From the analysis of the cyclotron resonance, we experimentally obtain the band structure of the three-dimensional topological insulator based on a HgTe thin film. Top gating was used to shift the Fermi level in the film, allowing us to detect separate resonance modes corresponding to the surface states at two opposite film interfaces, the bulk conduction band, and the valence band. The experimental band structure agrees reasonably well with the predictions of the $\mathbf{k}·\mathbf{p}$ model. Due to the strong hybridization of the surface and bulk bands, the dispersion of the surface states is close to parabolic in the broad range of the electron energies.

A cardinal obstacle to understanding and predicting quantitatively the properties of solids and large molecules is that, for these systems, it is very challenging to describe beyond the mean-field level the quantum-mechanical interactions between electrons belonging to different atoms. Here we show that there exists an exact dual equivalence relationship between the seemingly distinct physical problems of describing local and nonlocal interactions in many-electron systems. This is accomplished using a theoretical construction analog to the quantum link approach in lattice gauge theories, featuring the nonlocal electron-electron interactions as if they were mediated by auxiliary high-energy fermionic particles interacting in a purely local fashion. Besides providing an alternative theoretical direction of interpretation, this result may allow us to study both local and nonlocal interactions on the same footing, utilizing the powerful state-of-the-art theoretical and computational frameworks already available.

$\mathrm{BaSn}{\mathrm{O}}_3$ (BSO) is a wide-band-gap oxide in which very high levels of $n$-type doping have been demonstrated. Here we perform a detailed investigation of the conduction-band structure of BSO, reporting band velocities and effective masses as a function of energy, and explore whether sufficiently high doping levels can be achieved to fill the conduction band to energies near the inflection point. The presence of carriers near the inflection point can lead to negative differential resistance (NDR) due to the effective mass above the inflection point being negative. Our first-principles calculations, based on density functional theory with a hybrid functional, show that BSO has an inflection point 2.29 eV above the conduction-band minimum and that secondary conduction-band valleys are at least 2 eV higher in energy. We discuss the options available to achieve the required $n$-type doping levels to reach the inflection point in BSO.

We present an alternative perspective on semiconductor band-gap energies in terms of structural motifs, viewed through the lens of an Ising model as a means of quantifying the corresponding degree of lattice ordering. The validity of the model is demonstrated experimentally first through ${\mathrm{ZnSnN}}_2$ as an archetype ternary heterovalent semiconductor, in which variation of cation disorder enables the band gap to be tuned from above its equilibrium phase value, through zero, to negative values which correspond to inverted bands. The model is then applied to example binary compounds InN, GaN, and ZnO where anion-cation antisite defects form the basis for structural motifs, and we present experimental evidence that the same range of band-gap tuning is also possible for such materials. The case of alloys is treated by applying a three-spin Potts model to ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$. The Ising model also applies to elemental semiconductors, and is used to explain the wide range of reported values for silicon and nanoporous graphene in the context of vacancy-based structural motifs.

We study the influence of nuclei-induced frequency focusing on the mode locking of spin coherence in quantum dots subjected to a periodic train of optical pulses. In particular, we address the question whether or not nuclei-induced frequency focusing always enhances the effect of spin mode locking. We combine two advanced semiclassical approaches and extend the resulting model by including the full dynamics of the optically excited trion state. In order to reduce the discrepancy to a full quantum model, we establish a nondeterministic pulse description by interpreting each pump pulse as a measurement. Both extensions lead to significant qualitative changes of the physics. Their combination improves the description of the corresponding experiments. Importantly, we observe the emergence of dynamic nuclear polarization, i.e., the formation of a nonzero average polarization of the nuclear spin bath, leading to a certain increase of the coherence time.

We present the phase diagram of free charges (electrons and holes), excitons, and biexcitons in highly excited CdSe nanoplatelets that predicts a crossover to a biexciton-dominated region at easily attainable low temperatures or high photoexcitation densities. Our findings extend previous work describing only free charges and excitons by introducing biexcitons into the equation of state, while keeping the exciton and biexciton binding energies constant in view of the relatively low density of free charges in this material. Our predictions are experimentally testable in the near future and offer the prospect of creating a quantum degenerate, and possibly even superfluid, biexciton gas. Furthermore, we also provide simple expressions giving analytical insight into the regimes of photoexcitation densities and temperatures in which excitons and biexcitons dominate the response of the nanoplatelets.

