A partially gapped spectrum due to the application of a magnetic field is one of the main probes of Rashba spin-orbit coupling in nanowires. Such a “helical gap” manifests itself in the linear conductance, as well as in dynamic response functions such as the spectral function, the structure factor, or the tunneling density of states. In this paper we investigate theoretically the signature of the helical gap in these observables with a particular focus on the interplay between Rashba spin-orbit coupling and electron-electron interactions. We show that in a quasi-one-dimensional wire, interactions can open a helical gap even without magnetic field. We calculate the dynamic response functions using bosonization, a renormalization group analysis, and the exact form factors of the emerging sine-Gordon model. For special interaction strengths, we verify our results by re-fermionization. We show how the two types of helical gaps, caused by magnetic fields or interactions, can be distinguished in experiments.

The electron spin dynamics in cubic GaN is comprehensively investigated by time-resolved magneto-optical Kerr-rotation spectroscopy over a wide range of temperatures, magnetic fields, and doping densities. The spin dynamics is found to be governed by the interplay of spin relaxation of localized electrons and Dyakonov-Perel relaxation of delocalized electrons. Localized electrons significantly contribute to spin relaxation up to room temperature at moderate doping levels, while Dyakonov-Perel relaxation dominates for high temperatures or degenerate doping levels. Quantitative agreement to Dyakonov-Perel theory requires a larger value of the spin-splitting constant than theoretically predicted. Possible reasons for this discrepancy are discussed, including the role of charged dislocations.

A complete set of tight-binding parameters for the description of the quasiparticle dispersion relations of black phosphorous (BP) and $N$-layer phosphorene with $N=1...\infty$ is presented. The parameters, which describe valence and conduction bands, are fit to angle-resolved photoemission spectroscopy (ARPES) data of pristine and lithium doped BP. We show that zone-folding of the experimental three-dimensional electronic band structure of BP is a simple and intuitive method to obtain the layer-dependent two-dimensional electronic structure of few-layer phosphorene. Zone folding yields the band gap of $N$-layer phosphorene in excellent quantitative agreement to experiments and ab initio calculations. A combined analysis of optical absorption and ARPES spectra of pristine and doped BP is used to estimate a value for the exciton binding energy of BP.

We study Weyl semimetals in the presence of generic disorder, consisting of a random vector potential as well as a random scalar potential. We derive renormalization group flow equations to second order in the disorder strength. These flow equations predict a disorder-induced phase transition between a pseudoballistic weak-disorder phase and a diffusive strong-disorder phase for a sufficiently strong random scalar potential or for a pure three-component random vector potential. We verify these predictions using a numerical study of the density of states near the Weyl point and of quantum transport properties at the Weyl point. In contrast, for a pure single-component random vector potential, the diffusive strong-disorder phase is absent.

We study composite Fermi liquid (CFL) states in the lowest Landau level (LLL) limit at a generic filling $\nu =\frac{1}{n}$. We begin with the old observation that, in compressible states, the composite fermion in the lowest Landau level should be viewed as a charge-neutral particle carrying vorticity. This leads to the absence of a Chern-Simons term in the effective theory of the CFL. We argue here that instead a Berry curvature should be enclosed by the Fermi surface of composite fermions, with the total Berry phase fixed by the filling fraction ${\varphi }_B=-2\pi \nu$. We illustrate this point with the CFL of fermions at filling fractions $\nu =1/2q$ and (single and two-component) bosons at $\nu =1/(2q+1)$. The Berry phase leads to sharp consequences in the transport properties including thermal and spin Hall conductances. We emphasize that these results only rely on the LLL limit and do not require particle-hole symmetry, which is present microscopically only for fermions at $\nu =1/2$. Nevertheless, we show that the existing LLL theory of the composite Fermi liquid for bosons at $\nu =1$ does have an emergent particle-hole symmetry. We interpret this particle-hole symmetry as a transformation between the empty state at $\nu =0$ and the boson integer quantum hall state at $\nu =2$. This understanding enables us to define particle-hole conjugates of various bosonic quantum Hall states which we illustrate with the bosonic Jain and Pfaffian states. For bosons at $\nu =1$ we construct paired non-Abelian states distinct from both the standard bosonic Pfaffian and its particle hole conjugate and show how they may arise naturally out of the neutral vortex composite Fermi liquid. The bosonic particle-hole symmetry can be realized exactly on the surface of a three-dimensional boson topological insulator. We also show that with the particle-hole and spin $SU\left(2\right)$ rotation symmetries, there is no gapped topological phase for bosons at $\nu =1$. Finally we comment on systems that are not strictly in the lowest Landau level limit and argue that our theory should still be applicable at low energy.

