The formal basis for fully relativistic Korringa-Kohn-Rostoker (KKR) or multiple scattering calculations for the electronic Green function in case of a general potential is discussed. Simple criteria are given to identify situations that require to distinguish between right- and left-hand-side solutions to the Dirac equation when setting up the electronic Green function. In addition, various technical aspects of an implementation of the relativistic KKR for general local and nonlocal potentials will be discussed.

We investigate the spin injection and the spin transport in paramagnetic insulators described by simple Heisenberg interactions using auxiliary particle methods. Some of these methods allow access to both paramagnetic states above magnetic transition temperatures and magnetic states at low temperatures. It is predicted that the spin injection at an interface with a normal metal is rather insensitive to temperatures above the magnetic transition temperature. On the other hand below the transition temperature, it decreases monotonically and disappears at zero temperature. We also analyze the bulk spin conductance. It is shown that the conductance becomes zero at zero temperature as predicted by linear spin wave theory but increases with temperature and is maximized around the magnetic transition temperature. These findings suggest that the compromise between the two effects determines the optimal temperature for spintronics applications utilizing magnetic insulators.

The electrical and thermal Hall conductivities of the cuprate superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y, {\sigma }_{xy}$ and ${\kappa }_{xy}$, were measured in a magnetic field up to 35 T, at a hole concentration (doping) $p=0.11$. In the $T=0$ limit, we find that the Wiedemann-Franz law, ${\kappa }_{xy}/T=({\pi }^2/3){(k_{\mathrm{B}}/e)}^2{\sigma }_{xy}$, is satisfied for fields immediately above the vortex-melting field $H_{\mathrm{vs}}$. This rules out the existence of a vortex liquid at $T=0$ and it puts a clear constraint on the nature of the normal state in underdoped cuprates, in a region of the doping phase diagram where charge-density-wave order is known to exist. As the temperature is raised, the Lorenz ratio, $L_{\mathrm{xy}}={\kappa }_{\mathrm{xy}}/\left({\sigma }_{\mathrm{xy}}T\right)$, decreases rapidly, indicating that strong small-$q$ scattering processes are involved.

We merge advanced ab initio schemes (standard density functional theory, hybrid functionals, and the $GW$ approximation) with model Hamiltonian approaches (tight-binding and Heisenberg Hamiltonian) to study the evolution of the electronic, magnetic, and dielectric properties of the manganite family $R{\mathrm{MnO}}_3$ $(R=\text{La},\text{Pr},\text{Nd},\text{Sm},\text{Eu},\text{and Gd})$. The link between first principles and tight binding is established by downfolding the physically relevant subset of $3d$ bands with $e_g$ character by means of maximally localized Wannier functions (MLWFs) using the VASP2WANNIER90 interface. The MLWFs are then used to construct a general tight-binding Hamiltonian written as a sum of the kinetic term, the Hund's rule coupling, the JT coupling, and the electron-electron interaction. The dispersion of the tight-binding (TB) $e_g$ bands at all levels are found to match closely the MLWFs. We provide a complete set of TB parameters which can serve as guidance for the interpretation of future studies based on many-body Hamiltonian approaches. In particular, we find that the Hund's rule coupling strength, the Jahn-Teller coupling strength, and the Hubbard interaction parameter $U$ remain nearly constant for all the members of the $R{\mathrm{MnO}}_3$ series, whereas the nearest-neighbor hopping amplitudes show a monotonic attenuation as expected from the trend of the tolerance factor. Magnetic exchange interactions, computed by mapping a large set of hybrid functional total energies onto an Heisenberg Hamiltonian, clarify the origin of the A-type magnetic ordering observed in the early rare-earth manganite series as arising from a net negative out-of-plane interaction energy. The obtained exchange parameters are used to estimate the Néel temperature by means of Monte Carlo simulations. The resulting data capture well the monotonic decrease of the ordering temperature down the series from $R=\text{La}$ to Gd, in agreement with experiments. This trend correlates well with the modulation of structural properties, in particular with the progressive reduction of the Mn-O-Mn bond angle which is associated with the quenching of the volume and the decrease of the tolerance factor due to the shrinkage of the ionic radii of $R$ going from La to Gd.

Pyrochlore oxides possessing “all-in-all-out” spin ordering have attracted burgeoning interest as a rich ground of emergent states. This ordering has two distinct types of magnetic domains (all-in-all-out or all-out-all-in) with broken time-reversal symmetry, and a nontrivial metallic surface state has been theoretically demonstrated to appear at their domain wall. Here, we report on the observation of this metallic conduction at the single all-in-all-out/all-out-all-in magnetic domain wall formed at the heterointerface of two pyrochlore iridates. By utilizing the different magnetoresponses of them with different lanthanide ions, the domain wall is controllably inserted at the heterointerface, the surface state being detected as an anomalous conduction enhancement with a ferroic hysteresis. Our establishment paves the way for further investigation and manipulation of this new type of surface transport.

