We theoretically study the effects of surface roughness on the magnetic response of small unconventional superconductors by solving the Eilenberger equation for the quassiclassical Green function and the Maxwell equation for the vector potential simultaneously and self-consistently. The paramagnetic phase of spin-singlet $d$-wave superconducting disks is greatly suppressed by the surface roughness, whereas that of spin-triplet $p$-wave disks is robust even in the presence of the roughness. This difference derives from the orbital symmetry of paramagnetic odd-frequency Cooper pairs appearing at the surface of the disks. The orbital part of the paramagnetic pairing correlation has $p$-wave symmetry in the $d$-wave disks, whereas it has $s$-wave symmetry in the $p$-wave disks. Calculating the free energy, we also confirm that the paramagnetic state is more stable than the normal state, which indicates a possibility of detecting the paramagnetic effect in experiments. Indeed, our results are consistent with an experimental finding on high-$T_c$ thin films.

We study a 0-$\pi$ dc superconducting quantum interference device (SQUID) with asymmetric inductances and critical currents of the two Josephson junctions (JJs). By considering such a dc SQUID as a black box with two terminals, we calculate its effective current-phase relation $I_s\left(\psi \right)$ and the Josephson energy $U\left(\psi \right)$, where $\psi$ is the Josephson phase across the terminals. We show that there is a domain of parameters where the black box has the properties of a $\phi$ JJ with degenerate ground state phases $\psi =\pm \phi$. The $\phi$ domain is rather large, so one can easily construct a $\phi$ JJ experimentally. We derive the current phase relation and show that it can be tuned in situ by applying an external magnetic flux resulting in a continuous transition between the systems with static solutions $\psi =\pm \phi ,\psi ={\phi }_0 \left({\phi }_0\ne 0,\pi \right)$ and even $\psi ={\phi }_0\pm \phi$. The dependence of ${\phi }_0$ on applied magnetic flux is not $2\pi$ (one flux quantum) periodic.

We derive expressions for density-density and spin-spin correlation functions in the (greatly enhanced) pseudogap phase of spin-orbit-coupled Fermi gases. Density-density correlation functions are found to be relatively insensitive to the presence of these Rashba spin-orbit effects. To arrive at spin-spin correlation functions we derive new $f$-sum rules, valid even in the absence of a spin conservation law. Our spin-spin correlation functions are shown to be fully consistent with these $f$-sum rules. Importantly, they provide a clear signature of the Rashba band structure and separately help to establish the presence of a pseudogap.

First-principles alloy theory, formulated within the exact muffin-tin orbital method in combination with the coherent-potential approximation, is used to study the mechanical properties of ferromagnetic body-centered cubic (bcc) ${\mathrm{Fe}}_{1-x}{\mathrm{M}}_x$ alloys (M = Mn or Ni, $0\le x\le 0.1$). We consider several physical parameters accessible from ab initio calculations and their combinations in various phenomenological models to compare the effect of Mn and Ni on the properties of Fe. Alloying is found to slightly alter the lattice parameters and produce noticeable influence on elastic moduli. Both Mn and Ni decrease the surface energy and the unstable stacking fault energy associated with the $\left\{110\right\}$ surface facet and the $\left\{110\right\}\langle 111\rangle$ slip system, respectively. Nickel is found to produce larger effect on the planar fault energies than Mn. The semiempirical ductility criteria by Rice and Pugh consistently predict that Ni enhances the ductility of Fe but give contradictory results in the case of Mn doping. The origin of the discrepancy between the two criteria is discussed and an alternative measure of the ductile-brittle behavior based on the theoretical cleavage strength and single-crystal shear modulus $G\left\{110\right\}\langle 111\rangle$ is proposed.

