In most strongly correlated electron systems superconductivity appears nearby a magnetic quantum critical point (QCP) which is believed to cause unconventional behaviors. In order to explore this physics, we present here a study of the heavy-fermion superconductors ${\mathrm{CeIrSi}}_3$ and ${\mathrm{CeRhSi}}_3$ carried out using a newly developed system for high-resolution magnetic penetration-depth measurements under pressure. Superconductivity in ${\mathrm{CeIrSi}}_3$ shows a change from an excitation spectrum with a line-nodal gap to one which is entirely gapful when pressure is close but not yet at the QCP. In contrast, ${\mathrm{CeRhSi}}_3$ does not possess a $T=0$ quantum phase transition and the superconducting phase remains for all accessible pressures with a nodal gap. Combining both results suggests that in these compounds unconventional superconducting behaviors are rather connected with the coexisting antiferromagnetic order. This study provides another viewpoint on the interplay of superconductivity, magnetism, and quantum criticality in ${\mathrm{CeIrSi}}_3$ and ${\mathrm{CeRhSi}}_3$ and maybe in other heavy fermions.

We propose a theoretical model for a gapless spin liquid phase that may have been observed in a recent experiment on ${\mathrm{H}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$. Despite the insulating and nonmagnetic nature of the material, the specific heat coefficient $C/T\sim 1/\sqrt{T}$ in zero magnetic field and $C/T\sim T/B^{3/2}$ with finite magnetic field $B$ have been observed. In addition, the NMR relaxation rate shows $1/\left(T_{1}T\right)\sim {(C/T)}^2$. Motivated by the fact that the interlayer/in-plane lattice parameters are reduced/elongated by the hydrogen intercalation of the parent compound ${\mathrm{Li}}_2{\mathrm{IrO}}_3$, we consider four layers of the Kitaev honeycomb lattice model with additional interlayer exchange interactions. It is shown that the resulting spin liquid excitations reside mostly in the top and bottom layers of such a layered structure and possess a quartic dispersion. In an applied magnetic field, each quartic mode is split into four Majorana cones with the velocity $v\sim B^{3/4}$. We suggest that the spin liquid phase in these “defect” layers, placed between different stacking patterns of the honeycomb layers, can explain the major phenomenology of the experiment, which can be taken as evidence that the Kitaev interaction plays the primary role in the formation of a quantum spin liquid in this material.

Through Bi deposition on the single-crystalline $\mathrm{Mo}{\mathrm{S}}_2$ surface, we find that the density of the sulfur vacancy is a critical parameter for the growth of the crystalline Bi overlayer or cluster at room temperature. Also, the $\mathrm{Mo}{\mathrm{S}}_2$ band structure is significantly modified near Γ due to the orbital hybridization with an adsorbed Bi monolayer. Our experimental observations and analysis in combination with density functional theory calculation suggest the importance of controlling the sulfur vacancy concentration in realizing an exotic quantum phase based on the van der Waals interface of Bi and $\mathrm{Mo}{\mathrm{S}}_2$.

We present stationary and transient absorption measurements on 3D Au nanoparticle (NP)-decorated $\mathrm{Si}{\mathrm{O}}_2$ nanowire arrays. The 3D NP array has been produced by the dewetting of a thin Au film deposited on silica nanowires produced by oxidation of silicon nanowires. The experimental behaviors of the spectral and temporal dynamics observed in the experiment are accurately described by a two-step, three-temperature model. Using an arbitrary set of Au NPs with different aspect ratios, we demonstrate that the width of the experimental spectra, the energy shift of their position with time, and the asymmetry between the two positive wings in the dynamical variation of absorption can all be attributed to the nonuniform shape distribution of the Au NPs in the sample.

Using an analytically tractable kinetic model of a two-dimensional Fermi liquid of electrons, we characterize the crossovers among zero sound, first sound, and plasmons. For experimentally realized Fermi liquids in a hydrodynamic limit, both zero and first sound waves are essentially replaced by plasmons. The plasmon dispersion relation is robust against hydrodynamic effects up to acquiring the viscous-limited decay rate of a first sound wave in the hydrodynamic limit. We discuss implications for experiments in clean two-dimensional electron gases.