We present a microscopic theory of the equilibrium polariton condensate state of a semiconductor quantum well in a planar optical cavity. The theory accounts for the adjustment of matter excitations to the presence of a coherent photon field, predicts effective polariton-polariton interaction strengths that are weaker and condensate exciton fractions that are smaller than in the commonly employed exciton-photon model, and yields effective Rabi coupling strengths that depend on the detuning of the cavity-photon energy relative to the bare exciton energy. The dressed quasiparticle bands that appear naturally in the theory provide a mechanism for electrical manipulation of polariton condensates.

By comparing two expressions for the polarization function $\mathrm{\Pi }(\mathit{q},i\omega )$ given in terms of two different local-field factors, $G_{+}(\mathit{q},i\omega )$ and $G_s(\mathit{q},i\omega )$, we have derived the kinetic-energy-fluctuation (or sixth-power) sum rule for the momentum distribution function $n\left(\mathit{p}\right)$ in the three-dimensional electron gas. With use of this sum rule, together with the total-number (or second-power) and the kinetic-energy (or fourth-power) sum rules, we have obtained $n\left(\mathit{p}\right)$ in the low-density electron gas at negative compressibility (namely, $r_s>5.25$ with $r_s$ being the conventional density parameter) up to $r_s\approx 22$ by improving on the interpolation scheme due to Gori-Giorge and Ziesche proposed in 2002. The obtained results for $n\left(\mathit{p}\right)$ combined with the improved form for $G_s(\mathit{q},\omega +i{0}^{+})$ are employed to calculate the dynamical structure factor $S(\mathit{q},\omega )$ to reveal that a giant peak, even bigger than the plasmon peak, originating from an excitonic collective mode made of electron-hole pair excitations, emerges in the low-$\omega$ region at $\left|\mathit{q}\right|$ near $2p_{\mathrm{F}}$ ($p_{\mathrm{F}}$: the Fermi wave number). Connected with this mode, we have discovered a singular point in the retarded dielectric function at $\omega =0$ and $\left|\mathit{q}\right|\approx 2p_{\mathrm{F}}$.

We study Kondo screening obtained by coupling Majorana bound states, located on a topological superconducting island, to interacting electronic reservoirs. At the charge degeneracy points of the island, we formulate an exact mapping onto the spin-$1/2$ multichannel Kondo effect. The coupling to Majorana fermions transforms the tunneling terms into effective fermionic bilinear contributions with a Luttinger parameter $K$ in the leads that is effectively doubled. For strong interactions $K=1/2$, the intermediate fixed point of the standard multichannel Kondo model is exactly recovered. It evolves with $K$ and connects to strong coupling in the noninteracting case $K=1$, with maximum conductance between the leads and robustness against channel asymmetries similarly to the topological Kondo effect. For a number of leads above four, there exists a window of Luttinger parameters in which a quantum phase transition can occur between the strong coupling topological Kondo state and the partially conducting multichannel Kondo state.

We have investigated magnetic orders and excitations in a Y-type hexaferrite ${\mathrm{BaSrCo}}_2{\mathrm{Fe}}_{11}{\mathrm{AlO}}_{22}$ (BSCoFAO), which was reported to exhibit spin-driven ferroelectricity at room temperature [S. Hirose, K. Haruki, A. Ando, and T. Kimura, Appl. Phys. Lett. 104, 022907 (2014)]. By means of magnetization, electric polarization, and neutron-diffraction measurements using single-crystal samples, we establish a $H-T$ magnetic phase diagram for magnetic field perpendicular to the $c$ axis ($H_{\perp c}$). This system exhibits an alternating longitudinal conical (ALC) magnetic structure in the ground state, and it turns into a non-co-planar commensurate magnetic order with spin-driven ferroelectricity under $H_{\perp c}$. The field-induced ferroelectric phase remains as a metastable state after removing magnetic field below $\sim 250$ K. This metastability is the key to understanding of magnetic field reversal of the spin-driven electric polarization in this system. Inelastic polarized neutron-scattering measurements in the ALC phase reveal a magnetic excitation at around 7.5 meV, which is attributed to spin components oscillating in a plane perpendicular to the cone axis. This phasonlike excitation is expected to be an electric-field active magnon, i.e., electromagnon excitation, in terms of the magnetostriction mechanism.

