Electrical Control of the Zeeman Spin Splitting in Two-Dimensional Hole Systems.

Semiconductor holes with strong spin-orbit coupling allow all-electrical spin control, with broad applications ranging from spintronics to quantum computation. Using a two-dimensional hole system in a gallium arsenide quantum well, we demonstrate a new mechanism of electrically controlling the Zeeman splitting, which is achieved through altering the hole wave vector k. We find a threefold enhancement of the in-plane g-factor g_{∥}(k). We introduce a new method for quantifying the Zeeman splitting from magnetoresistance measurements, since the conventional tilted field approach fails for two-dimensional systems with strong spin-orbit coupling. Finally, we show that the Rashba spin-orbit interaction suppresses the in-plane Zeeman interaction at low magnetic fields. The ability to control the Zeeman splitting with electric fields opens up new possibilities for future quantum spin-based devices, manipulating non-Abelian geometric phases, and realizing Majorana systems in p-type superconductor systems.

Bound States of Skyrmions and Merons near the Lifshitz Point.

We study topological defects in anisotropic ferromagnets with competing interactions near the Lifshitz point. We show that Skyrmions and bimerons are stable in a large part of the phase diagram. We calculate Skyrmion-Skyrmion and meron-meron interactions and show that Skyrmions attract each other and form ring-shaped bound states in a zero magnetic field. At the Lifshitz point merons carrying a fractional topological charge become deconfined. These results imply that unusual topological excitations may exist in weakly frustrated magnets with conventional crystal lattices.

Mechanisms for Strong Anisotropy of In-Plane g-Factors in Hole Based Quantum Point Contacts.

In-plane hole g factors measured in quantum point contacts based on p-type heterostructures strongly depend on the orientation of the magnetic field with respect to the electric current. This effect, first reported a decade ago and confirmed in a number of publications, has remained an open problem. In this work, we present systematic experimental studies to disentangle different mechanisms contributing to the effect and develop the theory which describes it successfully. We show that there is a new mechanism for the anisotropy related to the existence of an additional B_{+}k_{-}^{4}σ_{+} effective Zeeman interaction for holes, which is kinematically different from the standard single Zeeman term B_{-}k_{-}^{2}σ_{+} considered until now.

Detection and Control of Spin-Orbit Interactions in a GaAs Hole Quantum Point Contact.

We investigate the relationship between the Zeeman interaction and the inversion-asymmetry-induced spin-orbit interactions (Rashba and Dresselhaus SOIs) in GaAs hole quantum point contacts. The presence of a strong SOI results in the crossing and anticrossing of adjacent spin-split hole subbands in a magnetic field. We demonstrate theoretically and experimentally that the anticrossing energy gap depends on the interplay between the SOI terms and the highly anisotropic hole g tensor and that this interplay can be tuned by selecting the crystal axis along which the current and magnetic field are aligned. Our results constitute the independent detection and control of the Dresselhaus and Rashba SOIs in hole systems, which could be of importance for spintronics and quantum information applications.

The amplitudes and the structure of the charge density wave in YBCO.

We find unknown s- and d-wave amplitudes of the recently discovered charge density wave (CDW) in underdoped cuprates. To do so we perform a combined analysis of experimental data for ortho-II YBa2Cu3Oy. The analysis includes data on nuclear magnetic resonance, resonant inelastic X-ray scattering, and hard X-ray diffraction. The amplitude of doping modulation found in our analysis is 3.5 · 10-3 in a low magnetic field and T = 60 K, the amplitude is 6.5 · 10-3 in a magnetic field of 30T and T = 1.3 K. The values are in units of elementary charge per unit cell of a CuO2 plane. We show that the data rule out a checkerboard pattern, and we also show that the data might rule out mechanisms of the CDW which do not include phonons.

Violation of the spin-statistics theorem and the bose-einstein condensation of particles with half-integer spin.

We consider the Bose condensation of bosonic particles with spin 1/2. The condensation is driven by an external magnetic field. Our work is motivated by ideas of quantum critical deconfinement and bosonic spinons in spin liquid states. We show that both the nature of the novel Bose condensate and the excitation spectrum are fundamentally different from that in the usual integer spin case. We predict two massive ("Higgs") excitations and two massless Goldstone excitations. One of the Goldstone excitations has a linear excitation spectrum and another has a quadratic spectrum. This implies that the Bose condensate does not support superfluidity, the Landau criterion is essentially violated. We formulate a "smoking gun" criterion for searches of the novel Bose condensation.

Topological insulating states in laterally patterned ordinary semiconductors.

We propose that ordinary semiconductors with large spin-orbit coupling, such as GaAs, can host stable, robust, and tunable topological states in the presence of quantum confinement and superimposed potentials with hexagonal symmetry. We show that the electronic gaps which support chiral spin edge states can be as large as the electronic bandwidth in the heterostructure miniband. The existing lithographic technology can produce a topological insulator operating at a temperature of 10-100 K. Improvement of lithographic techniques will open the way to a tunable room temperature topological insulator.

Quantum chaos and fluctuations in isolated nuclear-spin systems.

Using numerical simulations we investigate dynamical quantum chaos in isolated nuclear spin systems. We determine the structure of quantum states, investigate the validity of the Curie law for magnetic susceptibility and find the spectrum of magnetic noise. The spectrum is the same for positive and negative temperatures. The study is motivated by recent interest in condensed-matter experiments for searches of fundamental parity- and time-reversal-invariance violations. In these experiments nuclear spins are cooled down to microkelvin temperatures and are completely decoupled from their surroundings. A limitation on statistical sensitivity of the experiments arises from the magnetic noise.

Symmetry breaking in the collinear phase of the J1-J2 Heisenberg model.

The large J2 limit of the square-lattice J1-J2 Heisenberg antiferromagnet is a classic example of order by disorder where quantum fluctuations select a collinear ground state. Here, we use series expansion methods and a mean-field spin-wave theory to study the excitation spectra in this phase and look for a finite-temperature Ising-like transition, corresponding to a broken symmetry of the square lattice, as first proposed by Chandra et al. [Phys. Rev. Lett. 64, 88 (1990)]]. We find that the spectra reveal the symmetries of the ordered phase. However, we do not find evidence for a finite-T transition. We suggest a scenario for a T=0 transition based on quantum fluctuations.

Radiative corrections and parity nonconservation in heavy atoms.

The self-energy and the vertex radiative corrections to the effect of parity nonconservation in heavy atoms are calculated analytically in orders Zalpha2 and Z2alpha3ln((lambda(C)/r(0)), where lambda(C) and r(0) are the Compton wavelength and the nuclear radius, respectively. The sum of the radiative corrections is -0.85% for Cs and -1.41% for Tl. Using these results, we have performed analysis of the experimental data on atomic parity nonconservation. The values obtained for the nuclear weak charge, Q(W)=-72.90(28)exp(35)theor for Cs, and Q(W)=-116.7(1.2)exp(3.4)(theor) for Tl, agree with predictions of the standard model. As an application of our approach, we have also calculated analytically the dependence of the Lamb shift on the finite size of the nucleus.

Two-dimensional randomly frustrated spin-1/2 Heisenberg model.

We investigate the properties of S = 1/2 Heisenberg clusters with random frustration using exact diagonalizations. This is a model for a quantum spin glass. We show that the average ground state spin is S proportional to the square root of N, where N is the number of sites. We also calculate the magnetic susceptibility and the spin stiffness and low-energy excitations and discuss these in terms of a semiclassical picture.