The wave-function-matching (WFM) technique for first-principles transport-property calculations was bettered by Sørensen et al. so as to exclude rapidly decreasing evanescent waves [Sørensen et al., Phys. Rev. B 77, 155301 (2008)]. In their method, the translational invariance of the transmission probability is not preserved when moving the matching planes between electrode and transition regions, and the sum of transmission and reflection probabilities does not agree with the number of transport channels in the transition region. The lack of the translational invariance is caused by the overlap of the layers between the electrode and transition regions. We reformulate the WFM method by removing the layer overlap, and the translational invariance of the transmission probability becomes preserved. On the other hand, the error in the sum of transmission and reflection probabilities is attributed to using pseudoinverses that is accompanied by the exclusion of rapidly decreasing evanescent waves. We introduce a formulation to calculate the transmission/reflection probability without the pseudoinverses, resulting in that the sum of the transmission and reflection probabilities exactly agrees with the number of channels, and the accuracy is largely improved. In addition, we prove that the accuracy in the transmission probability obtained by our WFM technique is comparable to that obtained by a nonequilibrium Green's function method. Furthermore, we carry out electron transport calculations on two-dimensional graphene sheets embedded with B-N line defects sandwiched between a pair of semi-infinite graphene electrodes and find the dependence of the electron transmission on the transverse momentum perpendicular to the transport direction.

Electron confinement in fractal Sierpiński triangles (STs) on Ag(111) is investigated using scanning tunneling spectroscopy and theoretically simulated by employing an improved two-dimensional (2D) multiple scattering theory in which the energy-dependent phase shifts are explicitly calculated from the electrostatic potentials of the molecular building block of STs. Well-defined bound surface states are observed in three kinds of triangular cavities with their sides changing at a scale factor of 2. The decrease in length of the cavities results in an upshift of the resonances that deviates from an expected inverse quadratic dependence on the cavity length due to the less efficient confinement of smaller triangular cavities. Differential conductance maps at some specific biases present a series of alternative bright and dark rounded triangles preserving the symmetry of the boundary. Our improved 2D multiple scattering model reproduces the characteristics of the standing wave patterns and all features in the differential conductance spectra measured in experiments, illustrating that the elastic loss boundary scattering dominates the resonance broadening in these ST quantum corrals. Moreover, the self-similar structure of STs, that a larger central cavity is surrounded by three smaller ones with a half side length, gives rise to interactions of surface states confined in neighboring cavities, which are helpful for the suppression of the linewidth in differential conductance spectra.

The Majorana fermion can be described by a real wave function with only two phases (zero and $\pi$) which provide a controllable degree of freedom. We propose a strategy to regulate the phase of the chiral Majorana state by coupling with a scanning tunneling microscope tip in a system consisting of a quantum anomalous Hall insulator coupled with a superconductor. With the change in the chemical potential, the chiral Majorana state can be tuned alternately between zero and $\pi$, in which the perfect normal tunneling and perfect crossed Andreev reflection appear, respectively. The perfect crossed Andreev reflection, by which a Cooper pair can be split into two electrons going into different terminals completely, leads to a pumping current and distinct quantized resistances. These findings may provide a signature of Majorana fermions and pave a feasible avenue to regulate the phase of the Majorana state.

Topological invariants allow one to characterize Hamiltonians, predicting the existence of topologically protected in-gap modes. Those invariants can be computed by tracing the evolution of the occupied wave functions under twisted boundary conditions. However, those procedures do not allow one to calculate a topological invariant by evaluating the system locally, and thus require information about the wave functions in the whole system. Here we show that artificial neural networks can be trained to identify the topological order by evaluating a local projection of the density matrix. We demonstrate this for two different models, a one-dimensional topological superconductor and a two-dimensional quantum anomalous Hall state, both with spatially modulated parameters. Our neural network correctly identifies the different topological domains in real space, predicting the location of in-gap states. By combining a neural network with a calculation of the electronic states that uses the kernel polynomial method, we show that the local evaluation of the invariant can be carried out by evaluating a local quantity, in particular for systems without translational symmetry consisting of tens of thousands of atoms. Our results show that supervised learning is an efficient methodology to characterize the local topology of a system.