Quasiparticle interference patterns formed by a surface state on the Re(0001) surface were investigated using scanning tunneling spectroscopy. The energy dispersion is inferred from Fourier-transformed differential conductivity maps for occupied and unoccupied states. The band dispersion for occupied states agrees with earlier published results obtained by angle-resolved photoemission spectroscopy. An analysis of the phase of interference patterns at step edges reveals a drastic change in the effective energy barrier for backscattering above and below the Fermi level. The attenuation of the interference pattern with increasing distance indicates interband scattering is the dominant scattering mechanism. Step decoration by Ni has a negligible influence on the pattern, excluding spin-flip scattering as a dominant contribution. The one-dimensional Re/Au line interface, however, reverses the scattering barrier behavior, indicating a coupling of surface states.

Monolayer transition metal dichalcogenides (${\mathrm{MX}}_2$) are promising candidates for future electronics. Although the transport properties (e.g., mobility) at low electric field have been widely studied, there are limited studies on high-field properties, which are important for many applications. Particularly, there is lack of understanding of the physical origins underlying the property differences across different ${\mathrm{MX}}_2$. Here by combining first-principles calculations with Monte Carlo simulations, we study the high-field electron transport in defects-free unstrained and tensilely strained ${\mathrm{MX}}_2$ ($M$ = Mo, W and $X=\mathrm{S}$, Se). We find that ${\mathrm{WS}}_2$ has the highest peak velocity (due to its smallest effective mass) that can be reached at the lowest electric field (owing to its highest mobility). Strain can increase the peak velocity by increasing the scattering energy. After reaching the peak velocity, most ${\mathrm{MX}}_2$ demonstrates negative differential mobility (NDM). ${\mathrm{WS}}_2$ shows the largest NDM among unstrained ${\mathrm{MX}}_2$ due to the strongest effect of electron transfer from the low-energy small-mass valley to the high-energy large-mass valley. The tensile strain increases the valley separation, which on one hand suppresses the electron transfer in ${\mathrm{WS}}_2$, on the other hand allows the electrons to access the nonparabolic band region of the low-energy valley. The latter effect leads to an NDM for electrons in the low-energy valley, which can significantly increase the overall NDM at moderate strain. The valley-separation induced NDM in the low-energy valley is found to be a general phenomenon. Our work unveils the physical factors underlying the differences in high-field transport properties of different ${\mathrm{MX}}_2$, and also identifies the most promising candidate as well as effective approach for further improvement.

In this work we study the frontal collision of protons with the carbon atoms of a graphene surface with a low coverage of adsorbed potassium. It is aimed at the analysis of the effect of the adsorbates in both charge exchange and electron emission processes, when the binary collision occurs between the proton and a carbon atom of the surface. The frontal collision with the K adsorbate, already analyzed and discussed in a previous work, is compared with the frontal collision with different carbon neighbors. In the present work we studied the signals, due to the localized structures in the density matrix of the composed graphene plus potassium surface, that can be distinguished when the collision occurs either with the adsorbate, a nearby carbon atom, or a carbon atom that does not feel the presence of the adsorbate. The interacting system is described by the Anderson Hamiltonian which takes into account the electronic repulsion on the projectile site; the charge fractions, the energy distribution of electrons in the solid, and the electron emission after the collision are calculated by using the nonequilibrium Green-Keldysh functions formalism solved by the equation of motion method. In the binary collision with a carbon atom, the extended features of the band structure of graphene smooth the dependence of the projectile charge fractions on the incoming energy and notably decrease the negative ions formation. The localized structures of the density of matrix caused by the presence of the adsorbate are perceptible for scattered carbon atoms close to K. The intense emission of low energy electrons obtained in the case of the scattering by potassium is fundamentally associated with the very localized K-$4s$ empty band. This characteristic, although less marked, remain in the scattering by nearby carbon atoms, due to both the interaction with K along the projectile trajectory and the perturbed local density of states on the carbon atoms due to the adsorbate presence. In addition, the extended nature of the electronic structure of graphene allows for the emission of more energetic electrons.