Graphene and other two-dimensional materials display remarkable optical properties, including a simple transparency of $T\approx 1-\pi \alpha$ for visible light. Most theoretical rationalizations of this “universal” opacity employ a model coupling light to the electron's crystal momentum and put emphasis on the linear dispersion of the graphene bands. However, such a formulation of interband absorption is not allowable within band structure theory, because it conflates the crystal momentum label with the canonical momentum operator. We show that the physical origin of the optical behavior of graphene can be explained within a straightforward picture with the correct use of canonical momentum coupling. Its essence lies in the two-dimensional character of the density of states rather than in the precise dispersion relation, and therefore the discussion is applicable to other systems such as semiconductor membranes. At higher energies the calculation predicts a peak corresponding to a van Hove singularity as well as a specific asymmetry in the absorption spectrum of graphene, in agreement with previous results.

We report the observation by small-angle neutron scattering (SANS) of a magnetic helical structure confined in a thin film of the chiral lattice magnet FeGe. Twofold magnetic Bragg spots appearing below the magnetic transition temperature indicate the formation of a spin helix with a single propagation vector $\mathit{q}$ aligned perpendicular to the film plane. Due to magnetic anisotropy, the direction of $\mathit{q}$ is unaffected by an external magnetic field $\mathit{H}$. Instead we observe anisotropic deformations of the spin helix with respect to the $\mathit{H}$ direction. In the configuration with $\mathit{H}\perp \mathit{q}$, the helical pitch exhibits hysteretic elongation with $\mathit{H}$, while the system tends to maintain an integer number of spiral turns within the film thickness by continuously pushing out one turn. For $\mathit{H}\parallel \mathit{q}$, the helix is smoothly distorted to a conical structure with minimal change in the magnetic period. The direct measurement of $\mathit{q}$ by SANS establishes a correspondence between helix deformation and macroscopic features observed in magnetization and magnetoresistivity.

Charge order in underdoped and optimally doped high-$T_{\mathrm{c}}$ superconductors ${\mathrm{Bi}}_2{\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{CuO}}_{6+\delta }$ (Bi2201) is investigated by Cu $L_3$ edge resonant inelastic x-ray scattering. We have directly observed charge density modulation in the optimally doped Bi2201 at momentum transfer $Q_{\parallel }\simeq 0.23$ reciprocal lattice units, with smaller intensity and correlation length with respect to the underdoped sample. This demonstrates the short-range charge order in Bi2201 persists up to optimal doping, as in other hole-doped cuprates. We explored the nodal (diagonal) direction and found no charge order peak, confirming that charge density modulates only along the Cu-O bond directions. We measured the out-of-plane dependence of charge order, finding a flat response and no maxima at half integer L values. This suggests there is no out-of-plane phase correlation in single layer Bi2201, at variance from ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ and ${\mathrm{La}}_{2-x}{(\text{Ba},\text{Sr})}_x{\mathrm{CuO}}_4$. Combining our results with data from the literature we assess that charge order in Bi2201 exists in a large doping range across the phase diagram, i.e., $0.07\lesssim p\lesssim 0.16$, demonstrating thereby that it is intimately entangled with the antiferromagnetic background, the pseudogap, and superconductivity.

The “parity” anomaly—more accurately described as an anomaly in time-reversal or reflection symmetry—arises in certain theories of fermions coupled to gauge fields and/or gravity in a spacetime of odd dimension. This anomaly has traditionally been studied on orientable manifolds only, but recent developments involving topological superconductors have made it clear that one can get more information by asking what happens on an unorientable manifold. In this paper, we give a full description of the “parity” anomaly for fermions coupled to gauge fields and gravity in $2+1$ dimensions on a possibly unorientable spacetime. We consider an application to topological superconductors and another application to M theory. The application to topological superconductors involves using knowledge of the “parity” anomaly as an ingredient in constructing gapped boundary states of these systems and in particular in gapping the boundary of a $\nu =16$ system in a topologically trivial fashion. The application to M theory involves showing the consistency of the path integral of an M theory membrane on a possibly unorientable worldvolume. In the past, this has been done only in the orientable case.

