonon features in polariton spectra in transition metal dichalcogenides.

Various exotic magnetic ground states have been anticipated in the higher transition metal $(4d \mathrm{and} 5d)$ oxides with large atomic spin-orbit coupling (SOC). However, many such expectations were not met because the exact atomic SOC strength and its consequent influence on electronic and magnetic ground states were always masked by solid-state effects. Here, we attempt to dope a dilute amount of ${\mathrm{Ir}}^{5+}$ $(x=0.1–0.3)$ in place of ${\mathrm{Sb}}^{5+}$ in perfectly cubic ${\mathrm{Ba}}_2{\mathrm{YSbO}}_6$ with a target to minimize the effects of hopping between distant Ir ions and noncubic crystal field effect to promote the effect of SOC and to realize the coveted $J_{\text{eff}}=0$ ground state, expected for $jj$-coupled $5d^4{\mathrm{Ir}}^{5+}$ systems, purely from the consideration of atomic SOC. However, despite certain inhomogeneity in the distribution of the dopant ${\mathrm{Ir}}^{5+}$ ions in the system, our experimental results reveal high magnetic moments (away from the $J_{\text{eff}}$ = 0 picture) with strong nearest-neighbor interaction, but without any long-range ordering, for the lowest doped system which continues to decrease with increasing Ir content, completely contrary to the expectation of the $jj$-coupling description. This observation strongly indicates that presence of a localized Ir moment, originating from $L\text{−}S$ coupling interaction, might be the most appropriate mechanism here.

In condensed matter physics, non-Abelian statistics for Majorana zero modes (or Majorana Fermions) is very important, really exotic, and completely robust. The race for searching Majorana zero modes and verifying the corresponding non-Abelian statistics becomes an important frontier in condensed matter physics. In this paper we generalize the Majorana zero modes to non-Hermitian (NH) topological systems that show universal but quite different properties from their Hermitian counterparts. Based on the NH Majorana zero modes, the orthogonal and nonlocal Majorana qubits are well defined. In particular, due to the particle-hole-symmetry breaking, NH Majorana zero modes have anomalous non-Abelian statistics with continuously tunable braiding Berry phase from $\pi /8$ to $3\pi /8$. This is quite different from the usual non-Abelian statistics with fixed braiding Berry phase $\pi /4$. The one-dimensional NH Kitaev model is taken as an example to numerically verify the anomalous non-Abelian statistics for two NH Majorana zero modes. The numerical results are exactly consistent with the theoretical prediction. With the help of braiding these two zero modes, the $\pi /8$ gate can be reached and thus universal topological quantum computation becomes possible.

Higher-order topological phases as the generalization of Berry phases attract an enormous amount of research. The current theoretical models supporting higher-order topological phases, however, cannot give the connection between lower-order and higher-order topological phases when extending the lattice from lower to higher dimensions. Here, we theoretically propose and experimentally demonstrate a topological corner state constructed from the edge states in a one-dimensional lattice. The two-dimensional square lattice owns independent spatial modulation of coupling in each direction, and the combination of edge states in two directions comes up to the higher-order topological corner state in a two-dimensional lattice, revealing the connection of topological phase in lower- and higher-dimensional lattices. Our work deepens the understanding of the topological phases breaking through the lattice dimensions, and provides a promising tool constructing higher topological phases in higher-dimensional structures.

