Narrow Results

We have analyzed the mechanism of high T_c superconductivity from the viewpoint of chirality and Berry phase. It is observed that spin pairing and charge pairing is caused by a gauge force generated by magnetic flux quanta attached to them. Different phase structures associated with high T_c superconductivity have been studied from an analysis of the renormalization group equation involving the Berry phase factor μ. It is found that there are two crossovers above the superconducting temperature T_c, one corresponding to the glass phase and the other represents spin gap phase. However, the spin gap temperature is found to be dependent on T_c and shows a universal behaviour with respect to the hole doping δ/δ₀ with δ₀ being the optimal doping rate.

We use Lewis and Riesenfeld's quantum invariant theory to calculate the Lewis–Riesenfeld phases for a time-dependent frequency harmonic oscillator that is confined between a fixed boundary and a moving one. We also discuss the Berry phase for the system with a sinusoidally oscillating boundary.

We have studied here the charge and statistics of quasiparticle excitations in FQH states on the basis of the Berry phase approach incorporating the fact that even number of flux quanta can be gauged away when the Berry phase is removed to the dynamical phase. It is observed that the charge q and statistical parameter θ of a quasiparticle at filling factor ν = n/(2pn+1) are given by q = (n/2pn+1)e and θ = n/(2pn+1), with the fact that the charge of the quasihole is opposite to that of the quasielectron. Using Laughlin wave function for quasiparticles, numerical studies have been done following the work of Kjønsberg and Myrheim¹ for FQH states at ν = 1/3 and it is pointed out that as in case of quasiholes, the statistics parameter can be well defined for quasielectrons having the value θ = 1/3.

In this review article, we survey the relatively new theory of orbital magnetization in solids — often referred to as the "modern theory of orbital magnetization" — and its applications. Surprisingly, while the calculation of the orbital magnetization in finite systems such as atoms and molecules is straight forward, in extended systems or solids it has long eluded calculations owing to the fact that the position operator is ill-defined in such a context. Approaches that overcome this problem were first developed in 2005 and in the first part of this review we present the main ideas reaching from a Wannier function approach to semi-classical and finite-temperature formalisms. In the second part, we describe practical aspects of calculating the orbital magnetization, such as taking k-space derivatives, a formalism for pseudopotentials, a single k-point derivation, a Wannier interpolation scheme, and DFT specific aspects. We then show results of recent calculations on Fe, Co, and Ni. In the last part of this review, we focus on direct applications of the orbital magnetization. In particular, we will review how properties such as the nuclear magnetic resonance shielding tensor and the electron paramagnetic resonance g-tensor can be elegantly calculated in terms of a derivative of the orbital magnetization.

An extended electronic cloud can acquire different Aharonov–Bohm (AB) phases in its parts when these parts experience different solenoidal fields. This is demonstrated by two models that describe an electron moving within a confining circular tube around a solenoidal vector potential and outside a magnetic field domain (just as in a usual AB set up): one in which the motion of the electron along the tube is restricted and moves adiabatically and another in which it extends freely and without restriction on its speed. When the electron cloud is split into two parts circling in opposite directions, we show that when the two parts of the electronic cloud rejoin, they do so with different phases. This set-up complements (and confirms the finding of) our previous work [Europhys. Lett.93, 20001 (2011)], in which the vector source was moving and the electron position was fixed.

We show that topological frequency band structures emerge in one-dimensional (1D) electromagnetic (EM) lattices of metamaterial components without the application of an external magnetic field. Such lattices can be cavity arrays coupled with metamaterial elements which generate alternate positive and negative-phase hopping strengths. The topological nature of the band structure manifests itself by the occurrence of Dirac points in the band structure, by the emergence of edge modes in finite arrays as well as by a nonreciprocal scattering spectrum. Specific EM designs for demonstrating the above phenomena are discussed.

We consider two systems of wave equations whose wave packet solutions have trajectories that are altered by the “anomalous velocity” effect of a Berry curvature. The first is the matrix Weyl equation describing cyclotron motion of a charged massless fermion. The second is Maxwell equations for the whispering-gallery modes of light in a cylindrical waveguide. In the case of the massless fermion, the anomalous velocity is obscured by the contribution from the magnetic moment. In the whispering-gallery modes, the anomalous velocity causes the circumferential light ray to creep up the cylinder at the rate of one wavelength per orbit, and can be identified as a continuous version of the Imbert–Federov effect.

Within the framework of a simple model, we investigated the Berry phase of epitaxial graphene (EG) formed on a semiconductor substrate. We have shown that this value is equal to $\pi$ near the Dirac point. This result is in complete agreement with the experimental data. We have shown that the Berry phase of epitaxial graphene may differ from $\pi$ far away from Dirac point. In addition, we investigated the Landau levels (LLs) in the epitaxial graphene within the framework of the semiclassical approach.

In this paper, we employ the energy surface method to study a system of a two-level atom Bose–Einstein condensate coupled to a high-finesse optical cavity interacting with a single-mode electromagnetic field in the presence of the Stark-shift. The energy surface, the Phase transitions and the Berry phase of the two-level atom in Dicke model are obtained. Employing the Holstein–Primakoff representation of the angular momentum Lie algebra, the coupling line separation of the normal phase and the superradiant phase which occurs in a collection of fluorescent emitters (such as atoms), between a state containing few electromagnetic excitations are studied and a mean field description of the Dicke model is presented. We notice that in the thermodynamic limit, the energy surface takes a simple form for a direct description of the phase transition. Moreover, we show that the Stark-shift parameters and the atom–atom interactions can strongly affect the phase transition point. The results in the absence of the Stark-shift agree precisely with those obtained by Li, Liu and Zhou, who studied the same model using a different method.