We studied the lattice vibrations of two interpenetrating atomic sublattices via the Frenkel-Kontorova (FK) model of a linear chain of harmonically interacting atoms subjected to an on-site potential using the technique of thermodynamic Green's functions based on quantum field-theoretical methods. General expressions were deduced for the phonon frequency-wave-vector dispersion relations, number density, and energy of the FK model system. As the application of the theory, we investigated in detail cases of linear chains with various periods of the on-site potential of the FK model. Some unusual but interesting features for different amplitudes of the on-site potential of the FK model are discussed. In the commensurate structure, the phonon spectrum always starts at a finite frequency, and the gaps of the spectrum are true ones with a zero density of modes. In the incommensurate structure, the phonon spectrum starts from zero frequency, but at a nonzero wave vector; there are some modes inside these gap regions, but their density is very low. In our approximation, the energy of a higher-order commensurate state of the one-dimensional system at a finite temperature may become indefinitely close to the energy of an incommensurate state. This finding implies that the higher-order incommensurate-commensurate transitions are continuous ones and that the phase transition may exhibit a “devil's staircase” behavior at a finite temperature.

We applied the formulas for the phonon spectral-density function that we presented in the previous paper of this series to analyze the thermal conductivity of the lattice in the framework of the Frenkel-Kontorova (FK) model. We found that two extra mechanisms of phonon scattering (different from the point impurities, three-phonon processes, and boundary scattering typical of all crystals), viz., resonance, and anharmonic scattering, that mainly influences the thermal conductivity of the lattice. The frequencies of resonance scattering are discrete, and their number increases from a finite number to infinity with their transition from the commensurate to the incommensurate state. Changing the amplitude and period of the FK model changes the frequencies and the frequency number of resonance scattering and the intensity of anharmonic scattering. We analyze these changes in detail. Our theory can explain all existing numerical results on this problem and suggest strategies to reduce the thermal conductivity of the lattice of layered materials.

By means of a mean-field model extended to include magnetovolumic effects, we study the effect of external fields on the thermal response characterized either by the isothermal entropy change and/or the adiabatic temperature change. The model includes two different situations induced by the magnetovolumic coupling: (i) a first-order paramagnetic-to-ferromagnetic phase transition that entails a volume change; (ii) an inversion of the effective exchange interaction that promotes the occurrence of an antiferromagnetic phase at low temperatures. In both cases, we study the magnetocaloric and barocaloric effects as well as the corresponding cross-caloric responses. By comparing the present theoretical results with available experimental data for several materials, we conclude that the present thermodynamical model reproduces the general trends associated with the considered caloric and cross-caloric responses.

We report systematic studies on the spin current transport and relaxation mechanism in thin films of the highly doped organic polymer poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS), in which hopping charge transport is dominant. In this study, we determined the spin diffusion length, spin lifetime, and spin diffusion constant using different experimental techniques. The experimentally obtained spin lifetime is much shorter than that of nondoped organic semiconductors. This clearly shows considerable enhancement of spin relaxation in highly doped PEDOT molecules, which form the trapping centers of hopping transport. Also, we obtained a longer spin diffusion length than the average hopping length, indicating that spins are almost conserved during the hopping process. These facts suggest that spin relaxation of this material mainly occurs in the nanograins of the PEDOT molecules.

We present a detailed investigation of spectroscopic features located at the central metal ion of MnPc (where Pc represents phthalocyanine) on Ag(001) by means of scanning tunneling spectroscopy (STS) and first-principles theory. STS data taken close to the Fermi level reveal an asymmetric feature that cannot be fitted with a single Fano function representing a one-channel Kondo effect. Instead, our data indicate the existence of a second superimposed feature. Two potential physical origins, a second Kondo channel related to the $d_{xz/yz}$ orbitals, and a spectral feature of the $d_{z^2}$ orbital itself, are discussed. A systematic experimental and theoretical comparison of MnPc with CoPc and FePc indicates that the second feature observed on MnPc is caused by the $d_{z^2}$ orbital. This conclusion is corroborated by STM-induced dehydrogenation experiments on FePc and MnPc which in both cases result in a gradual shift towards more positive binding energies and a narrowing of the Kondo resonance. Theoretical analysis reveals that the latter is caused by the reduced hybridization between the $d$ orbital and the substrate. Spatially resolved differential conductivity maps taken close to the respective peak positions show that the intensity of both features is highest over the central Mn ion, thereby providing further evidence against a second Kondo channel originating from the $d_{xz/yz}$ orbital of the central Mn ion.