Slow and confined light have been exploited in optoelectronics to enhance light-matter interactions. Here we describe the GaAs/AlAs semiconductor microcavity as a device that, depending on the excitation conditions, either confines or slows down both light and optically generated acoustic phonons. The localization of photons and phonons in the same place of space amplifies optomechanical processes. Picosecond laser pulses are used to study through time-resolved reflectivity experiments the coupling between photons and both confined and slow acoustic phonons when the laser is tuned either with the cavity (confined) optical mode or with the stop-band edge (slow) optical modes. A model that fully takes into account the modified propagation of the acoustic phonons and light in these resonant structures is used to describe the laser detuning dependence of the coherently generated phonon spectra and amplitude under these different modes of laser excitation. We observe that confined light couples only to confined mechanical vibrations, while slow light can generate both confined and slow coherent vibrations. A strong enhancement of the optomechanical coupling using confined photons and vibrations, and also with properly designed slow photon and phonon modes, is demonstrated. The prospects for the use of these optoelectronic devices in confined and slow optomechanics are addressed.

Surface codes offer a very promising avenue towards fault-tolerant quantum computation. We argue that two-dimensional interacting networks of Majorana bound states in topological superconductor/semiconductor heterostructures hold several key advantages in that direction, concerning both the hardware realization and the actual operation of the code. We here discuss how topologically protected logical qubits in this Majorana surface code architecture can be defined, initialized, manipulated, and read out. All physical ingredients needed to implement these operations are routinely used in topologically trivial quantum devices. By means of quantum interference terms in linear conductance measurements, single-electron pumping protocols, and gate-tunable tunnel barriers, the full set of quantum gates required for universal quantum computation can be achieved. In particular, we show that designated multistep pumping sequences via tunnel-coupled quantum dots realize high-fidelity ancilla states for phase gates.

We present a combined experimental and theoretical study of the evolution of the low-temperature Fermi surface of lead telluride (PbTe) when holes are introduced through sodium substitution on the lead site. Our Shubnikov-de Haas measurements for samples with carrier concentrations up to $9.4\times {10}^{19}{\mathrm{cm}}^{-3}$ (0.62 Na at. $\%$) show the qualitative features of the Fermi surface evolution (topology and effective mass) predicted by our density functional (DFT) calculations within the generalized gradient approximation (GGA): we obtain perfect ellipsoidal $L$ pockets at low and intermediate carrier concentrations, evolution away from ideal ellipsoidicity for the highest doping studied, and cyclotron effective masses increasing monotonically with doping level, implying deviations from perfect parabolicity throughout the whole band. Our measurements show, however, that standard DFT calculations underestimate the energy difference between the $L$ point and $\mathrm{\Sigma }$-line valence band maxima, since our data are consistent with a single-band Fermi surface over the entire doping range studied, whereas the calculations predict an occupation of the $\mathrm{\Sigma }$ pockets at higher doping. Our results for low and intermediate compositions are consistent with a nonparabolic Kane-model dispersion, in which the $L$ pockets are ellipsoids of fixed anisotropy throughout the band, but the effective masses depend strongly on Fermi energy.

The dynamical processes associated with electric field manipulation of the polarization in a ferroelectric remain largely unknown but fundamentally determine the speed and functionality of ferroelectric materials and devices. Here we apply subpicosecond duration, single-cycle terahertz pulses as an ultrafast electric field bias to prototypical ${\mathrm{BaTiO}}_3$ ferroelectric thin films with the atomic-scale response probed by femtosecond x-ray-scattering techniques. We show that electric fields applied perpendicular to the ferroelectric polarization drive large-amplitude displacements of the titanium atoms along the ferroelectric polarization axis, comparable to that of the built-in displacements associated with the intrinsic polarization and incoherent across unit cells. This effect is associated with a dynamic rotation of the ferroelectric polarization switching on and then off on picosecond time scales. These transient polarization modulations are followed by long-lived vibrational heating effects driven by resonant excitation of the ferroelectric soft mode, as reflected in changes in the $c$-axis tetragonality. The ultrafast structural characterization described here enables a direct comparison with first-principles-based molecular-dynamics simulations, with good agreement obtained.

