Wavefunction Topology of Two-dimensional Time-Reversal Symmetric Superconductors

We discuss the topology of the wavefunctions of two-dimensional time-reversal symmetric superconductors. We consider (a) the planar state, (b) a system with broken up-down reflection symmetry, and (c) a system with general spin-orbit interaction. We show explicitly how the relative sign of the order parameter on the two Fermi surfaces determines this topology, and clarify the meaning of the Z ₂ classification for these topological states.     

Experimental determination of the symmetry of the order parameter in YBCO

At present, the symmetry of the order parameter in the high temperature superconductor YBCO is quite controversial. Recent experiments using SQUIDs and Josephson junctions appear to support competing theories, with some experiments supporting a d_x2_–y2 pairing symmetry for the order parameter and others a s-wave pairing symmetry. We note that a number of factors such as trapped flux, magnetic field gradients and SQUID asymmetries could lead such measurements astray. We use a Scanning SQUID Microscope and a time-reversal invariance test to resolve these experimental problems. We find the order parameter in YBCO has a time-reversal invariant d_x2–_y2 symmetric component. We estimate the amplitude of anyimaginary s-wave symmetric component to be less than 4% and anyreal s-wave component to be less than 82%.     

Ground-State Properties of Electron-Electron Quantum Bilayers

The ground-state behavior of electron-electron quantum bilayer systems within the neutralizing background and zero magnetic field is studied by including unequal density of layers. The quantum self-consistent mean-field approximation of Singwi, Tosi, Land and Sjölander (qSTLS) is used to study the intra- and inter layer properties, such as the static pair-correlation functions, the static structure factors, the static density susceptibility and the static local-field correction factors over a wide range of layer density parameter r _s?? and layer spacing d. We find that the inclusion of unequal density brings a phase transition from charge density wave (CDW) to coupled Wigner crystal (WC) ground state at the close proximity of the layers. We also find that inclusion of unequal density markedly reduce critical r _s?? for the onset of Wigner crystallization. The results are compared with recent findings of the equal density effects in electron-electron quantum bilayer systems.     

Estimating Bounds on Collisional Relaxation Rates of Spin-Polarized 87Rb Atoms at Ultracold Temperatures

We present quantum scattering calculations for the collisional relaxation rate coefficient of spin-polarized ⁸⁷Rb(f = 2,m = 2) atoms, which determines the loss rate of cold Rb atoms from a magnetic trap. Unlike the lighter alkali atoms, spin-polarized ⁸⁷Rb atoms can undergo dipolar relaxation due to both the normal spin-spin dipole interaction and a second-order spin-orbit interaction with distant electronic states of the dimer. We present ab initio calculations for the second-order spin-orbit terms for both Rb₂ and Cs₂. The corrections lead to a reduction in the relaxation rate for ⁸⁷Rb. Our primary concern is to analyze the sensitivity of the ⁸⁷Rb trap loss to the uncertainties in the ground state molecular potentials. Since the scattering length for the a³Σ⁺_u state is already known, the major uncertainties are associated with the X¹Σ⁺_g potential. After testing the effect of systematically modifying the short-range form of the molecular potentials over a reasonable range, and introducing our best estimate of the second-order spin-orbit interaction, we estimate that in the low temperature limit the rate coefficient for loss of Rb atoms from the f = 2,m = 2 state is between 0.4 × 10⁻¹⁵ cm³/s and 2.4 × 10⁻¹⁵ cm³/s (where this number counts two atoms lost per collision). In a pure condensate the rate coefficient would be reduced by 1/2.     

Is the Roton in Superfluid 4He the Ghost of a Bragg Spot?