We study the Kitaev-Heisenberg model with spin-1 local degree of freedom on a honeycomb lattice numerically by the infinite density matrix renormalization group method on a cylinder geometry. By tuning the relative value of the Kitaev and Heisenberg exchange couplings, we obtain the phase diagram with two spin liquid phases and four symmetry-broken phases. We identify that the spin liquid phases are gapless by calculating the central charge at the pure Kitaev points without the Heisenberg interactions. Comparing to its spin-1/2 counterpart, the position and number of gapless modes of the spin-1 case are quite different. Due to the approximate $Z_2$ local conservations, the expectation value of the Wilson loop operator measuring the flux of each plaquette stays near to 1, and the static spin-spin correlations remain short range in the entire spin liquid phases.

We develop a bosonization formalism that captures nonperturbatively the interaction effects on the $\mathbf{Q}=0$ continuum of excitations of nodal fermions above one dimension. Our approach is a natural extension of the classic bosonization scheme for higher dimensional Fermi surfaces to include the $\mathbf{Q}=0$ neutral excitations that would be absent in a single-band system. The problem is reduced to solving a boson bilinear Hamiltonian. We establish a rigorous microscopic footing for this approach by showing that the solution of such boson bilinear Hamiltonian is exactly equivalent to performing the infinite sum of Feynman diagrams associated with the Kadanoff-Baym particle-hole propagator that arises from the self-consistent Hartree-Fock approximation to the single-particle Green's function. We apply this machinery to compute the interaction corrections to the optical conductivity of two-dimensional Dirac fermions with Coulomb interactions reproducing the results of perturbative renormalization group at weak coupling and extending them to the strong-coupling regime.

We investigate the electronic and magnetic properties of the kagome mineral averievite $\left(\mathrm{Cs}\mathrm{Cl}\right){\mathrm{Cu}}_5{\mathrm{V}}_2{\mathrm{O}}_{10}$ and its phosphate analog $\left(\mathrm{Cs}\mathrm{Cl}\right){\mathrm{Cu}}_5{\mathrm{P}}_2{\mathrm{O}}_{10}$ using first-principles calculations. The crystal structure of these compounds features ${\mathrm{Cu}}^{2+}$ kagome layers sandwiched between ${\mathrm{Cu}}^{2+}-{\mathrm{P}}^{5+}$/${\mathrm{Cu}}^{2+}-{\mathrm{V}}^{5+}$ honeycomb planes, with pyrochlore slabs made of corner-sharing Cu tetrahedra being formed. The induced chemical pressure effect upon substitution of V by P causes significant changes in the structure and magnetic properties. Even though the in-plane antiferromagnetic (AFM) coupling $J_1$ within the kagome layer is similar in the two materials, the interplane AFM coupling $J_2$ between kagome and honeycomb layers is five times larger in the P variant, increasing the degree of magnetic frustration in the constituting Cu tetrahedra.

Probing extended polyene systems with energy in excess of the bright state ($1{}^1{B}_u^{+}$/$S_2$) band edge generates triplets via singlet fission. This process is not thought to involve the $2{}^1{A}_g^{-}$/$S_1$ state, suggesting that other states play a role. Using density matrix renormalization group (DMRG) calculations of the Pariser-Parr-Pople-Peierls Hamiltonian, we investigate candidate states that could be involved in singlet fission. We find that the relaxed $1{}^1{B}_u^{-}$ and $3{}^1{A}_g^{-}$ singlet states and $1{}^5{A}_g^{-}$ quintet state lie below the $S_2$ state. The $1{}^1{B}_u^{-}$, $3{}^1{A}_g^{-}$, and $1{}^5{A}_g^{-}$ states are all thought to have triplet-pair character, which is confirmed by our calculations of bond dimerization, spin-spin correlation, and wave function overlap with products of triplet states. We thus show that there is a family of singlet excitations (i.e., $2{}^1{A}_g^{-}$, $1{}^1{B}_u^{-}$, $3{}^1{A}_g^{-}$, $\cdots$), composed of both triplet-pair and electron-hole character, which are fundamentally the same excitation, but have different center-of-mass energies. The lowest energy member of this family, the $2{}^1{A}_g^{-}$ state, cannot undergo singlet fission. But higher-energy members (e.g., the $3{}^1{A}_g^{-}$) state, owing to their increased kinetic energy and reduced electron-lattice relaxation, can undergo singlet fission for certain chain lengths.

