We study the fate of quantum correlations at finite temperature in the two-dimensional toric code using the logarithmic entanglement negativity. We are able to obtain exact results that give us insight into how thermal excitations affect quantum entanglement. The toric code has two types of elementary excitations (defects) costing different energies. We show that an $O\left(1\right)$ density of the lower energy defect is required to degrade the zero-temperature entanglement between two subsystems in contact with one another. However, one type of excitation alone is not sufficient to kill all quantum correlations, and an $O\left(1\right)$ density of the higher energy defect is required to cause the so-called sudden death of the negativity. Interestingly, if the energy cost of one of the excitations is taken to infinity, quantum correlations survive up to arbitrarily high temperatures, a feature that is likely shared with other quantum spin liquids and frustrated systems in general, when projected down to their low-energy states. We demonstrate this behavior both for small subsystems, where we can prove that the negativity is a necessary and sufficient condition for separability, as well as for extended subsystems, where it is only a necessary condition. We further observe that the negativity per boundary degree of freedom at a given temperature increases (parametrically) with the size of the boundary, and that quantum correlations between subsystems with extended boundaries are more robust to thermal fluctuations.

We explore the effects of various kinds of random disorder on the quasiparticle density of states of two-dimensional $d$-wave superconductors using an exact real-space method, incorporating realistic details known about the cuprates. Random on-site energy and pointlike unitary impurity models are found to give rise to a vanishing DOS at the Fermi energy for narrow distributions and low concentrations, respectively, and lead to a finite, but suppressed, DOS at unrealistically large levels of disorder. Smooth disorder arising from impurities located away from the copper-oxide planes meanwhile gives rise to a finite DOS at realistic impurity concentrations. For the case of smooth disorder whose average potential is zero, a resonance is found at zero energy for the quasiparticle DOS at large impurity concentrations. We discuss the implications of these results on the computed low-temperature specific heat, the behavior of which we find is strongly affected by the amount of disorder present in the system. We also compute the localization length as a function of disorder strength for various types of disorder and find that intermediate- and high-energy states are quasiextended for low disorder, and that states near the Fermi energy are strongly localized and have a localization length that exhibits an unusual dependence on the amount of disorder. We comment on the origin of disorder in the cuprates and provide constraints on these based on known results from scanning tunneling spectroscopy and specific heat experiments.

We investigate the microscopic mechanisms of the charge-density-wave (CDW) formation in a monolayer ${\mathrm{TiSe}}_2$ using a realistic multiorbital $d-p$ model with electron-phonon coupling and intersite Coulomb (excitonic) interactions. First, we estimate the tight-binding bands of Ti $3d$ and Se $4p$ orbitals in the monolayer ${\mathrm{TiSe}}_2$ on the basis of the first-principles band-structure calculations. We thereby show orbital textures of the undistorted band structure near the Fermi level. Next, we derive the electron-phonon coupling using the tight-binding approximation and show that the softening occurs in the transverse phonon mode at the $M$ point of the Brillouin zone. The stability of the triple-$q$ CDW state is thus examined to show that the transverse phonon modes at the $M_1, M_2$, and $M_3$ points are frozen simultaneously. Then, we introduce the intersite Coulomb interactions between the nearest-neighbor Ti and Se atoms that lead to the excitonic instability between the valence Se $4p$ and conduction Ti $3d$ bands. Treating the intersite Coulomb interactions in the mean-field approximation, we show that the electron-phonon and excitonic interactions cooperatively stabilize the triple-$q$ CDW state in ${\mathrm{TiSe}}_2$. We also calculate a single-particle spectrum in the CDW state and reproduce the band folding spectra observed in photoemission spectroscopies. Finally, to clarify the nature of the CDW state, we examine the electronic charge density distribution and show that the CDW state in ${\mathrm{TiSe}}_2$ is of a bond type and induces a vortexlike antiferroelectric polarization in the kagome network of Ti atoms.

We generalize the previous exact results of the Nagaoka-type itinerant ferromagnetic states in a three-dimensional $t_{2g}$ orbital system to allow for multiple holes. The system is a simple cubic lattice with each site possessing $d_{xy},d_{yz}$, and $d_{xz}$ orbitals, which allow two-dimensional hopping within each orbital plane. In the strong-coupling limit of $U\to \infty$, the orbital-generalized Nagaoka ferromagnetic states are proved to be degenerate with the ground state in the thermodynamic limit when the hole number per orbital layer scales slower than $L^{\frac{1}{2}}$. This result is valid for arbitrary values of the ferromagnetic Hund's coupling $J>0$ and interorbital repulsion $V\ge 0$. The stability of the Nagaoka-type state at finite electron densities with respect to a single spin flip is investigated. These results provide helpful guidance for studying the mechanism of itinerant ferromagnetism for the $t_{2g}$ orbital materials.