It has always been assumed that the roton in ⁴He had to do with local vorticity—hence the name! We present here an alternate view: the roton is viewed as a “soft mode”, precursor of a crystallization instability. In such a picture the liquid is “nearly solid”, and the long observed similarities of heat propagation in liquid and solid phases are naturally explained. In this qualitative paper we consider three models successively. A lattice gas with one atom per site displays a Mott localization transition, as shown by the Bangalore group. The important result is the vanishing of the superfluid order parameter (condensate fraction N _o) at the transition. There is no breakdown of translational symmetry and consequently no soft mode. Another lattice model with half filling, with an added nearest neighbour repulsion, was studied by Matsubara and Matsuda in the early 1950s it displays a first order transition between a superfluid and a localized charge density wave state. The excitation spectrum has a soft mode at zone edge near the transition, signalling the proximity of the CDW instability. Finally, we consider the realistic situation of a continuous system with no preexisting lattice. We approach the problem from the limit N _o = 0 instead of the ideal gas N _o = N. When N _o = 0 the quasiparticle spectrum and the charge density spectrum are decoupled. The latter should have a soft mode ω=ω_m if crystallization is close. That soft mode is a normal state property that has nothing to do with superfluidity. A small N _o acts to hybridize quasiparticles and density fluctuations: the resulting anticrossing lowers ω_m ² as well as the ground state energy. We show that N _o is bounded for two reasons: (i) if ω _m ² turns negative, the liquid is unstable towards freezing (ii) depletion due to quantum fluctuation exceeds N _o if the latter is too large. The resulting upper bound noindent for N/N _{o is} ? 1, a consequence of the deep roton minimum. The whole paper is qualitative, based on outrageous simplifications in order to make algebra tractable.     

Ground state cooling,quantum state engineering and study of decoherence of ions in Paul traps

Abstract

We investigate single ions of ⁴⁰Ca⁺ in Paul traps for quantum information processing. Superpositions of the S_½ electronic ground state and the metastable D_5/2; state are used to implement a qubit. Laser light on the S_½ ? D_5/2 transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state (n = 0), we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190ms. We also report on ground state cooling of two ions.     

Spin-orbit coupling induced interference in quantum corrals

Lack of inversion symmetry at a metallic surface can lead to an observable spin-orbit interaction. For certain metal surfaces, such as the Au(111) surface, the experimentally observed spin-orbit coupling results in spin rotation lengths on the order of tens of nanometers, which is the typical length scale associated with quantum corral structures formed on metal surfaces. In this work, multiple scattering theory is used to calculate the local density of states (LDOS) of quantum corral structures composed of nonmagnetic adatoms in the presence of spin-orbit coupling. Contrary to previous theoretical predictions, spin-orbit coupling induced modulations are observed in the theoretical LDOS, which should be observable using scanning tunneling microscopy.     

First-Principles Investigation of Electronic Structure Features of TbOFeAs Compound

We report a theoretical investigation on the electronic and magnetic properties of rare-earth pnictide parent compound, such as TbOFeAs. Employing first-principles method supplemented by the local spin density approximation (LSDA), we discuss the electronic structure with the incorporation of the role of Coulomb on-site repulsion (U) of Tb 4f states as well as the spin-orbit (SO) coupling on the magnetic and nonmagnetic phases. For ferromagnetic (FM) and antiferromagnetic (AFM) phases, we have determined the spin and orbital magnetic moments of Tb ions and confer the significance of the spin-orbit interaction of Tb 4f states in this parent compound. In the FM state, the reduction of Fe moment is about a factor of 3.5 with respect to AFM configuration. The most energetically favorable state is AFM configuration. Our theoretical findings surmise that the magnetic moments on Fe sites carry an AFM order. Based on LSDA + U + SO approximation, we infer that the Tb magnetic moments also carry an AFM order, albeit the spin Tb sites in TbO layer possess the same orientation as the Fe spins in FeAs layer. With the incorporation of on-site Coulomb repulsion and spin-orbit interaction in AFM state, the Fe 3d states are large near the Fermi level and this phase is illustrating a metallic behavior. Moreover, the Fermi surface topology and nesting features are presented.     

Fundamentals and applications of isotope effect in solids

Over the last five decades, the isotope effect in solids has been one of the major researches in solid state science. Most of the physical properties of a solid depend to a greater or lesser degree on its isotopic composition. Scientific interest, technological promise and increased availability of highly enriched isotopes have led to a sharp rise in the number of experimental and theoretical studies with isotopically controlled semiconductor and insulator crystals. A great number of stable isotopes and well-developed methods of their separation have made it possible to date to grow crystals of C, LiH, ZnO, ZnSe, CuCl, GaN, GaAs, CdS, Cu₂O, Si, Ge and α-Sn with a controllable isotopic composition. The use of such objects allows the investigation of not only the isotope effects in lattice dynamics (elastic, thermal and vibrational properties) but also the influence of such effects on the electronic states via electron-phonon coupling (the renormalization of the band-to-band transition energy E_g, the exciton binding energy E_b and the size of the longitudinal-transverse splitting Δ_LT). Capture of thermal neutrons by isotope nuclei followed by nuclear decay produces new elements, resulting in a large number of possibilities for isotope selective doping of solids used in opto-, quantum electronics, fiber optics, etc. The nonlinear dependence of the free exciton luminescence (especially ¹²C_x¹³C_1−x, LiH_xD_1−x) intensity on the excitation density allows us to consider these crystals as potential solid state lasers in the UV part of the spectrum. Isotopic information storage may consist in assigning the information “zero” or “one” to mono-isotopic microislands (or even to a single atom) within a bulk crystalline (or thin film) structure. Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. It shows how the use of quantum physics could revolutionize the way of communication and process information. Although modern computers rely on quantum mechanics to operate, the information itself is still encoded classically. A new approach is to treat information as a quantum concept and to ask what new insights can be gained by encoding this information in an individual quantum system. Isotope information storage and isotope quantum computers are briefly discussed. The review concludes with an outline of the main features of isotope physics in solids, and avenues for future research and applications.     