Until recently, spin polarization in nonmagnetic materials was the exclusive territory of noncentrosymmetric structures. It was recently shown that a form of “hidden spin polarization” (named the “Rashba-2” or “R-2” effect) could exist in globally centrosymmetric crystals provided the individual layers belong to polar point group symmetries. This realization could considerably broaden the range of materials that might be considered for spin-polarization spintronic applications to include the hitherto “forbidden spintronic compound” that belongs to centrosymmetric symmetries. Here we take the necessary steps to transition from such general, material-agnostic condensed matter theory arguments to material-specific “design principles” that could aid future laboratory search of R-2 materials. Specifically, we (i) classify different prototype layered structures that have been broadly studied in the literature in terms of their expected R-2 behavior, including the $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$-structure type (a prototype topological insulator), $\mathrm{Mo}{\mathrm{S}}_2$-structure type (a prototype valleytronic compound), and $\mathrm{LaBiO}{\mathrm{S}}_2$-structure type (a host of superconductivity upon doping); (ii) formulate the properties that ideal R-2 compounds should have in terms of combination of their global unit cell symmetries with specific point group symmetries of their constituent “sectors”; and (iii) use first-principles band theory to search for compounds from the prototype family of $\mathrm{LaOBi}{\mathrm{S}}_2$-type structures that satisfy these R-2 design metrics. We initially consider both stable and hypothetical $M^{\prime }\mathrm{O}M{X}_2$ (M': Sc, Y, La, Ce, Pr, Nd, Al, Ga, In, Tl; M: P, As, Sb, Bi; X: S, Se, Te) compounds to establish an understanding of trends of R-2 with composition, and then indicate the predictions that are expected to be stable and synthesizable. We predict large spin splittings (up to $\sim 200\mathrm{meV}$ for holes in $\mathrm{LaOBiT}{\mathrm{e}}_2$) as well as surface Rashba states. Experimental testing of such predictions is called for.

We investigate copper (Cu) precipitation at small-angle tilt boundaries on (220) in Czochralski-grown p-type silicon (Si) ingots using transmission electron microscopy, atom probe tomography, and ab initio calculations. In the initial stage of precipitation, Cu atoms agglomerate along the boundaries, forming coherent layers (less than about 2 nm thick) of ${\mathrm{Cu}}_3\mathrm{Si}$ with a body-centered-cubic structure in a metastable state ($a=0.285$ nm). As the layers thicken, they become semicoherent with misfit dislocations on the (220) interphase boundaries, reducing coherency strains. Subsequently, the metastable layers convert into incoherent polyhedrons of orthorhombic ${\eta }^{\prime \prime }\text{−}{\mathrm{Cu}}_3\mathrm{Si}$ in the equilibrium state, forming interphase boundaries on {112} in Si. These results are similar to the Cu precipitation processes found in metallic alloys: the formation of Guinier-Preston zones followed by a conversion into the equilibrium $\theta$ phase.

We investigate theoretically polygonal quantum rings and focus mostly on the triangular geometry where the corner effects are maximal. Such rings can be seen as short core-shell nanowires, a generation of semiconductor heterostructures with multiple applications. We show how the geometry of the sample determines the electronic energy spectrum, and also the localization of electrons, with effects on the optical absorption. In particular, we show that irrespective of the ring shape low-energy electrons are always attracted by corners and are localized in their vicinity. The absorption spectrum in the presence of a magnetic field shows only two peaks within the corner-localized state domain, each associated with different circular polarization. This picture may be changed by an external electric field which allows previously forbidden transitions, and thus enables the number of corners to be determined. We show that polygonal quantum rings allow absorption of waves from distant ranges of the electromagnetic spectrum within one sample.

We develop a coupled-wire construction of chiral spin liquids. The starting points are individual wires of electrons in the Mott regime that are subject to a Zeeman field and Rashba spin-orbit coupling. Suitable spin-flip couplings between the wires yield an Abelian chiral spin liquid state which supports spinon excitations above a bulk gap and chiral edge states. The approach generalizes to non-Abelian chiral spin liquids at level $k$ with parafermionic edge states.

