Parity Conservation Research Articles

Suppressing quasiparticle poisoning with a voltage-controlled filter

Topological quantum computation requires parity conservation of the bound states in the extended superconducting networks in which nonequilibrium quasiparticles are often observed. Here, the authors demonstrate that a section of a nanowire with epitaxial aluminum and hard superconducting gap can prevent the quasiparticle tunneling between the two gapless regions. Such a quasiparticle filter can be used to prevent spreading of nonequilibrium quasiparticles to regions of the device that need to have conserved parity.

Constraining graviton non-Gaussianity through the CMB bispectra

Tensor non-Gaussianities are a key ingredient to test the symmetries and the presence of higher spin fields during the inflationary epoch. Indeed, the shape of the three point correlator of the graviton is totally fixed by the symmetries of the de Sitter stage and, in the case of parity conservation, gets contributions only from the ordinary gravity action plus a higher derivative term called the (Weyl)$^3$ action. We discuss current and future bounds on the three point tensor contribution from the (Weyl)$^3$ term using cosmic microwave background (CMB) bispectra. Our results indicate that forthcoming experiments, such as LiteBIRD, CMB-S4 and CORE, will detect the presence of the (Weyl)$^3$ term if $M_p^4 L^4 \sim 10^{17} r^{-4}$, where $L$ parametrizes the strength of the (Weyl)$^3$ term and $r$ is the tensor-to-scalar ratio, which corresponds to $L\gtrsim 3.2 \times 10^5 M_p^{-1}$, while the current upper limit is $M_p^4 L^4 = (1.1 \pm 4.0) \times 10^{19} r^{-4}$ (68%CL).

Synthetic Weyl Points and Chiral Anomaly in Majorana Devices with Nonstandard Andreev-Bound-State Spectra.

We demonstrate how to design various nonstandard types of Andreev-bound-state (ABS) dispersions, via a composite construction relying on Majorana bound states (MBSs). Here, the MBSs appear at the interface of a Josephson junction consisting of two topological superconductors (TSCs). Each TSC harbors multiple MBSs per edge by virtue of a chiral or unitary symmetry. We find that, while the ABS dispersions are 2π periodic, they still contain multiple crossings which are protected by the conservation of fermion parity. A single junction with four interface MBSs and all MBS couplings fully controllable, or networks of such coupled junctions with partial coupling tunability, open the door for topological band structures with Weyl points or nodes in synthetic dimensions, which in turn allow for fermion-parity (FP) pumping with a cycle set by the ABS-dispersion details. In fact, in the case of nodes, the FP pumping is a manifestation of chiral anomaly in 2D synthetic spacetime. The possible experimental demonstration of ABS engineering in these devices further promises to unveil new paths for the detection of MBSs and higher-dimensional chiral anomaly.

Superadiabatic generation of cat states in bosonic Josephson junctions under particle losses

We investigate a superadiabatic scheme to produce a cat state in a bosonic Josephson junction in absence and presence of particle losses. The generation scheme is based on shortcuts to adiabaticity and strongly relies on the parity conservation. The parity conservation also ensures that the produced state is a superposition of cat states with various sizes, i.e., a "cats state". Parity is also the quantity to be measured in order to utilize the produced state in interferometry. The generation scheme still works even if a number of particle losses during generation are substantial.

Asymmetric dark matter, inflation, and leptogenesis from B−L symmetry breaking

We propose a unified setup for dark matter, inflation and baryon asymmetry generation through the neutrino mass seesaw mechanism. Our scenario emerges naturally from an extended gauge group containing $B-L$ as a non-commutative symmetry, broken by a singlet scalar that also drives inflation. Its decays reheat the universe, producing the lightest right-handed neutrino. Automatic matter parity conservation leads to the stability of an asymmetric dark matter candidate, directly linked to the matter-antimatter asymmetry in the universe.