Using exact diagonalization technique, we investigate the many-body localization phenomenon in the 1D Heisenberg chain comparing several disorder models. In particular we consider a family of discrete distributions of disorder strengths and compare the results with the standard uniform distribution. Both statistical properties of energy levels and the long time nonergodic behavior are discussed. The results for different discrete distributions are essentially identical to those obtained for the continuous distribution, provided the disorder strength is rescaled by the standard deviation of the random distribution. Only for the binary distribution significant deviations are observed.

The aim of the presented research is to design a nanodevice, based on a ${\mathrm{MoS}}_2$ monolayer, performing operations on a well-defined valley qubit. We show how to confine an electron in a gate-induced quantum dot within the monolayer, and to perform the not operation on its valley degree of freedom. The operations are carried out all electrically via modulation of the confinement potential by oscillating voltages applied to the local gates. Such quantum dot structure is modeled realistically. Through these simulations we investigate the possibility of realization of a valley qubit in analogy with a realization of the spin qubit. We accurately model the potential inside the nanodevice accounting for proper boundary conditions on the gates and space-dependent materials permittivity by solving the generalized Poisson's equation. The time evolution of the system is supported by realistic self-consistent Poisson-Schrödinger tight-binding calculations. The tight-binding calculations are further confirmed by simulations within the effective continuum model.

Massless Dirac fermions in graphene can acquire a mass through different kinds of sublattice-symmetry-breaking perturbations, and there is a growing need to determine this mass using a conventional method. We describe how the mass caused by a staggered sublattice potential changes the phonon self-energy and explain the mechanism in terms of the pseudospin polarization of massive Dirac fermions. We argue that the mass is detectable using Raman spectroscopy.

Remarkable features have been predicted for the mechanical fluctuations at the bistability transition of a classical oscillator coupled capacitively to a quantum dot [Micchi et al., Phys. Rev. Lett. 115, 206802 (2015)]. These results have been obtained in the regime $\hslash {\omega }_0\ll k_{B}T\ll \hslash \mathrm{\Gamma }$, where ${\omega }_0, T$, and $\mathrm{\Gamma }$ are the mechanical resonating frequency, the temperature, and the tunneling rate, respectively. A similar behavior could be expected in the quantum regime of $\hslash \mathrm{\Gamma }\ll k_{B}T\ll \hslash {\omega }_0$. We thus calculate the energy- and displacement-fluctuation spectra and study their behavior as a function of the electromechanical coupling constant when the system enters the Frank-Condon regime. We find that in analogy with the classical case, the energy-fluctuation spectrum and the displacement spectrum widths show a maximum for values of the coupling constant at which a mechanical bistability is established.

Using first-principles calculations, we investigate the electronic properties of the two-dimensional $\mathrm{Ga}X$/${MX}_2$ ($M$ = Mo, W; $X$ = S, Se, Te) heterostructures. Orbital hybridization between $\mathrm{Ga}X$ and ${MX}_2$ is found to result in Rashba splitting at the valence-band edge around the $\mathrm{\Gamma }$ point, which grows for increasing strength of the spin-orbit coupling in the $p$ orbitals of the chalcogenide atoms. The location of the valence-band maximum in the Brillouin zone can be tuned by strain and application of an out-of-plane electric field. The coexistence of Rashba splitting (in-plane spin direction) and band splitting at the $K$ and $K^{\prime }$ valleys (out-of-plane spin direction) makes $\mathrm{Ga}X$/${MX}_2$ heterostructures interesting for spintronics and valleytronics. They are promising candidates for two-dimensional spin-field-effect transistors and spin-valley Hall effect devices. Our findings shed light on the spin-valley coupling in van der Waals heterostructures.