We develop an analytically solvable classical kinetic model of spatially dispersive transport in Dirac materials accounting for strong electron-electron (e-e) and electron-hole (e-h) collisions. We use this model to track the evolution of graphene conductivity and properties of its collective excitations across the hydrodynamic-to-ballistic crossover. We find the relaxation rate of electric current by e-e collisions that is possible due to the lack of Galilean invariance and introduce a universal numerical measure of this noninvariance. We find the two branches of collective excitations in the Dirac fluid: plasmons and electron-hole sound. The sound waves persist at frequencies exceeding the e-e collision frequency, have a small viscous damping at the neutrality point, but acquire large damping due to e-h friction even at slight doping. On the contrary, plasmons acquire strong frictional damping at the neutrality point and become well defined in doped samples.

Alloys of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and ${\mathrm{Sb}}_2{\mathrm{Te}}_3\left[{\left({\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x\right)}_2{\mathrm{Te}}_3\right]$ have played an essential role in the exploration of topological surface states, allowing us to study phenomena that would otherwise be obscured by bulk contributions to conductivity. Despite intensive transport and angle resolved photoemission (ARPES) studies, important questions about this system remain unanswered. For example, previous studies reported the chemical tuning of the Fermi level to the Dirac point by controlling the Sb:Bi composition ratio, but the optimum ratio varies widely across various studies. Moreover, it is unclear how the quasiparticle lifetime is affected by the disorder resulting from Sb/Bi alloying. In this work, we use scanning tunneling microscopy and spectroscopy to study the electronic structure of epitaxially grown (Bi,${\mathrm{Sb})}_2{\mathrm{Te}}_3$ thin films at the nanoscale. We study Landau levels (LLs) to determine the effect of disorder on the quasiparticle lifetime as well as the position of the Dirac point with respect to the Fermi energy. A plot of the LL peak widths shows that despite the intrinsic disorder, the quasiparticle lifetime is not significantly degraded. We further determine that the ideal Sb concentration to place the Fermi energy to within a few meV of the Dirac point is $x\sim 0.7$, but that postannealing temperatures can have a significant effect on the crystallinity and Fermi level position. Specifically, high postgrowth annealing temperature can result in better crystallinity and surface roughness, but also produces a larger Te defect density which adds $n$-type carriers. Finally, in combination with quasiparticle interference imaging, the dispersion is revealed over a large energy range above the Fermi energy, in a regime inaccessible to ARPES. Interestingly, the surface state dispersion for the $x\sim 0.7$ sample shows great similarity to pristine ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. This work provides microscopic information on the role of disorder and composition in determining carrier concentration, surface state dispersion, and quasiparticle lifetime in (${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$)${}_2{\mathrm{Te}}_3$.

Density functional theory (DFT) exploits an independent-particle-system construction to replicate the densities and current of an interacting system. This construction is used here to access the exact effective potential and bias of nonequilibrium systems with disorder and interactions. Our results show that interactions smoothen the effective disorder landscape but do not necessarily increase the current due to the competition of disorder screening and effective bias. This puts forward DFT as a diagnostic tool to understand disorder screening in a wide class of interacting disordered systems.

We consider the string-net model obtained from $SU{\left(2\right)}_2$ fusion rules. These fusion rules are shared by two different sets of anyon theories. In this paper, we study the competition between the two corresponding non-Abelian quantum phases in the ladder geometry. A detailed symmetry analysis shows that the nontrivial low-energy sector corresponds to the transverse-field cluster model that displays a critical point described by the $so{\left(2\right)}_1$ conformal field theory. Other sectors are obtained by freezing spins in this model.

Besides optical valley selectivity, strong spin-orbit interaction along with Berry curvature effects also leads to unconventional valley- and spin-polarized Landau levels in monolayer transition metal dichalcogenides (TMDCs) under a perpendicular magnetic field. We find that these unique properties are inherited to the magneto-optical absorption spectrum of the TMDC quantum rings (QRs). In addition, it is robust against variation of the magnetic flux and of the QR geometry. In stark contrast to the monolayer bulk material, the ${\mathrm{MoS}}_2$ QRs manifest themselves in both the optical valley selectivity and unprecedented size tunability of the frequency of the light absorbed. We also find that when the magnetic field setup is changed, the phase transition from Aharonov-Bohm (AB) quantum interference to aperiodic oscillation of magneto-optical absorption spectrum takes place. The exciton spectrum in a realistic finite thickness ${\mathrm{MoS}}_2$ QR is also discussed.