Stability of entanglement-spectrum crossing in quench dynamics of one-dimensional gapped free-fermion systems

In a recent work by Gong and Ueda (arXiv:1710.05289), the classification of (1+1)-dimensional quench dynamics for the ten Altland-Zirnbauer classes is achieved, and entanglement-spectrum crossings of the time-dependent states for the topological classes (AIII, DIII, CII, BDI, and D) are discovered as a consequence of the bulk-edge correspondence. We note that, their classification scheme relies on the limit that the energy spectrum of the post-quench Hamiltonian is flat, because any finite band dispersion leads to the break down of time-reversal and chiral symmetries for the parent Hamiltonian (which are used for the classification). We show that, because of the reduction of symmetry by finite energy dispersion, the gapless entanglement-spectrum crossing in the flat-band limit in classes AIII, DIII, and CII is unstable, and could be gapped without closing the bulk gap. The entanglement-spectrum crossing in classes BDI and D is still stable against energy dispersion. We show that the quench process for classes BDI and D can be understood as a $\mathbb{Z}_2$ fermion parity pump, and the entanglement-spectrum crossing for this case is protected by the conservation of fermion parity.

Universality classes of absorbing phase transitions in generic branching-annihilating particle systems with nearest-neighbor bias.

We study absorbing phase transitions in systems of branching annihilating random walkers and pair contact process with diffusion on a one-dimensional ring, where the walkers hop to their nearest neighbor with a bias ε. For ε=0, three universality classes-directed percolation (DP), parity-conserving (PC), and pair contact process with diffusion (PCPD)-are typically observed in such systems. We find that the introduction of ε does not change the DP universality class but alters the other two universality classes. For nonzero ε, the PCPD class crosses over to DP, and the PC class changes to a new universality class.

From one-dimensional charge conserving superconductors to the gapless Haldane phase

We develop a framework to analyze one-dimensional topological superconductors with charge conservation. In particular, we consider models with $N$ flavors of fermions and $(\mathbb{Z}_2)^N$ symmetry, associated with the conservation of the fermionic parity of each flavor. For a single flavor, we recover the result that a distinct topological phase with exponentially localized zero modes does not exist due to absence of a gap to single particles in the bulk. For $N>1$, however, we show that the ends of the system can host low-energy, exponentially-localized modes. The analysis can readily be generalized to systems in other symmetry classes. To illustrate these ideas, we focus on lattice models with $SO\left(N\right)$ symmetric interactions, and study the phase transition between the trivial and the topological gapless phases using bosonization and a weak-coupling renormalization group analysis. As a concrete example, we study in detail the case of $N=3$. We show that in this case, the topologically non-trivial superconducting phase corresponds to a gapless analogue of the Haldane phase in spin-1 chains. In this phase, although the bulk is gapless to single particle excitations, the ends host spin-$1/2$ degrees of freedom which are exponentially localized and protected by the spin gap in the bulk. We obtain the full phase diagram of the model numerically, using density matrix renormalization group calculations. Within this model, we identify the self-dual line studied by Andrei and Destri [Nucl. Phys. B, 231(3), 445-480 (1984)], as a first-order transition line between the gapless Haldane phase and a trivial gapless phase. This allows us to identify the propagating spin-$1/2$ kinks in the Andrei-Destri model as the topological end-modes present at the domain walls between the two phases.

Geometric Josephson effects in chiral topological nanowires

One of the salient signatures of Majorana zero modes and topological superconductivity is a $4\pi$-periodic Josephson effect due to the combination of fermion parity conservation and the presence of a topologically protected odd number of zero energy crossings in the Andreev spectrum. In this paper, we study this effect in Josephson junctions composed of two semiconducting nanowires with Rashba spin-orbit coupling and induced superconductivity from the proximity effect. For certain orientations of the external magnetic field, such junctions possess a chiral symmetry and we show how this symmetry allows the Andreev spectrum and the protected crossings to be shifted by introducing a relative angle between the two wires. The junction then displays a geometrically induced anomalous Josephson effect, the flow of a supercurrent in the absence of external phase bias. Furthermore, we derive a proportionality relation between the local current density and the local curvature for a single curved wire. This result can be viewed as a one-dimensional analogue of the recently proposed geo-Josephson effect [Kvorning et al., arXiv:1709.00482]. Our two proposed effects can in principle be used as signatures of topological superconductivity in one dimension.