${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ is the archetype of the spin-orbit Mott insulator, but the nature of the metallic states that may emerge from this type of insulator is still not very well known. We study with angle-resolved photoemission the insulator-to-metal transition observed in ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{O}}_4$ when Ir is substituted by Rh ($0.02<x<0.35$). The originality of the Rh doping is that Ir and Rh, which are formally isovalent, adopt different charge states, a rather unusual and inhomogeneous situation. We show that the evolution to the metallic state can be essentially understood as a shift of the Fermi level into the lower Hubbard band of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. The Mott gap appears quite insensitive to the introduction of up to $\sim 20\%$ holes in this band. The metallic phase, which forms for $x>0.07$, is not a Fermi liquid. It is characterized by the absence of quasiparticles, unrenormalized band dispersion compared to calculations, and an $\sim 30\text{−}\mathrm{meV}$ pseudogap on the entire Fermi surface.

Fractional quantum Hall (FQH) system at Landau level filling fraction $\nu =5/2$ has long been suggested to be non-Abelian, either Pfaffian (Pf) or antiPfaffian (APf) states by numerical studies, both with quantized Hall conductance ${\sigma }_{xy}=5e^2/2h$. Thermal Hall conductances of the Pf and APf states are quantized at ${\kappa }_{xy}=7/2$ and ${\kappa }_{xy}=3/2$, respectively, in a proper unit. However, a recent experiment shows the thermal Hall conductance of $\nu =5/2$ FQH state is ${\kappa }_{xy}=5/2$. It has been speculated that the system contains random Pf and APf domains driven by disorders, and the neutral chiral Majorana modes on the domain walls may undergo a percolation transition to a ${\kappa }_{xy}=5/2$ phase. In this paper, we do perturbative and nonperturbative analyses on the domain walls between Pf and APf. We show the domain wall theory possesses an emergent SO(4) symmetry at energy scales below a threshold ${\mathrm{\Lambda }}_1$, which is lowered to an emergent $U\left(1\right)\times U$(1) symmetry at energy scales between ${\mathrm{\Lambda }}_1$ and a higher value ${\mathrm{\Lambda }}_2$, and is finally lowered to the composite fermion parity symmetry ${\mathbb{Z}}_2^F$ above ${\mathrm{\Lambda }}_2$. Based on the emergent symmetries, we propose a phase diagram of the disordered $\nu =5/2$ FQH system and show that a ${\kappa }_{xy}=5/2$ phase arises at disorder energy scales $\mathrm{\Lambda }>{\mathrm{\Lambda }}_1$. Furthermore, we show the gapped double-semion sector of $N_D$ compact domain walls contributes nonlocal topological degeneracy $2^{N_D-1}$, causing a low-temperature peak in the heat capacity. We implement a nonperturbative method to bootstrap generic topological $1+1\mathrm{D}$ domain walls (two-surface defects) applicable to any $2+1\mathrm{D}$ non-Abelian topological order. We also identify potentially relevant spin topological quantum field theories (TQFTs) for various $\nu =5/2$ FQH states in terms of fermionic version of $U{\left(1\right)}_{\pm 8}$ Chern-Simons $\mathrm{theory}\times {\mathbb{Z}}_8$-class TQFTs.

The delicate interplay of competing phases in quantum materials is dominated by parameters such as the crystal field potential, the spin-orbit coupling, and, in particular, the electronic correlation strength. Whereas small quantitative variations of the parameter values can thus qualitatively change the material, these values can hitherto hardly be obtained with reasonable precision, be it theoretically or experimentally. Here we propose a solution combining resonant x-ray reflectivity (RXR) with multiplet ligand field theory (MLFT). We first perform ab initio DFT calculations within the MLFT framework to get initial parameter values, which we then use in a fit of the theoretical model to RXR. To validate our method, we apply it to NiO and ${\mathrm{SrTiO}}_3$ and obtain parameter values, which are amended by as much as $20\%$ compared to the ab initio results. Our approach is particularly useful to investigate topologically trivial and nontrivial correlated insulators, staggered moments in magnetically or orbitally ordered materials, and reconstructed interfaces.