Microscopic structural evolution in terms of porosity in high-Tc superconductors

The low critical current densities of high-Tc superconductors materials can be related to the microstructural imperfections such as pores and microcracks, which reduce the effective current carrying cross section. The present work examines the characterisation of the state of microstructure and its evolution during thermal treatment of Bi₂Sr₂Ca₁Cu₂O₈. The dilatometric analysis was used to study the shrinkage mechanism during sintering. The microstructure of the sintered samples was characterised in terms of pores distribution and apparent density. Open porosity was measured by mercury porosimeter. In order to compare the results, ultrasonic characterisation such as the longitudinal and transverse wave velocities in the ceramic was carried out. From an ultrasonic point of view, these microstructural features act as inhomogeneities and the ultrasonic parameters will depend on the geometrical arrangement of microstructure (pores have an effect both on Young’s modulus and attenuation).     

Non-classicality of photon-added-then-subtracted and photon-subtracted-then-added states

We formulate the density matrices of a quantum state obtained by first adding multi-photons to and then subtracting multi-photons from any arbitrary state as well as performing the same process in the reverse order. Considering the field to be initially in a thermal (or in an even coherent) state, we evaluate the photon number distribution, Wigner function and Mandel's Q parameter of the resulting field. We show graphically that the order in which multi-photons are added and subtracted has a noticeable effect on the temporal behavior of these statistical properties.     

Magnetic Correlation in BETS2(Cl2TCNQ)

We carried out⁷⁷Se NMR measurements on BETS₂(Cl₂TCNQ) under pressure in order to investigate the magnetic properties of the insulating state which appears above 0.6 GPa. The relaxation rate 1/T₁ at 0.7 GPa shows small peak-like anomaly at 20 K, indicating a spin density wave transition as observed in BETS₂(Br₂TCNQ).     

Berry Phase and Topological Spin Transport in the Chiral d-Density Wave State

In this paper we demonstrate the possibility of dissipationless spin transport in the chiral d-density wave state, by the sole application of a uniform Zeeman field gradient. The occurrence of these spontaneous spin currents is attributed to the parity (℘) and time-reversal ( ) violation induced by the density wave order parameter. We calculate the spin Hall conductance and reveal its intimate relation to the Berry phase which is generated when the Zeeman field is applied adiabatically. Finally, we demonstrate that in the zero temperature and doping case, the spin Hall conductance is quantized as it becomes a topological invariant.      

Time Reversal for the Polarization State in Optical Systems

Abstract

The time-reversal operator for the polarization state can be successfully implemented in any optical system where a beam retraces its path. A Faraday rotator followed by a mirror realizes a device whose representative matrix is similar to the quantum mechanics time-reversal operator for the spin. Any effect of the medium birefringence is cancelled and, for linear polarization, the beam always returns opposite polarized with respect to the entrance state. Analogies with the operation of a phase-conjugation mirror are pointed out and suggested consequences of the novel optical configuration are given.     