We carried out ${}^{75}\mathrm{As}$ nuclear magnetic resonance (NMR) measurements on the trigonal $\mathrm{Ca}{\mathrm{Mn}}_2{\mathrm{As}}_2$ and $\mathrm{Sr}{\mathrm{Mn}}_2{\mathrm{As}}_2$ insulators exhibiting antiferromagnetic (AFM) ordered states below Néel temperatures $T_{\mathrm{N}}=62$ and 120 K, respectively. In the paramagnetic state above $T_{\mathrm{N}}$, typical quadrupolar-split ${}^{75}\mathrm{As}$ NMR spectra were observed for both systems. The ${}^{75}\mathrm{As}$ quadrupolar frequency ${\nu }_{\mathrm{Q}}$ for $\mathrm{Ca}{\mathrm{Mn}}_2{\mathrm{As}}_2$ decreases with decreasing temperature, while ${\nu }_{\mathrm{Q}}$ for $\mathrm{Sr}{\mathrm{Mn}}_2{\mathrm{As}}_2$ increases, showing an opposite temperature dependence. In the AFM state, the relatively sharp and distinct ${}^{75}\mathrm{As}$ NMR lines were observed in $\mathrm{Sr}{\mathrm{Mn}}_2{\mathrm{As}}_2$ and the NMR spectra were shifted to lower fields for both magnetic fields $H\parallel c$ axis and $H\parallel ab$ plane, suggesting that the internal fields $B_{\mathrm{int}}$ at the As site produced by the Mn ordered moments are nearly perpendicular to the external magnetic field direction. No obvious distribution of $B_{\mathrm{int}}$ was observed in $\mathrm{Sr}{\mathrm{Mn}}_2{\mathrm{As}}_2$, which clearly indicates a commensurate AFM state. In sharp contrast to $\mathrm{Sr}{\mathrm{Mn}}_2{\mathrm{As}}_2$, broad and complex NMR spectra were observed in $\mathrm{Ca}{\mathrm{Mn}}_2{\mathrm{As}}_2$ in the AFM state, which clearly shows a distribution of $B_{\mathrm{int}}$ at the As site, indicating an incommensurate state. From the analysis of the characteristic shape of the observed spectra, the AFM state of $\mathrm{Ca}{\mathrm{Mn}}_2{\mathrm{As}}_2$ was determined to be a two-dimensional incommensurate state where Mn ordered moments are aligned in the $ab$ plane. A possible origin for the different AFM states in the systems was discussed. Both $\mathrm{Ca}{\mathrm{Mn}}_2{\mathrm{As}}_2$ and $\mathrm{Sr}{\mathrm{Mn}}_2{\mathrm{As}}_2$ show very large anisotropy in the nuclear spin-lattice relaxation rate $1/T_1$ in the paramagnetic state. $1/T_1$ for $H\parallel ab$ is much larger than that for $H\parallel c$, indicating strong anisotropic AFM spin fluctuations in both compounds.

We study an interface between a Kitaev spin liquid (KSL) in the chiral phase and a nonchiral superconductor. When the coupling across the interface is sufficiently strong, the interface undergoes a transition into a phase characterized by a condensation of a bound state of a Bogoliubov quasiparticle in the superconductor and an emergent fermionic excitation in the spin liquid. In the condensed phase, electrons in the superconductor can coherently convert into emergent fermions in the spin liquid and vice versa. As a result, the chiral Majorana edge mode of the spin liquid becomes visible in the electronic local density of states at the interface, which can be measured in scanning tunneling spectroscopy experiments. We demonstrate the existence of this phase transition, and the nonlocal order parameter that characterizes it, using density matrix renormalization group simulations of a KSL strip coupled at its edge to a superconductor. An analogous phase transition can occur in a simpler system composed of a one-dimensional spin chain with a spin-flip ${\mathbb{Z}}_2$ symmetry coupled to a superconductor.

We report full vector mapping of local magnetization in CeAlSi, a Weyl semimetal in which both inversion and time-reversal symmetries are broken. The vector maps reveal unanticipated features both within domains and at their boundaries. Boundaries between domains form two kinds of walls with distinct topology and, therefore, different interactions with Weyl fermions. Domain walls aligned along the tetragonal axes, e.g., (100), exhibit emergent chirality forbidden by the bulk space group, whereas diagonal walls are nonchiral. Within the domains, we observe that the previously reported set of four easy axes aligned along the in-plane diagonals of the tetragonal structure actually split to form an octet with decreasing temperature below the magnetic transition. All the above phenomena are ultimately traced to the noncollinear magnetic structure of CeAlSi.

We study quantum effects of the vacuum light-matter interaction in materials embedded in optical cavities. We focus on the electronic response of a two-dimensional semiconductor placed inside a planar cavity. By using a diagrammatic expansion of the electron-photon interaction, we describe signatures of light-matter hybridization characterized by large asymmetric shifts of the spectral weight at resonant frequencies. We follow the evolution of the light dressing from the cavity to the free-space limit. In the cavity limit, light-matter hybridization results in a modification of the optical gap with sizable spectral weight appearing below the bare gap edge. In the limit of large cavities, we find a residual redistribution of spectral weight which becomes independent of the distance between the two mirrors. We show that the photon dressing of the electronic response can be fully explained by using a classical description of light. The classical description is found to hold up to a strong coupling regime of the light-matter interaction highlighted by the large modification of the photon spectra with respect to the empty cavity. We show that, despite the strong coupling, quantum corrections are negligibly small and weakly dependent on the cavity confinement. As a consequence, in contrast to the optical gap, the single-particle electronic band gap is not sensibly modified by strong coupling. Our results show that quantum corrections are dominated by off-resonant photon modes at high energy. As such, cavity confinement can hardly be seen as a knob to control the quantum effects of the light-matter interaction in vacuum.