Based on ab initio theoretical calculations of the optical spectra of vertical heterostructures of ${\mathrm{MoSe}}_2$ (or ${\mathrm{MoS}}_2$) and ${\mathrm{WSe}}_2$ sheets, we reveal two spin-orbit-split Rydberg series of excitonic states below the $A$ excitons of ${\mathrm{MoSe}}_2$ and ${\mathrm{WSe}}_2$ with a significant binding energy on the order of 250 meV for the first excitons in the series. At the same time, we predict from accurate many-body ${\mathrm{G}}_0{\mathrm{W}}_0$ calculations that crystallographically aligned ${\mathrm{MoSe}}_2\text{/}{\mathrm{WSe}}_2$ heterostructures exhibit an indirect fundamental band gap. Due to the type-II nature of the ${\mathrm{MoSe}}_2\text{/}{\mathrm{WSe}}_2$ heterostructure, the indirect transition and the exciton Rydberg series corresponding to a direct transition exhibit a distinct interlayer nature with spatial charge separation of the coupled electrons and holes. Our calculations confirm the recent experimental observation of a doublet nature of the long-lived states in photoluminescence spectra of $\mathrm{Mo}{X}_2\text{/}\mathrm{W}{Y}_2$ heterostructures, and we attribute these two contributions to momentum-direct interlayer excitons at the $K$ point of the hexagonal Brillouin zone and to momentum-indirect excitons at the indirect fundamental band gap. Our calculations further suggest a noticeable effect of stacking order on the electronic band gaps and on the peak energies of the interlayer excitons and their oscillation strengths.

We discuss neutral and charged complexes (biexcitons and trions) formed by indirect excitons in layered quasi-two-dimensional semiconductor heterostructures. Indirect excitons—long-lived neutral Coulomb-bound pairs of electrons and holes of different layers—have been known for semiconductor coupled quantum wells and have recently been reported for van der Waals heterostructures such as double bilayer graphene and transition-metal dichalcogenides. Using the configuration space approach, we derive the analytical expressions for the trion and biexciton binding energies as a function of interlayer distance. The method captures essential kinematics of complex formation to reveal significant binding energies, up to a few tens of meV for typical interlayer distances $\sim 3–5\text{Å}$, with the trion binding energy always being greater than that of the biexciton. Our results can contribute to the understanding of more complex many-body phenomena such as exciton Bose–Einstein condensation and Wigner-like electron-hole crystallization in layered semiconductor heterostructures.

We report experiments on the dynamic response of an interacting mesoscopic capacitor consisting of a quantum dot with two confined spin-split levels of the lowest Landau level. In high magnetic fields, states inside the dot are regulated by a mixture of Coulomb interaction and Landau-level quantization, and electrons distribute on two spatially separated regions. Quantum point contact voltage and magnetic field are employed to manipulate the number and distribution of electrons inside the quantum dot. We find that the periodicity of the electrochemical capacitance oscillations is dominated by the charging energy, and their amplitudes, due to internal charge transfer and strong internal capacitive coupling, show rich variations of modulations. Magnetocapacitance displays a sawtoothlike manner and may differ in tooth directions for different voltages, which, we demonstrate, result from a sawtoothlike electrochemical potential change induced by internal charge transfer and field-sensitive electrostatic potential. We further build a charge stability diagram, which, together with all other capacitance properties, is consistently interpreted in terms of a double-dot model. The demonstrated technique is of interest as a tool for fast and sensitive charge state readout of a double-quantum-dot qubit in the gigahertz frequency quantum electronics.

Identification of kinetic and thermodynamic factors that control crystal nucleation and growth represents a central challenge in materials synthesis. Here we report that apparently defect-free growth of ${\mathrm{La}}_2{\mathrm{MnNiO}}_6$ (LMNO) thin films supported on ${\mathrm{SrTiO}}_3$ (STO) proceeds up to 1–5 nm, after which it is disrupted by precipitation of NiO phases. Local geometric phase analysis and ensemble-averaged x-ray reciprocal space mapping show no change in the film strain away from the interface, indicating that mechanisms other than strain relaxation induce the formation of the NiO phases. Ab initio simulations suggest that the electrostatic potential build-up associated with the polarity mismatch at the film-substrate interface promotes the formation of oxygen vacancies with increasing thickness. In turn, oxygen deficiency promotes the formation of Ni-rich regions, which points to the built-in potential as an additional factor that contributes to the NiO precipitation mechanisms. These results suggest that the precipitate-free region could be extended further by either incorporating dopants that suppress the built-in potential or by increasing the oxygen fugacity in order to suppress the formation of oxygen vacancies.

