A theoretical study of the localization properties of nanowires of dopants in silicon (Si) fabricated by ionic implantation or scanning tunnel microscope lithography is presented for a model incorporating the currently unavoidable imprecision in individual donor positioning. Experiments have shown that Ohm's law holds in some cases, in apparent defiance to the Anderson localization theory in one dimension. We investigate how valley interference affects the traditional theory of electronic structure of disordered systems. Each isolated donor orbital is realistically described by multivalley effective-mass theory. We extend this model to describe chains of donors as a linear combination of dopant orbitals. Disorder in donor positioning is taken into account, leading to an intricate disorder distribution of hoppings between nearest-neighbor donor sites (donor-donor tunnel coupling)—an effect of valley interference. A decay length, related to the usual localization length, is obtained for phosphorous (P) donor chains from a transfer-matrix approach and is further compared with the chain length. We quantitatively determine the impact of uncertainties $\delta R$ in the implantation position relative to a target and also compare our results with those obtained without valley interference. We analyze systematically the aimed interdonor separation dependence $\left(R_0\right)$ and show that fairly diluted donor chains ($R_0=7.7$ nm) may be as long as 100 nm before the effective onset of Anderson localization, as long as the positioning error is under a lattice parameter ($\delta R<0.543$ nm).

We report the discovery of a topological semimetal, ${\mathrm{TaSb}}_2$, which crystallizes in a base-centered monoclinic, centrosymmetric structure. The compound undergoes a metal-insulator-like transition under magnetic field and exhibits a clear resistivity plateau below $T_c=13$ K. The ultrahigh carrier mobility and extreme large magnetoresistance for longitudinal resistivity are observed at low temperatures in addition to a quantum oscillation behavior with nontrivial Berry phases. Moreover, the negative magnetoresistance is observed when the applied field is parallel to the current direction up to 9 T. The Hall resistivity shows the nearly linear field dependence suggestive of electron-hole noncompensation behavior. These findings uncover a materials basis represented by ${\mathrm{TaSb}}_2$ as a platform of topological materials for future theoretical and experimental investigations.

We present a strong-coupling approach to the theory of high-temperature superconductivity based on the observation of a quantum critical point in the plaquette within the $t,t^{\prime }$ Hubbard model. The crossing of ground-state energies in the $N=2–4$ sectors occurs for parameters close to the optimal doping. The theory predicts the maximum of the $d_{x^2-y^2}$-wave order parameter at the border between localized and itinerant electron behaviors and gives a natural explanation for the pseudogap formation via the soft-fermion mode related to local singlet states of the plaquette in the environment. Our approach follows the general line of resonating valence-bond theory stressing a crucial role of singlets in the physics of high-$T_c$ superconductors but focuses on the formation of local singlets, similar to phenomena observed in frustrated one-dimensional quantum spin models.

We present a microscopic calculation of spatially indirect exciton states in semiconductor coupled quantum wells and polaritons formed from their coupling to the optical mode of a microcavity. We include the presence of electric and magnetic fields applied perpendicular to the quantum well plane. Our model predicts the existence of polaritons that are in the strong-coupling regime and at the same time possess a large static dipole moment. We demonstrate, in particular, that a magnetic field can compensate for the reduction in light-matter coupling that occurs when an electric field impresses a dipole moment on the polariton.

We study Majorana fermions in a two-dimensional topological superconductor placed in a transverse magnetic-field $B$. We consider a topological insulator/superconductor heterostructure and a two-dimensional $p$-wave superconductor. A single field-generated vortex creates two Majorana fermions, one of which is hosted at the vortex core. The wave function of the second Majorana state is localized in the superconductor volume along a circle with a radius of $r^{*}\propto B^{-1}$ centered at the vortex core. In the case of many vortices, the sensitivity of $r^{*}$ to the magnetic field $B$ may be used to control the coupling between the Majorana fermions. The latter property could be an asset for quantum computations.

Using density-functional theory we compute the formation energies of vacancies $\square$ in the framework of type I ${\mathrm{Ba}}_8{\mathrm{Zn}}_x{\mathrm{Ge}}_{46-x-y}{\square }_y$ clathrates as a function of Zn substitutions. While resolving the contradiction on the experimental reports on the relation between the concentration of Zn, $x$, and the number of framework vacancies, $y$, our study confirms the observations that vacancies are destabilized with the increase in $x$: Up to three vacancies per formula unit can be stabilized for $0\le x<6$, while they are unstable for $x\ge 6$. This behavior arises from the lower formation energy of (charged) Zn substitution in the Ge framework as compared to a (charged) vacancy creation. Finally our study reveals the stability of a high-temperature $T$ phase ${\mathrm{Ba}}_8{\mathrm{Zn}}_6{\mathrm{Ge}}_{40}$ that has high electronic carrier concentration, whereby the carriers also show high-$T$-induced variation effective for its thermoelectric application.