Equilibrium and real-time properties of the spin correlation function in the two-impurity Kondo model

We investigate the equilibrium and real-time properties of the spin correlation function $\langle \vec{S}_1\vec{S}_2 \rangle$ in the two-impurity Kondo model for different distances $R$ between the two-impurity spins. It is shown that the competition between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the Kondo effect governs the amplitude of $\langle \vec{S}_1\vec{S}_2 \rangle$. For distances $R$ exceeding the Kondo length scale, the Kondo effect also has a profound effect on the sign of the correlation function. For ferromagnetic Heisenberg couplings $J$ between the impurities and the conduction band, the Kondo effect is absent and the correlation function only decays for distances beyond a certain length scale introduced by finite temperature. The real-time dynamics after a sudden quench of the system reveals that correlations propagate through the conduction band with Fermi velocity. We identify two distinct timescales for the long time behavior which reflects that for small $J$ the system is driven by the RKKY interaction while for large $J$ the Kondo effect dominates. Interestingly, we find that at certain distances a one-dimensional dispersion obeying $\epsilon(k)=\epsilon(-k)$ may lead to a local parity conservation of the impurities such that $\langle \vec{S}_1\vec{S}_2 \rangle$ becomes a conserved quantity for long times and does not decay to its equilibrium value.

On-shell gauge invariant three-point amplitudes

Assuming locality, Lorentz invariance and parity conservation we obtain a set of differential equations governing the 3-point interactions of massless bosons, which in turn determines the polynomial ring of these amplitudes. We derive all possible 3-point interactions for tensor fields with polarisations that have total symmetry and mixed symmetry under permutations of Lorentz indices. Constraints on the existence of gauge-invariant cubic vertices for totally symmetric fields are obtained in general spacetime dimensions and are compared with existing results obtained in the covariant and light-cone approaches.Expressing our results in spinor helicity formalism we reproduce the perhaps mysterious mismatch between the covariant approach and the light cone approach in 4 dimensions. Our analysis also shows that there exists a mismatch, in the 3-point gauge invariant amplitudes corresponding to cubic self-interactions, between a scalar field ϕ and an antisymmetric rank-2 tensor field Aμν . Despite the well-known fact that in 4 dimensions rank-2 anti-symmetric fields are dual to scalar fields in free theories, such duality does not extend to interacting theories.

Realistic quantum critical point in one-dimensional two-impurity models

We show that the two-impurity Anderson model exhibits an additional quantum critical point at infinitely many specific distances between both impurities for an inversion symmetric one-dimensional dispersion. Unlike the quantum critical point previously established, it is robust against particle-hole or parity symmetry breaking. The quantum critical point separates a spin doublet from a spin singlet ground state and is, therefore, protected. A finite single-particle tunneling $t$ or an applied uniform gate voltage will drive the system across the quantum critical point. The discriminative magnetic properties of the different phases cause a jump in the spectral functions at low temperature, which might be useful for future spintronics devices. A local parity conservation will prevent the spin-spin correlation function from decaying to its equilibrium value after spin manipulations.

Persistent current and zero-energy Majorana modes in a p -wave disordered superconducting ring

We discuss the emergence of zero-energy Majorana modes in a disordered finite-length $p$-wave one-dimensional superconducting ring, pierced by a magnetic flux $\mathrm{\ensuremath{\Phi}}$ tuned at an appropriate value $\mathrm{\ensuremath{\Phi}}={\mathrm{\ensuremath{\Phi}}}_{*}$. In the absence of fermion parity conservation, we evidence the emergence of the Majorana modes by looking at the discontinuities in the persistent current $I[\mathrm{\ensuremath{\Phi}}]$ at $\mathrm{\ensuremath{\Phi}}={\mathrm{\ensuremath{\Phi}}}_{*}$. By monitoring the discontinuities in $I[\mathrm{\ensuremath{\Phi}}]$, we map out the region in parameter space characterized by the emergence of Majorana modes in the disordered ring.