We show how the area law for entanglement entropy may be violated by free fermions on a lattice, and we look for conditions leading to the emergence of a volume law. We give an explicit construction of the states with maximal entanglement entropy based on the fact that, once a bipartition of the lattice in two complementary sets $A$ and $\overline{A}$ is given, the states with maximal entanglement entropy (volume law) may be factored into Bell pairs (BPs) formed by two states with support on $A$ and $\overline{A}$. We then exhibit, for translational invariant fermionic systems on a lattice, a Hamiltonian whose ground state is such that it yields an exact volume law. As expected, the corresponding Fermi surface has a fractal topology. We also provide some examples of fermionic models for which the ground state may have an entanglement entropy $S_A$ between the area and the volume law, building an explicit example of a one-dimensional free fermion model where $S_A\left(L\right)\propto L^{\beta }$, with $\beta$ being intermediate between $\beta =0$ (area law) and $\beta =1$ (BP state inducing volume law). For this model, the dispersion relation has a “zigzag” structure leading to a fractal Fermi surface whose counting box dimension equals, for large lattices, $\beta$. Our analysis clearly relates the violation of the area law for the entanglement entropy of the ground state to the emergence of a nontrivial topology of the Fermi surface.

We describe a coupled-chain construction for chiral spin liquids in two-dimensional spin systems. Starting from a one-dimensional zigzag spin chain and imposing SU(2) symmetry in the framework of non-Abelian bosonization, we first show that our approach faithfully describes the low-energy physics of an exactly solvable model with a three-spin interaction. Generalizing the construction to the two-dimensional case, we obtain a theory that incorporates the universal properties of the chiral spin liquid predicted by Kalmeyer and Laughlin: charge-neutral edge states, gapped spin-1/2 bulk excitations, and ground-state degeneracy on the torus signaling the topological order of this quantum state. In addition, we show that the chiral spin liquid phase is more easily stabilized in frustrated lattices containing corner-sharing triangles, such as the extended kagome lattice, than in the triangular lattice. Our field-theoretical approach invites generalizations to more exotic chiral spin liquids and may be used to assess the existence of the chiral spin liquid as the ground state of specific lattice systems.

We present a theoretical study of the exciton binding energy for anisotropic two-dimensional crystals. We obtain analytical expressions from variational wave functions in different limits of the screening length to exciton size ratio and compare them with numerical solutions, both variational and exact. As an example, we apply these results to phosphorene, a monolayer of black phosphorous. Aided by density-functional-theory calculations for the evaluation of the two-dimensional polarizability, our analytical solution for the exciton binding energy gives a result which compares well with numerical ones and, in turn, with experimental values, as recently reported.

All local electronic properties of graphene on a hexagonal boron nitride (hBN) substrate exhibit spatial moiré patterns related to lattice constant and orientation differences between shared triangular Bravais lattices. We apply a previously derived effective Hamiltonian for the $\pi$ bands of graphene on hBN to address the carrier dependence of transport properties, concentrating on the conductivity features at four electrons and four holes per unit cell. These transport features measure the strength of Bragg scattering of $\pi$ electrons off the moiré pattern, and they exhibit a striking particle-hole asymmetry that we trace to specific features of the effective Hamiltonian that we interpret physically.

Knowledge of the mean-free-path distribution of heat-carrying phonons is key to understanding phonon-mediated thermal transport. We demonstrate that thermal conductivity measurements of thin membranes spanning a wide thickness range can be used to characterize how bulk thermal conductivity is distributed over phonon mean free paths. A noncontact transient thermal grating technique was used to measure the thermal conductivity of suspended Si membranes ranging from 15–1500 nm in thickness. A decrease in the thermal conductivity from 74–13% of the bulk value is observed over this thickness range, which is attributed to diffuse phonon boundary scattering. Due to the well-defined relation between the membrane thickness and phonon mean-free-path suppression, combined with the range and accuracy of the measurements, we can reconstruct the bulk thermal conductivity accumulation vs. phonon mean free path, and compare with theoretical models.

${\text{SrRu}}_2{\text{O}}_6$ is a layered honeycomb-lattice material with an extraordinarily high magnetic ordering temperature. We investigated this material using density functional calculations. We find that the energy scales for moment formation and ordering are similar and high. Additionally, we find that the magnetic anisotropy is high and favors moments oriented along the $c$ axis. This provides an explanation for the exceptionally high ordering temperature. Finally, the compound is found to be semiconducting at the bare density functional level, even without magnetic order. Experimental consequences of this scenario for the high ordering temperature are discussed.