${\mathrm{Ba}}_2{\mathrm{CoGe}}_2{\mathrm{O}}_7$ exhibits a collinear-antiferromagnetic structure with the easy axis along $\langle 100\rangle$ directions and an antiferroelectric order with the polarization axis along the [001] direction. By applying the electric field the magnetic moment rotates from $\langle 100\rangle$ to [110] directions and, simultaneously, the antiferroelectric state changes to the ferroelectric state gradually. This magnetoelectric effect, i.e., continuous control of the local magnetic moment by the electric field, is quantitatively explained by the Hamiltonian including the dielectric energy.

We show spin-transfer-torque-driven vortex oscillations in current-perpendicular-to-plane giant magnetoresistance junctions using epitaxially grown ${\mathrm{Co}}_2{\mathrm{Fe}}_x{\mathrm{Mn}}_{1-x}\mathrm{Si}$ (CFMS) Heusler alloy thin films. The soft magnetic property and high spin polarization of CFMS enable us to realize vortex oscillation emitting large microwave power with a low threshold current. The output power is maximized for a certain Fe-Mn composition ratio associated with a reduction of the threshold current for the oscillation, which is in agreement with a general model for spin-torque oscillation. Through comparison with an analytical theory that describes the translational motion of a vortex core, we show that the vortex core motion excited in the present device is inhomogeneous along the thickness direction. In spite of the inhomogeneity, the gyration radius at the CFMS/spacer interface region was estimated to be $\sim 75\%$ of the actual ferromagnetic layer radius, which indicates that the CFMS-based all-metallic junction is useful for achieving large-amplitude vortex core motion. This comprehensive investigation would also be useful for designing high-performance all-metallic nano-oscillators based on magnetic vortex dynamics.

The critical current of a Josephson junction is an oscillatory function of the enclosed magnetic flux $\mathrm{\Phi }$, because of quantum interference modulated with periodicity $h/2e$. We calculate these Fraunhofer oscillations in a two-dimensional (2D) ballistic superconductor–normal-metal–superconductor (SNS) junction. For a Fermi circle the amplitude of the oscillations decays as $1/\mathrm{\Phi }$ or faster. If the Fermi circle is strongly warped, as it is on a square lattice near the band center, we find that the amplitude decays slower, $\propto 1/\sqrt{\mathrm{\Phi }}$, when the magnetic length $l_m=\sqrt{\hslash /eB}$ drops below the separation $L$ of the NS interfaces. The crossover to the slow decay of the critical current is accompanied by the appearance of a 2D array of current vortices and antivortices in the normal region, which form a bipartite rectangular lattice with lattice constant $\simeq l_m^2/L$. The 2D lattice vanishes for a circular Fermi surface, when only the usual single row of Josephson vortices remains.

Magnetocrystalline anisotropy at Heusler $\mathrm{alloy}|\mathrm{MgO}$ interfaces has been studied using first-principles calculations. It has been found that Co-terminated ${\mathrm{Co}}_2\mathrm{FeAl}|\mathrm{MgO}$ interfaces show perpendicular magnetic anisotropy up to 1.31 mJ/${\mathrm{m}}^2$, while those with FeAl termination exhibit in-plane magnetic anisotropy. Atomic layer-resolved analysis indicates that the origin of perpendicular magnetic anisotropy in ${\mathrm{Co}}_2\mathrm{FeAl}|\mathrm{MgO}$ interfaces can be attributed to the out-of-plane orbital contributions of interfacial Co atoms. At the same time, ${\mathrm{Co}}_2\mathrm{MnGe}$ and ${\mathrm{Co}}_2\mathrm{MnSi}$ interfaced with MgO tend to favor in-plane magnetic anisotropy for all terminations.

Superconducting thin films of the noncentrosymmetric superconductor ${\mathrm{Nb}}_{0.18}{\mathrm{Re}}_{0.82}$ were successfully deposited by UHV sputtering technique. X-ray diffraction analysis indicated that the films are polycrystalline, with a preferential ($nn0$) orientation and the lattice parameter in agreement with the expected single $\alpha$-Mn cubic phase. A detailed electrical characterization of the samples as a function of the thickness ($3.5\text{nm}\le d\le 142$ nm) was performed both in the normal and in the superconducting states, revealing a well-established superconducting ordering, as well as an estimated value of the upper critical field, ${\mu }_0{H}_{c2}$, comparable with the Pauli limit. Finally, the symmetry of the order parameter was probed by tunneling spectroscopy on Al/${\mathrm{Al}}_2{\mathrm{O}}_3/{\mathrm{Nb}}_{0.18}{\mathrm{Re}}_{0.82}$ heterostructures, which provides evidence for a single $s$-wave superconducting gap.