Coexistence of Superconductivity and Spin Density Wave (SDW) in Ferropnictide Ba<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>K<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Fe<Subscript>2</Subscript>As<Subscript>2</Subscript>

This work focuses on the theoretical investigation of the coexistence of superconductivity and spin density wave (SDW) in ferropnictide Ba_1?x K _x Fe₂As₂. By developing a model Hamiltonian for the system and by using quantum field theory Green’s function formalism, we have obtained mathematical expressions for superconducting transition temperature (T _C), spin density wave transition temperature (T _sdw), superconductivity order parameter (Δ_Sc), and spin density wave order parameter (Δ_sdw). By employing the experimental and theoretical values of the parameters in the obtained expressions, phase diagrams of superconducting transition temperature (T _C) versus superconducting order parameter (Δ_Sc) and spin density wave transition temperature (T _sdw), versus spin density wave order parameter (Δ_sdw) have been plotted. By combining the two phase diagrams, we have demonstrated the possible coexistence of superconductivity and spin density wave (SDW) in ferropnictide Ba_1?x K _x Fe₂As₂.     

Study of Solid 4He in Two Dimensions

Defects are believed to play a fundamental role in the supersolid state of ⁴He. We report on studies by exact Quantum Monte Carlo (QMC) simulations at zero temperature of the properties of solid ⁴He in presence of many vacancies, up to 30 in two dimensions (2D). In all studied cases the crystalline order is stable at least as long as the concentration of vacancies is below?2.5?%. In the 2D system for a small number, n _v , of vacancies such defects can be identified in the crystalline lattice and are strongly correlated with an attractive interaction. On the contrary when n _v ?10 vacancies in the relaxed system disappear and in their place one finds dislocations and a revival of the Bose-Einstein condensation. Thus, should zero-point motion defects be present in solid ⁴He, such defects would be dislocations and not vacancies, at least in 2D. In order to avoid using periodic boundary conditions we have studied the exact ground state of solid ⁴He confined in a circular region by an external potential. We find that defects tend to be localized in an interfacial region of width of about 15 ?. Our computation allows to put as upper bound limit to zero-point defects the concentration 3×10^?3 in the 2D system close to melting density.     

Zero-Point Vacancies in Quantum Solids

A Jastrow wave function (JWF) and a shadow wave function (SWF) describe a quantum solid with Bose–Einstein condensate; i.e. a supersolid. It is known that both JWF and SWF describe a quantum solid with also a finite equilibrium concentration of vacancies x _v . We outline a route for estimating x _v by exploiting the existing formal equivalence between the absolute square of the ground state wave function and the Boltzmann weight of a classical solid. We compute x _v for the quantum solids described by JWF and SWF employing very accurate numerical techniques. For JWF we find a very small value for the zero point vacancy concentration, x _v =(1.4±0.1)×10^?6. For SWF, which presently gives the best variational energy of solid ⁴He, we find the significantly larger value x _v =(1.4±0.1)×10^?3 at a density close to melting. We also study two and three vacancies with SWF. We find that there is a strong short range attraction but the vacancies do not form a bound state, at variance with the exact finite temperature PIMC results.     

Emergence of Nontrivial Low-Energy Dirac Fermions in Antiferromagnetic EuCd2As2

Parity-time symmetry plays an essential role for the formation of Dirac states in Dirac semimetals. So far, all of the experimentally identified topologically nontrivial Dirac semimetals (DSMs) possess both parity and time reversal symmetry. The realization of magnetic topological DSMs remains a major issue in topological material research. Here, combining angle-resolved photoemission spectroscopy with density functional theory calculations, it is ascertained that band inversion induces a topologically nontrivial ground state in EuCd₂As₂. As a result, ideal magnetic Dirac fermions with simplest double cone structure near the Fermi level emerge in the antiferromagnetic (AFM) phase. The magnetic order breaks time reversal symmetry, but preserves inversion symmetry. The double degeneracy of the Dirac bands is protected by a combination of inversion, time-reversal, and an additional translation operation. Moreover, the calculations show that a deviation of the magnetic moments from the c-axis leads to the breaking of C3 rotation symmetry, and thus, a small bandgap opens at the Dirac point in the bulk. In this case, the system hosts a novel state containing three different types of topological insulator: axion insulator, AFM topological crystalline insulator (TCI), and higher order topological insulator. The results provide an enlarged platform for the quest of topological Dirac fermions in a magnetic system.     

Axial Phase of Quantum Fluids in Nanotubes

We explore the equations of state and other properties of various quantum fluids (³He, ⁴He, their mixtures, and H₂) confined within individual carbon nanotubes. Above a threshold number of particles, N _a, the fluid density near the axis begins to grow above a negligibly small value. The properties of this axial fluid phase are sensitive to the tube size and hence to the transverse compression in the case of a bundle of nanotubes. We consider He at zero temperature and H₂ at low temperatures.