We expand the concept of frustration in Mott insulators and quantum spin liquids to metals with flat bands. We show that when interorbital hopping $t_2$ dominates over intraorbital hopping $t_1$, in a multiband system with strong spin-orbit coupling $\lambda$, electronic states with a narrow bandwidth $\mathrm{\Delta }\sim {\left(t_2\right)}^2/\lambda$ are formed compared to a bandwidth of order $t_1$ for intraorbital hopping dominated models. We demonstrate the evolution of the electronic structure, Berry phase distributions for time-reversal and inversion breaking cases, and their imprint on the optical absorption in a tight-binding model of $d$-orbital hopping on a honeycomb lattice. Going beyond quantum Hall effects and twisted bilayer graphene, we provide an alternative mechanism and a richer materials' platform for achieving flat bands poised at the brink of instabilities toward novel correlated and fractionalized metallic phases.

Disorder caused by defects plays an important role on the emergence of exotic physical phenomena in quantum states of materials, including charge density waves (CDWs). Usually, the coexistence of multiphase CDWs aroused by defects is manifested in multiple domains resulting from phase separation. By using scanning tunneling microscopy, we reveal an intertwining of two CDW phases without explicit domain boundaries on a cleaved surface of layered intercalation compounds ${\mathrm{In}}_x\mathrm{Ta}{\mathrm{Se}}_2$ ($x=0.58$), which undergoes commensurate CDW transitions twice by cooling. The two CDW phases, i.e., $2\times \sqrt{3}$ and $2\times 2$ phases at higher and lower temperature, respectively, have very similar atomic arrangements in the $\mathrm{Ta}{\mathrm{Se}}_2$ layers and thus are very sensitive to the random potentials induced by the intercalated In atoms. Moreover, the translational symmetry breaking of the $2\times \sqrt{3}$ phase results in the presence of another intertwined $\sqrt{7}\times \sqrt{7}$ phase. These findings provide insight into the microscopic effect of defects on multiphase CDWs and reveal a coexisting manner of CDW phases.

Spin qubits are contenders for scalable quantum computation because of their long coherence times demonstrated in a variety of materials, but individual control by frequency-selective addressing using pulsed spin resonance creates severe technical challenges for scaling up to many qubits. This individual resonance control strategy requires each spin to have a distinguishable frequency, imposing a maximum number of spins that can be individually driven before qubit crosstalk becomes unavoidable. Here we describe a complete strategy for controlling a large array of spins in quantum dots dressed by an on-resonance global field, namely, a field that is constantly driving the spin qubits, to dynamically decouple from the effects of background magnetic field fluctuations. This approach—previously implemented for the control of single electron spins bound to electrons in impurities—is here harmonized with all other operations necessary for universal quantum computing with spins in quantum dots. We define the logical states as the dressed qubit states and discuss initialization and readout utilizing Pauli spin blockade, as well as single- and two-qubit control in the new basis. Finally, we critically analyze the limitations imposed by qubit variability and potential strategies to improve performance.

We introduce extended density matrix embedding theory (EDMET), a static quantum embedding theory explicitly self-consistent with respect to local two-body physics. This overcomes the biggest practical and conceptual limitation of more traditional one-body embedding methods, namely the lack of screening and treatment of longer-range interactions. This algebraic zero-temperature embedding augments a local interacting cluster model with a minimal number of bosons from a description of the full system correlations via the random phase approximation, and admits an analytic approach to build a self-consistent Coulomb-exchange-correlation kernel. For extended Hubbard models with nonlocal interactions, this leads to the accurate description of phase transitions, static quantities, and dynamics. We also move towards ab initio systems via the Parriser-Parr-Pople model of conjugated coronene derivatives, finding good agreement with experimental optical gaps.