Motivated by the recent realization of the three-dimensional hyperhoneycomb and stripyhoneycomb lattices in lithium iridate (${\mathrm{Li}}_2{\mathrm{IrO}}_3$), we study the possible spin-singlet superconducting states on the whole series of harmonic honeycomb lattices. Beginning with an isolated out-of-plane twist making the honeycomb lattice three-dimensional, we find that the chiral $d\pm i{d}^{\prime }$ state, well-known from the honeycomb lattice, is realized in the largest members of the series at low to intermediate doping. Along the twist, four chiral edge states form a two-dimensional dispersive band. Reducing the distance between the twists to form the smaller members of the harmonic honeycomb lattices, the degeneracy between the $d$-wave states is lifted, which finally destroys the chiral state. By analyzing the hyper- and stripyhoneycomb lattices and generalizing using the $D_{2h}$ point group of all the harmonic honeycomb lattices, we show that the superconducting state often belongs to the trivial irreducible representation. This state has nodal lines at low to intermediate doping, which is possible because the full lattice symmetry allows sign changes between different sets of bonds. We also find time-reversal symmetry broken states, which are either fully gapped or feature nodal points, in certain parts of the phase diagram. Finally, we draw a comparison between the states classified in terms of the $D_{2h}$ symmetries and those observed on the $D_{6h}$ honeycomb lattice.

We study magnetotransport properties of the electron-doped superconductor ${\mathrm{Pr}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_{4\pm \delta }$ with $x=0.14$ in magnetic fields up to 92 T, and observe Shubnikov-de Haas magnetic quantum oscillations. The oscillations display a single frequency $F=255\pm 10$ T, indicating a small Fermi pocket that is $\sim 1\%$ of the two-dimensional Brillouin zone and consistent with a Fermi surface reconstructed from the large holelike cylinder predicted for these layered materials. Despite the low nominal doping, all electronic properties including the effective mass and Hall effect are consistent with overdoped compounds. Our study demonstrates that the exceptional chemical control afforded by high quality thin films will enable Fermi surface studies deep into the overdoped cuprate phase diagram.

We use renormalization group (RG) analysis and dimensional regularization techniques to study potential superconductivity-inducing four-fermion interactions in systems with critical Fermi surfaces of general dimensions $\left(m\right)$ and codimensions $\left(d-m\right)$, arising as a result of quasiparticle interaction with a gapless Ising-nematic order parameter. These are examples of non-Fermi liquid states in $d$ spatial dimensions. Our formalism allows us to treat the corresponding zero-temperature low-energy effective theory in a controlled approximation close to the upper critical dimension $d=d_c\left(m\right)$. The fixed points are identified from the RG flow equations, as functions of $d$ and $m$. We find that the flow toward the non-Fermi liquid fixed point is preempted by Cooper pair formation for both the physical cases of $(d=3,m=2)$ and $(d=2,m=1)$. In fact, there is a strong enhancement of superconductivity by the order parameter fluctuations at the quantum critical point.

We study indicators of broken time-reversal and parity symmetries in gapped topological phases of matter. We focus on phases realized by Levin-Wen string-net models and generalize the string-net model to describe phases which break parity and time-reversal symmetries. We do this by introducing an extra degree of freedom into the string-net graphical calculus, which takes the form of a branch cut located at each vertex of the underlying string-net lattice. We also work with string-net graphs defined on arbitrary (nontrivalent) graphs, which reveals otherwise hidden information about certain configurations of anyons in the string-net graph. Most significantly, we show that objects known as higher Frobenius-Schur indicators can provide several efficient ways to detect whether a given topological phase breaks parity or time-reversal symmetry.

We report studies of low-field conductivity, σ, of nanosized samples of orthorhombic $\mathrm{Ta}{\mathrm{S}}_3$ as a function of strain, ε. The σ(ε) curves show steplike changes associated with the “quantization” of the wave vector, $q$, of the charge-density wave. Based on the effect we have revealed the change of the $q$-vector with strain: its in-chain component (normalized by the reciprocal lattice constant) is found to increase with sample stretch. A similar $q$(ε) dependence results from the analysis of the σ(ε) hysteresis for macroscopic samples. This means that the strain-induced anomalies cannot be explained by the transition of the CDW to fourfold commensurability with the pristine lattice (lock-in transition), as it was supposed earlier. We also discuss the metastable length states and the elastic anomalies in $\mathrm{Ta}{\mathrm{S}}_3$ in light of the observed $q$(ε) dependence.

By measuring the thermoelectric effect in high-mobility quantum wells with two occupied subbands in perpendicular magnetic field, we detect magnetophonon oscillations due to interaction of electrons with acoustic phonons. These oscillations contain specific features identified as combined resonances caused by intersubband phonon-assisted transitions of electrons in the presence of Landau quantization. The quantum theory of phonon-drag magnetothermoelectric effect, generalized to the case of multisubband occupation, describes our experimental findings.

A combined experimental and theoretical approach to the coupling between frequency-shift $\left(\mathrm{\Delta }f\right)$, damping, and tunneling current ($I_t$) in combined noncontact atomic force microscopy/scanning tunneling microscopy using quartz tuning forks (QTF)-based probes is reported. When brought into oscillating tunneling conditions, the tip located at the QTF prong's end radiates an electromagnetic field which couples to the QTF prong motion via its piezoelectric tensor and loads its electrodes by induction. Our approach explains how those $I_t$-related effects ultimately modify the $\mathrm{\Delta }f$ and the damping measurements. This paradigm to the origin of the coupling between $I_t$ and the nc-AFM regular signals relies on both the intrinsic piezoelectric nature of the quartz constituting the QTF and its electrodes design.