This paper presents the theory, implementation, and application of a quantum transport modeling approach based on the nonequilibrium Green's function formalism and a full-band empirical pseudopotential Hamiltonian. We here propose to employ a hybrid real-space/plane-wave basis that results in a significant reduction of the computational complexity compared to a full plane-wave basis. To this purpose, we provide a theoretical formulation in the hybrid basis of the quantum confinement, the self-energies of the leads, and the coupling between the device and the leads. After discussing the theory and the implementation of the new simulation methodology, we report results for complete, self-consistent simulations of different electron devices, including a silicon Esaki diode, a thin-body silicon field effect transistor (FET), and a germanium tunnel FET. The simulated transistors have technologically relevant geometrical features with a semiconductor film thickness of about 4 nm and a channel length ranging from 10 to 17 nm. We believe that the newly proposed formalism may find applications also in transport models based on ab initio Hamiltonians, as those employed in density functional theory methods.

The surface of a Weyl semimetal (WSM) displays Fermi arcs, i.e., disjoint segments of a two-dimensional Fermi contour. We present a quantum-mechanical nonlocal theory of chiral Fermi arc plasmons in WSMs with broken time-reversal symmetry. These are collective excitations constructed from topological Fermi arc and bulk electron states and arising from electron-electron interactions, which are treated in the realm of the random phase approximation. Our theory includes quantum effects associated with the penetration of the Fermi arc surface states into the bulk and dissipation, which is intrinsically nonlocal in nature and arises from decay processes mainly involving bulk electron-hole pair excitations.

The electrons in the edge channels of two-dimensional topological insulators can be described as a helical Tomonaga-Luttinger liquid. They couple to nuclear spins embedded in the host materials through the hyperfine interaction, and are therefore subject to elastic spin-flip backscattering on the nuclear spins. We investigate the nuclear-spin-induced edge resistance due to such backscattering by performing a renormalization-group analysis. Remarkably, the effect of this backscattering mechanism is stronger in a helical edge than in nonhelical channels, which are believed to be present in the trivial regime of InAs/GaSb quantum wells. In a system with sufficiently long edges, the disordered nuclear spins lead to an edge resistance which grows exponentially upon lowering the temperature. On the other hand, electrons from the edge states mediate an anisotropic Ruderman-Kittel-Kasuya-Yosida nuclear spin-spin interaction, which induces a spiral nuclear spin order below the transition temperature. We discuss the features of the spiral order, as well as its experimental signatures. In the ordered phase, we identify two backscattering mechanisms, due to charge impurities and magnons. The backscattering on charge impurities is allowed by the internally generated magnetic field, and leads to an Anderson-type localization of the edge states. The magnon-mediated backscattering results in a power-law resistance, which is suppressed at zero temperature. Overall, we find that in a sufficiently long edge the nuclear spins, whether ordered or not, suppress the edge conductance to zero as the temperature approaches zero.

In a superconductor the third-harmonic generation (THG) of a strong THz pulse is enhanced below $T_c$ by the resonant excitation of lattice-modulated charge fluctuations, which modulate the response according to the polarization of the field. Here we compute the THG within a multiband model for the prototype NbN superconductor. We show that the nonresonant contribution coming from the instantaneous electronic response and the finite width of the pulse significantly suppress the polarization dependence of the signal, challenging its observation in real systems.

Results from hybrid density functional theory calculations on the thermodynamic stability and optical properties of the Zn vacancy $\left(V_{\text{Zn}}\right)$ complexed with common donor impurities in ZnO are reported. Complexing $V_{\text{Zn}}$ with donors successively removes its charge-state transition levels in the band gap, starting from the most negative one. Interestingly, the presence of a donor leads only to modest shifts in the positions of the $V_{\text{Zn}}$ charge-state transition levels, the sign and magnitude of which can be interpreted from a polaron energetics model by taking hole-donor repulsion into account. By employing a one-dimensional configuration coordinate model, luminescence lineshapes and positions were calculated. Due to the aforementioned effects, the isolated $V_{\text{Zn}}$ gradually changes from a mainly nonradiative defect with transitions in the infrared region in $n$-type material, to a radiative one with broad emission in the visible range when complexed with shallow donors.