Recent experiments access the time-resolved photoelectron signal originating from plasmon satellites in correlated materials and address their buildup and decay in real time. Motivated by these developments, we present the Kadanoff-Baym formalism for the nonequilibrium time evolution of interacting fermions and bosons. In contrast to the fermionic case, the bosons are described by second-order differential equations. Solution of the bosonic Kadanoff-Baym equations—which is the central ingredient of this work—requires substantial modification of the usual two-times electronic propagation scheme. The solution is quite general and can be applied to a number of problems, such as the interaction of electrons with quantized photons, phonons, and other bosonic excitations. Here the formalism is applied to the photoemission from a deep core hole accompanied by plasmon excitation. We compute the time-resolved photoelectron spectra and discuss the effects of intrinsic and extrinsic electron energy losses and their interference.

We develop a general hydrodynamic framework for computing direct current, thermal, and electric transport in a strongly interacting finite-temperature quantum system near a Lorentz-invariant quantum critical point. Our framework is nonperturbative in the strength of long-wavelength fluctuations in the background-charge density of the electronic fluid and requires the rate of electron-electron scattering to be faster than the rate of electron-impurity scattering. We use this formalism to compute transport coefficients in the Dirac fluid in clean samples of graphene near the charge neutrality point, and find results insensitive to long-range Coulomb interactions. Numerical results are compared to recent experimental data on thermal and electrical conductivity in the Dirac fluid in graphene and a substantially improved quantitative agreement over existing hydrodynamic theories is found. We comment on the interplay between the Dirac fluid and acoustic and optical phonons, and qualitatively explain the experimentally observed effects. Our work paves the way for quantitative contact between experimentally realized condensed matter systems and the wide body of high-energy inspired theories on transport in interacting many-body quantum systems.

Low-temperature ultrasound velocity measurements are presented on the frustrated spin system ${\mathrm{SrDy}}_2{\mathrm{O}}_4$ that allow us to define high-resolution phase diagrams with the magnetic field applied along all three principal axes. For $H\left|\right|b$, a region of field-induced long-range order is delimited by a dome of first-order phase transitions. An unusual magnetization process is observed with significant irreversibility at very low temperatures when passing between the low-field spin liquid phase and the long-range ordered phase which we attribute to large energy barriers. For $H\left|\right|c$, the system appears to remain effectively one dimensional, exhibiting two transitions as a function of magnetic field, but no finite-temperature long-range order.

Experimental and theoretical studies on ratchet effects in graphene with a lateral superlattice excited by alternating electric fields of terahertz frequency range are presented. A lateral superlattice deposited on top of monolayer graphene is formed either by periodically repeated metal stripes having different widths and spacings or by interdigitated comblike dual-grating-gate (DGG) structures. We show that the ratchet photocurrent excited by terahertz radiation and sensitive to the radiation polarization state can be efficiently controlled by the back gate driving the system through the Dirac point as well as by the lateral asymmetry varied by applying unequal voltages to the DGG subgratings. The ratchet photocurrent includes the Seebeck thermoratchet effect as well as the effects of “linear” and “circular” ratchets, sensitive to the corresponding polarization of the driving electromagnetic force. The experimental data are analyzed for the electronic and plasmonic ratchets taking into account the calculated potential profile and the near field acting on carriers in graphene. We show that the photocurrent generation is based on a combined action of a spatially periodic in-plane potential and the spatially modulated light due to the near-field effects of the light diffraction.

We study the effect of anisotropy of the Rashba coupling on the extrinsic spin Hall effect due to spin-orbit active adatoms on graphene. In addition to the intrinsic spin-orbit coupling, a generalized anisotropic Rashba coupling arising from the breakdown of both mirror and hexagonal symmetries of pristine graphene is considered. We find that Rashba anisotropy can strongly modify the dependence of the spin Hall angle on carrier concentration. Our model provides a simple and general description of the skew scattering mechanism due to the spin-orbit coupling that is induced by proximity to large adatom clusters.