Ferroelectric control of interfacial magnetism has attracted much attention. However, the coupling of these two functionalities has not been understood well at the atomic scale. The lack of scientific progress is mainly due to the limited characterization methods by which the interface's magnetic properties can be probed at an atomic level. Here, we use polarized neutron reflectometry to probe the evolution of the magnetic moment at interfaces in ferroelectric/strongly correlated oxide $\left[\mathrm{PbZ}{\mathrm{r}}_{0.2}\mathrm{T}{\mathrm{i}}_{0.8}{\mathrm{O}}_3/\mathrm{L}{\mathrm{a}}_{0.8}\mathrm{S}{\mathrm{r}}_{0.2}\mathrm{Mn}{\mathrm{O}}_3\left(\mathrm{PZT}/\mathrm{LSMO}\right)\right]$ heterostructures. We find that the magnetization at the surfaces and interfaces of our LSMO films without PZT are always deteriorated and such magnetic deterioration can be greatly improved by interfacing with a strongly polar PZT film. Magnetoelectric coupling of magnetism and ferroelectric polarization was observed within a couple of nanometers of the interface via an increase in the LSMO surface magnetization to $4.0{\mu }_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$, a value nearly 70% higher than the surface magnetization of our LSMO film without interfacing with a ferroelectric layer. We attribute this behavior to hole depletion driven by the ferroelectric polarization. These compelling results not only probe the presence of nanoscale magnetic suppression and its control by ferroelectrics, but also emphasize the importance of utilizing probing techniques that can distinguish between bulk and interfacial phenomena.

The $A\text{-site}$ spinel material ${\mathrm{CoAl}}_2{\mathrm{O}}_4$ is a physical realization of the frustrated diamond-lattice antiferromagnet, a model in which unique incommensurate or “spin-spiral-liquid” ground states are predicted. Our previous single-crystal neutron scattering study instead classified it as a “kinetically inhibited” antiferromagnet, where the long-ranged correlations of a collinear Néel ground state are blocked by the freezing of domain-wall motion below a first-order phase transition at $T^{*}=6.5$ K. This paper provides new data sets from a number of experiments, which support and expand this work in several important ways. We show that the phenomenology leading to the kinetically inhibited order is unaffected by sample measured and instrument resolution, while new low-temperature measurements reveal spin correlations are unchanging between $T=2$ K and 250 mK, consistent with a frozen state. Polarized diffuse neutron measurements show several interesting magnetic features, which can be entirely explained by the existence of short-ranged Néel order. Finally, and crucially, this paper presents some neutron scattering studies of single crystalline ${\mathrm{MnAl}}_2{\mathrm{O}}_4$, which acts as an unfrustrated analog to ${\mathrm{CoAl}}_2{\mathrm{O}}_4$ and shows all the hallmarks of a classical antiferromagnet with a continuous phase transition to Néel order at $T_N=39$ K. Direct comparison between the two compounds indicates that ${\mathrm{CoAl}}_2{\mathrm{O}}_4$ is unique, not in the nature of high-temperature diffuse correlations, but rather in the nature of the frozen state below $T^{*}$. The higher level of cation inversion in the ${\mathrm{MnAl}}_2{\mathrm{O}}_4$ sample indicates that this behavior is primarily an effect of greater next-nearest-neighbor exchange.

Within the hierarchical quantum master equation (HQME) framework, an approach is presented, which allows a numerically exact description of nonequilibrium charge transport in nanosystems with strong electronic-vibrational coupling. The method is applied to a generic model of vibrationally coupled transport considering a broad spectrum of parameters ranging from the nonadiabatic to the adiabatic regime and including both resonant and off-resonant transport. We show that nonequilibrium effects are important in all these regimes. In particular, in the off-resonant transport regime, the inelastic cotunneling signal is analyzed for a vibrational mode in full nonequilibrium, revealing a complex interplay of different transport processes and deviations from the commonly used $G_0/2$ rule of thumb. In addition, the HQME approach is used to benchmark approximate master equation and nonequilibrium Green's function methods.