The high-pressure behavior of monoclinic ($P{2}_1/c$) $\alpha$-chalcocite, ${\mathrm{Cu}}_2\mathrm{S}$, was investigated at ambient temperature by single-crystal x-ray diffraction, electrical resistance measurements, and optical absorption spectroscopy up to 16 GPa. The experiments were complemented by density-functional-theory-based calculations. Single-crystal x-ray diffraction data show that monoclinic $\alpha$-chalcocite undergoes two pressure-induced first-order phase transitions at $\sim 3.1$ and $\sim 7.1$ GPa. The crystal structure of the first high-pressure polymorph, HP1, was solved and refined in space group $P{2}_1/c$ with $a=10.312\left(4\right)\AA , b=6.737\left(3\right)\AA , c=7.305\left(1\right)\AA$, and $\beta =100.17{\left(2\right)}^{\circ }$ at 6.2(3) GPa. The crystal structure of the second high-pressure polymorph, HP2, was solved and refined in space group $P{2}_1/c$ with $a=6.731\left(4\right)\AA , b=6.689\left(2\right)\AA , c=6.967\left(8\right)\AA$, and $\beta =93.18{\left(3\right)}^{\circ }$ at 7.9(4) GPa. Electrical resistance measurements upon compression and optical absorption experiments upon decompression show that the structural changes in $\alpha$-chalcocite are accompanied by changes of the electrical and optical properties. Upon pressure release, the band gap $E_g$ of $\alpha$-chalcocite (1.24 eV at ambient conditions) widens across the first structural phase transition, going from 1.24 eV at 2.2 GPa ($\alpha$-chalcocite) to 1.35 eV at 2.6 GPa (HP1), and closes significantly across the second phase transition, going from 1.32 eV at 4.4 GPa (HP1) to 0.87 eV at 4.9 GPa (HP2). The electrical resistance shows similar behavior: its highest value is for the first high-pressure polymorph (HP1), and its lowest value is for the second high-pressure polymorph (HP2) of $\alpha$-chalcocite. These results are interpreted on the basis of calculated electronic band structures.

We report a muon spin rotation/relaxation ($\mu \mathrm{SR}$) study of single-crystalline samples of the $\alpha -{\mathrm{RuCl}}_3$ honeycomb magnet, which is presumed to be a model compound for the Kitaev-Heisenberg interaction. It is inferred from magnetic susceptibility and specific-heat measurements that the present samples exhibit successive magnetic transitions at different critical temperatures $T_{\mathrm{N}}$ with decreasing temperature, eventually falling into the $T_{\mathrm{N}}=7$ K antiferromagnetic (7 K) phase that has been observed in only single-crystalline specimens with the least stacking fault. Via $\mu \mathrm{SR}$ measurements conducted under a zero external field, we show that such behavior originates from a phase separation induced by the honeycomb plane stacking fault, yielding multiple domains with different $T_{\mathrm{N}}$'s. We also perform $\mu \mathrm{SR}$ measurements under a transverse field in the paramagnetic phase to identify the muon site from the muon-Ru hyperfine parameters. Based on a comparison of the experimental and calculated internal fields at the muon site for the two possible spin structures inferred from neutron diffraction data, we suggest a modulated zigzag spin structure for the 7 K phase, with the amplitude of the ordered magnetic moment being significantly reduced from that expected for the orbital quenched spin-1/2 state.

We study the phases of a spin system on the kagome lattice with nearest-neighbor $XXZ$ interactions with anisotropy ratio $\mathrm{\Delta }$ and Dzyaloshinskii-Moriya interactions with strength $D$. In the classical limit where the spin $S$ at each site is very large, we find a rich phase diagram of the ground state as a function of $\mathrm{\Delta }$ and $D$. There are five distinct phases which correspond to different ground-state spin configurations in the classical limit. We use spin-wave theory to find the bulk energy bands of the magnons in some of these phases. We also study a strip of the system which has infinite length and finite width; we find states which are localized near one of the edges of the strip with energies which lie in the gaps of the bulk states. In the ferromagnetic phase in which all the spins point along the $+\widehat{z}$ or $-\widehat{z}$ direction, the bulk bands are separated from each other by finite energy gaps. This makes it possible to calculate the Berry curvature at all momenta, and hence the Chern numbers for every band; the number of edge states is related to the Chern numbers. Interestingly, we find that there are four different regions in this phase where the Chern numbers are different. Hence there are four distinct topological phases even though the ground-state spin configuration is identical in all these phases. We calculate the thermal Hall conductivity of the magnons as a function of the temperature in the above ferromagnetic phase; we find that this can distinguish between the various topological phases. These results are valid for all values of $S$. In the other phases, there are no gaps between the different bands; hence the edge states are not topologically protected.