The concept of the Brillouin zone (BZ) in relation to a photonic crystal fabricated in an optically anisotropic material is explored both experimentally and theoretically. In experiment we used femtosecond laser pulses to excite THz polaritons and image their propagation in lithium niobate and lithium tantalate photonic crystal (PhC) slabs. We directly measured the dispersion relation inside PhCs and observed that the lowest band gap expected to form at the BZ boundary forms inside the BZ in the anisotropic lithium niobate PhC. Our analysis shows that in an anisotropic material the BZ—defined as the Wigner-Seitz cell in the reciprocal lattice—is no longer bounded by Bragg planes and thus does not conform to the original definition of the BZ by Brillouin. We construct an alternative Brillouin zone defined by Bragg planes and show its utility in identifying features of the dispersion bands. We show that for an anisotropic two-dimensional PhC without dispersion, the Bragg plane BZ can be constructed by applying the Wigner-Seitz method to a stretched or compressed reciprocal lattice. We also show that in the presence of the dispersion in the underlying material or in a slab waveguide, the Bragg planes are generally represented by curved surfaces rather than planes. The concept of constructing a BZ with Bragg planes should prove useful in understanding the formation of dispersion bands in anisotropic PhCs and in selectively tailoring their optical properties.

We report an investigation of the superconducting order parameter of the noncentrosymmetric compound ${\mathrm{PbTaSe}}_2$, which is believed to have a topologically nontrivial band structure. Precise measurements of the London penetration depth $\mathrm{\Delta }\lambda \left(T\right)$ obtained using a tunnel diode oscillator (TDO) based method show an exponential temperature dependence at $T\ll T_c$, suggesting a nodeless superconducting gap structure. A single-gap $s$-wave model well describes the corresponding normalized superfluid density ${\rho }_s\left(T\right)$, with a gap magnitude of $\mathrm{\Delta }\left(0\right)\simeq 1.88T_c$. This is very close to the value of $1.76T_c$ for weak-coupling BCS superconductors, indicating conventional fully-gapped superconductivity in ${\mathrm{PbTaSe}}_2$.

We synthesize and partly review recent developments relating the physics of the half-filled Landau level in two dimensions to correlated surface states of topological insulators in three dimensions. The latter are in turn related to the physics of certain three-dimensional quantum spin liquid states. The resulting insights provide an interesting answer to the old question of how particle-hole symmetry is realized in composite fermion liquids. Specifically the metallic state at filling $\nu =\frac{1}{2}$—described originally in pioneering work by Halperin, Lee, and Read as a liquid of composite fermions—was proposed recently by Son to be described by a particle-hole symmetric effective field theory distinct from that in the prior literature. We show how the relation to topological insulator surface states leads to a physical understanding of the correctness of this proposal. We develop a simple picture of the particle-hole symmetric composite fermion through a modification of older pictures as electrically neutral “dipolar” particles. We revisit the phenomenology of composite fermi liquids (with or without particle-hole symmetry), and show that their heat/electrical transport dramatically violates the conventional Wiedemann-Franz law but satisfies a modified one. We also discuss the implications of these insights for finding physical realizations of correlated topological insulator surfaces.

By using variational wave functions and quantum Monte Carlo techniques, we investigate the complete phase diagram of the Heisenberg model on the anisotropic triangular lattice, where two out of three bonds have superexchange couplings $J$ and the third one has instead $J^{\prime }$. This model interpolates between the square lattice and the isotropic triangular one, for $J^{\prime }/J\le 1$, and between the isotropic triangular lattice and a set of decoupled chains, for $J/J^{\prime }\le 1$. We consider all the fully symmetric spin liquids that can be constructed with the fermionic projective-symmetry group classification (Zhou and Wen, arXiv:cond-mat/0210662) and we compare them with the spiral magnetic orders that can be accommodated on finite clusters. Our results show that, for $J^{\prime }/J\le 1$, the phase diagram is dominated by magnetic orderings, even though a spin-liquid state may be possible in a small parameter window, i.e., $0.7\lesssim J^{\prime }/J\lesssim 0.8$. In contrast, for $J/J^{\prime }\le 1$, a large spin-liquid region appears close to the limit of decoupled chains, i.e., for $J/J^{\prime }\lesssim 0.6$, while magnetically ordered phases with spiral order are stabilized close to the isotropic point.

We present a theory of magnetotransport phenomena related to the chiral anomaly in Weyl semimetals. We show that conductivity, thermal conductivity, thermoelectric, and the sound absorption coefficients exhibit strong and anisotropic magnetic field dependencies. We also discuss properties of magnetoplasmons and magnetopolaritons, whose existences are entirely determined by the chiral anomaly. Finally, we discuss the conditions of applicability of the quasiclassical description of electron transport phenomena related to the chiral anomaly.