Although the adiabatic heuristic argument of the fractional quantum Hall states has been successful, continuous modification of the statistics of anyons is strictly prohibited due to algebraic constraints of the braid group on a torus. We have numerically shown that the adiabatic heuristic principle for anyons is still valid even though the Hamiltonians cannot be modified continuously. The Chern number of the ground-state multiplet is the adiabatic invariant, while the number of the topological degeneracy behaves wildly. A generalized Streda formula is proposed that explains the degeneracy pattern. Nambu-Goldstone modes associated with the anyon superconductivity are also suggested numerically.

Two charge density wave transition can be detected in $\mathrm{La}\mathrm{Au}{\mathrm{Sb}}_2$ at $\sim 110$ and $\sim 90\mathrm{K}$ by careful electrical transport measurements. Whereas control of the Au site occupancy in $\mathrm{La}{\mathrm{Au}}_x{\mathrm{Sb}}_2$ (for $0.9\lesssim x\lesssim 1.0$) can suppress each of these transitions by $\sim 80\mathrm{K}$, the application of hydrostatic pressure can completely suppress the lower transition by $\sim 7.5\mathrm{kbar}$ and the upper transition by $\sim 17\mathrm{kbar}$. Clear anomalies in the resistance as well as the magnetoresistance are observed to coincide with the pressures at which the charge density wave transitions are driven to zero.

We examine the impact of quantum confinement on the interaction potential between two charges in two-dimensional semiconductor nanosheets in solution. The resulting effective potential depends on two length scales, namely, the thickness $d$ and an emergent length scale $d^{*}\equiv \epsilon d/{\epsilon }_{\text{sol}}$, where $\epsilon$ is the permittivity of the nanosheet and ${\epsilon }_{\text{sol}}$ is the permittivity of the solvent. In particular, quantum confinement, and not electrostatics, is responsible for the logarithmic behavior of the effective potential for separations smaller than $d$, instead of the one-over-distance bulk Coulomb interaction. Finally, we corroborate that the exciton binding energy also depends on the two-dimensional Bohr radius $a_0$ in addition to the length scales $d$ and $d^{*}$ and analyze the consequences of this dependence.

The dynamical and nonlocal dielectric function of a two-dimensional electron gas with finite-energy bandwidth is computed within a random-phase approximation. For large bandwidth, the plasmon dispersion has two separate branches at small and large momenta. The large-momenta branch exhibits negative quasiflat dispersion. The two branches merge with decreasing bandwidth. We discuss how the maximum-energy plasmon mode, which resides at energies larger than all particle-hole continuum, can potentially open a route to low-loss plasmons. Moreover, we discuss the bandwidth effects on the static screening of the charged and magnetic impurities.

When an atomically thin van der Waals magnet forms a long-period moiré pattern with a magnetic substrate, the sensitive dependence of interlayer magnetic coupling on the atomic registries can lead to moiré-defined magnetization textures in two-dimensional (2D) magnets. The recent discovery of 2D magnetic topological insulators such as ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ leads to the interesting possibility of exploring the interplay of such magnetization textures with topological surface states, which we explore here with a minimal model established for 2D ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. The sign flip of the exchange gap across a magnetization domain wall gives rise to a single in-gap chiral channel on each surface. In the periodic magnetization textures, such chiral spin channels at the domain walls couple to form a network and superlattice minibands emerge. We find that in magnetization textures with closed domain-wall geometries, the formed superlattice miniband is a gapped Dirac cone featuring orbital magnetization from the current circulation in the closed loops of chiral channels, while in magnetization textures with open domain wall geometries, a gapless mini-Dirac cone is found instead. The miniband Bloch states feature a spatial texture of spin and local current densities, which are clear manifestations of the spin-momentum locked chiral channels at the domain walls. The results suggest a platform to engineer spin and current flows through the manipulation of magnetization domains for spintronic devices.