Skyrmions are topological solitons that emerge in many physical contexts. In magnetism, they appear as textures of the spin-density field stabilized by different competing interactions and characterized by a topological charge that counts the number of times the order parameter wraps the sphere. They behave as classical objects when the spin texture varies slowly on the scale of the microscopic lattice of the magnet. However, the fast development of experimental tools to create and stabilize skyrmions in thin magnetic films has led to a rich variety of textures, sometimes of atomistic sizes. In this paper, we discuss, in a pedagogical manner, how to introduce quantum interference in the translational dynamics of skyrmion textures, starting from the micromagnetic equations of motion for a classical soliton. We study how the nontrivial topology of the spin texture manifests in the semiclassical regime, when the microscopic lattice potential is treated quantum-mechanically, but the external driving forces are taken as smooth classical perturbations. We highlight close relations to the fields of noncommutative quantum mechanics, Chern–Simons theories, and the quantum Hall effect.

Recent results on the semiclassical dynamics of an electron in a solid are explained using techniques developed for "exotic" Galilean dynamics. The system is indeed Hamiltonian and Liouville's theorem holds for the symplectic volume form. Suitably defined quantities satisfy hydrodynamic equations.

We apply the perturbation theory to investigate the behavior of the Berry phase of a composite system. The composite system consists of two weakly-coupled spin-½ particles, in which each particle is driven by a varying magnetic field. The result shows that the Berry phase for one subsystem is controlled by the state of the other subsystem. The method can also be used to deal with the effect of a spin environment on a single-particle system if the particle is weakly coupled to the spin environment.

We study shot noise for entangled electrons in a 4-lead beam-splitter with one incoming lead driven by adiabatically rotating magnetic fields. We propose a setup of an adiabatically rotating magnetic field which is appropriate for an electron beam to transport through. Using the scattering matrix approach, we find that shot noise for the singlet and that for the entangled triplet oscillates between bunching and antibunching due to the influence of the Berry phase. It provides us with a new approach for testing the Berry phase in electron transport on the basis of entanglement.

Starting with the interaction of interacting field and a two level atom we observe that the atom-interacting field system acquires a space parameter dependent Berry phase after the phase parameter slowly changes and ultimately returns to its initial form.

By calculating the Berry Phase (BP) of a central spin, the quantum criticality of the surrounding environment described by an XY spin chain with the three-site interaction in a transverse magnetic field is explored. The BP presents anomalous behavior along the critical region. The finite-size scaling behaviors suggest that the BP of the central spin can well capture the critical properties of the XY spin chain with the three-site interaction.

The application of geometric phases into robust control of quantal systems has triggered exploration of the geometric phase for coupled subsystems. Earlier studies have mainly focused on the situation where the external control parameters are in the free Hamiltonian of the subsystems, i.e. the controls exert only on the individual subsystems. Here we consider another circumstance that we can control the coupling ge^iϕ between the subsystems. By changing only the phase ϕ in the coupling constant, we derive the Berry phase acquired by the system and compare it to the geometric phase acquired by changing the coupling strength g. We find that the asymptotic behavior of the Berry phase depends on the relative Rabi frequency of the two subsystems, and it approaches π when the amplitude of the coupling tends to infinity.

Analytic formulas of Bell correlations are derived in terms of quantum probability statistics under the assumption of measuring outcome-independence and the Bell's inequalities (BIs) are extended to general bipartite-entanglement macroscopic quantum-states (MQS) of arbitrary spins. For a spin-½ entangled state we find analytically that the violations of BIs really resulted from the quantum nonlocal correlations. However, the BIs are always satisfied for the spin-1 entangled MQS. More generally the quantum nonlocality does not lead to the violation for the integer spins since the nonlocal interference effects cancel each other by the quantum statistical-average. Such a cancellation no longer exists for the half-integer spins due to the nontrivial Berry phase, and thus the violation of BIs is understood remarkably as an effect of geometric phase. Specifically, our generic observation of the spin-parity effect can be experimentally tested with the entangled photon-pairs.

We discuss the problem of the quantum particle behavior in an infinitely deep elliptical potential well with a moving boundary conditions. We show that this quantum system is equivalent to a particle interacting with a vector field. By introducing the squeezing transformations and making use of the removability of the topological term, the exact Berry phase in a cyclic evolution is calculated.

Bell’s inequalities (BIs) derived in terms of quantum probability statistics are extended to general bipartite-entangled states of arbitrary spins with parallel polarization. The original formula of Bell for the two-spin singlet is slightly modified in the parallel configuration, while the inequality formulated by Clauser–Horne–Shimony–Holt (CHSH) remains unchanged. The violation of BIs indeed resulted from the quantum nonlocal correlation for spin-$\frac{1}{2}$ case. However, the inequalities are always satisfied for the spin-1 entangled states regardless of parallel or antiparallel polarizations of two spins. The spin parity effect originally demonstrated with the antiparallel spin-polarizations (Z. Song, J.-Q. Liang and L.-F. Wei, Mod. Phys. Lett. B28 (2013) 145004) still exists for the parallel case. The quantum nonlocality does not lead to the violation for integer spins due to the cancellation of nonlocal interference effects by the quantum statistical average. Again, the violation of BIs seems to be a result of the measurement-induced nontrivial Berry phase (BP) for half-integer spins.

We present an S-matrix, a solution of the braid relation. A matrix representation of specialized Birman-Wenzl-Murakami algebra is obtained. Based on which, a unitary -matrix is generated via the Yang-Baxterization approach. Then we construct a Yang-Baxter Hamiltonian through the unitary -matrix. Berry phase of this Yang-Baxter system is investigated in detail.