Positioned between crystalline solids and liquids, disordered many-particle systems which are stealthy and hyperuniform represent new states of matter that are endowed with novel physical and thermodynamic properties. Such stealthy and hyperuniform states are unique in that they are transparent to radiation for a range of wave numbers around the origin. In this work, we employ recently developed inverse statistical-mechanical methods, which seek to obtain the optimal set of interactions that will spontaneously produce a targeted structure or configuration as a unique ground state, to investigate the spin-spin interaction potentials required to stabilize disordered stealthy hyperuniform one-dimensional (1D) Ising-type spin chains. By performing an exhaustive search over the spin configurations that can be enumerated on periodic 1D integer lattices containing $N=2,3,...,36$ sites, we were able to identify and structurally characterize all stealthy hyperuniform spin chains in this range of system sizes. Within this pool of stealthy hyperuniform spin configurations, we then utilized such inverse optimization techniques to demonstrate that stealthy hyperuniform spin chains can be realized as either unique or degenerate disordered ground states of radial long-ranged (relative to the spin-chain length) spin-spin interactions. Such exotic ground states appear to be distinctly different from spin glasses in both their inherent structural properties and the nature of the spin-spin interactions required to stabilize them. As such, the implications and significance of the existence of these disordered stealthy hyperuniform ground-state spin systems warrants further study, including whether their bulk physical properties and excited states, like their many-particle system counterparts, are singularly remarkable, and can be experimentally realized.

The ground state of the quantum spin ice candidate magnet ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ is known to be sensitive to weak disorder at the $\sim 1\%$ level which occurs in single crystals grown from the melt. Powders produced by solid state synthesis tend to be stoichiometric and display large and sharp heat capacity anomalies at relatively high temperatures, $T_C\sim 0.26$ K. We have carried out neutron elastic and inelastic measurements on well characterized and equilibrated stoichiometric powder samples of ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ which show resolution-limited Bragg peaks to appear at low temperatures, but whose onset correlates with temperatures much higher than $T_C$. The corresponding magnetic structure is best described as an icelike splayed ferromagnet. The spin dynamics in ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ are shown to be gapless on an energy scale $<0.09$ meV at all temperatures and organized into a continuum of scattering with vestiges of highly overdamped ferromagnetic spin waves present. These excitations differ greatly from conventional spin waves predicted for ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$'s mean field ordered state, but appear robust to weak disorder as they are largely consistent with those displayed by nonstoichiometric crushed single crystals and single crystals, as well as by powder samples of ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$'s sister quantum magnet ${\mathrm{Yb}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$.

Similar to static systems, periodically driven systems can host a variety of topologically nontrivial phases. Unlike the case of static Hamiltonians, the topological indices of bulk Floquet bands may fail to describe the presence and robustness of edge states, prompting the search for new invariants. We develop a unified description of topological phases and their invariants in driven systems by using scattering theory. We show that scattering matrix invariants correctly describe the topological phase, even when all bulk Floquet bands are trivial. Additionally, we use scattering theory to introduce and analyze new periodically driven phases, such as weak topological Floquet insulators, for which invariants were previously unknown. We highlight some of their similarities with static systems, including robustness to disorder, as well as some of the features unique to driven systems, showing that the weak phase may be destroyed by breaking translational symmetry not in space, but in time.

We show here that an extension of the Hamiltonian theory developed by us over the years furnishes a composite fermion (CF) description of the $\nu =1/2$ state that is particle-hole (PH) symmetric, has a charge density that obeys the magnetic translation algebra of the lowest Landau level (LLL), and exhibits cherished ideas from highly successful wave functions, such as a neutral quasiparticle with a certain dipole moment related to its momentum. We also a provide an extension away from $\nu =1/2$, which has the features from $\nu =1/2$ and implements the PH transformation on the LLL as an antiunitary operator $\mathcal{T}$ with ${\mathcal{T}}^2=-1$. This extension of our past work was inspired by Son, who showed that the CF may be viewed as a Dirac fermion on which the particle-hole transformation of LLL electrons is realized as time-reversal, and Wang and Senthil, who provided a very attractive interpretation of the CF as the bound state of a semion and antisemion of charge $\pm e/2$. Along the way, we also found a representation with all the features listed above except that now ${\mathcal{T}}^2=+1$. We suspect it corresponds to an emergent charge-conjugation symmetry of the $\nu =1$ boson problem analyzed by Read.

Hubbard-like Hamiltonians are widely used to describe on-site Coulomb interactions in magnetic and strongly-correlated solids, but there is much confusion in the literature about the form these Hamiltonians should take for shells of $p$ and $d$ orbitals. This paper derives the most general $s,p$, and $d$ orbital Hubbard-like Hamiltonians consistent with the relevant symmetries, and presents them in ways convenient for practical calculations. We use the full configuration interaction method to study $p$ and $d$ orbital dimers and compare results obtained using the correct Hamiltonian and the collinear and vector Stoner Hamiltonians. The Stoner Hamiltonians can fail to describe properly the nature of the ground state, the time evolution of excited states, and the electronic heat capacity.