Standard coupling unification in SO(10), hybrid seesaw neutrino mass and leptogenesis, dark matter, and proton lifetime predictions

We discuss gauge coupling unification of SU(3)C × SU(2)L × U(1)Y descending directly from non-supersymmetric SO(10) while providing solutions to the three out-standing problems of the standard model: neutrino masses, dark matter, and the baryon asymmetry of the universe. Conservation of matter parity as gauged discrete symmetry for the stability and identification of dark matter in the model calls for high-scale spontaneous symmetry breaking through 126H Higgs representation. This naturally leads to the hybrid seesaw formula for neutrino masses mediated by heavy scalar triplet and right-handed neutrinos. Being quadratic in the Majorana coupling, the seesaw formula predicts two distinct patterns of right-handed neutrino masses, one hierarchical and another not so hierarchical (or compact), when fitted with the neutrino oscillation data. Predictions of the baryon asymmetry via leptogenesis are investigated through the decays of both the patterns of RHν masses. A complete flavor analysis has been carried out to compute CP-asymmetries including washouts and solutions to Boltzmann equations have been utilised to predict the baryon asymmetry. The additional contribution to vertex correction mediated by the heavy left-handed triplet scalar is noted to contribute as dominantly as other Feynman diagrams. We have found successful predictions of the baryon asymmetry for both the patterns of right-handed neutrino masses. The SU(2)L triplet fermionic dark matter at the TeV scale carrying even matter parity is naturally embedded into the non-standard fermionic representation 45F of SO(10). In addition to the triplet scalar and the triplet fermion, the model needs a nonstandard color octet fermion of mass ∼ 5 × 107 GeV to achieve precision gauge coupling unification at the GUT mass scale MU0 = 1015.56 GeV. Threshold corrections due to superheavy components of 126H and other representations are estimated and found to be substantial. It is noted that the proton life time predicted by the model is accessible to the ongoing and planned experiments over a wide range of parameter space.

New G -parity violating amplitude in the J/ψ decay?

The $J/\psi$ meson has negative $G$-parity so that, in the limit of isospin conservation, its decay into $\pi^+\pi^-$ should be purely electromagnetic. However, the measured branching fraction $\mathcal{B}(J/\psi\to\pi^+\pi^-)$ exceeds by more than 3.9 standard deviations the expectation computed according to BaBar data on the $e^+e^-\to\pi^+\pi^-$ cross section. The possibility that the two-gluon plus one-photon decay mechanism is not suppressed by $G$-parity conservation is discussed, even by considering other multi-pion decay channels. As also obtained by phenomenological computation, such a decay mechanism could be responsible for the observed discrepancy. Finally, we notice that the BESIII experiment, having the potential to perform an accurate measurement of the $e^+e^-\to\pi^+\pi^-$ cross section in the 3 GeV energy region, can definitely prove or disprove this strong $G$-parity-violating mechanism by confirming or confuting the BaBar data.

Longitudinal asymmetry and proton spin rotation in p⃗d scattering with pionless effective field theory

The energy dependence of the longitudinal asymmetry $({A}_{L})$ and the spin rotation of the proton on the deuterium target in the $\stackrel{P\vec}{p}d$ scattering are presented using the pionless effective field theory formalism. The strong, weak, and Coulomb interactions have been introduced in the $\stackrel{P\vec}{p}d$ scattering. We have shown that in the presence of Coulomb interaction, the parity-conserving (PC) and the parity-violating (PV) sectors are modified. The PV two-body transitions diagrams have been evaluated with the inclusion of Coulomb interaction and consequently the PV observables are enhanced. The leading-order values of the ${A}_{L}$ and the spin rotation of the proton on the deuterium target are calculated at the proton laboratory energies above 0.7 MeV, in order to calculate the Coulomb effect perturbatively, up to 3 MeV where typical momenta is $Q\ensuremath{\ll}{m}_{\ensuremath{\pi}}$. With the lack of experimental data for the low-energy coupling constants (LECs), we have used two estimated sets for the five independent (PV) LECs of the weak $NN$ PV Lagrangian. The order of magnitude, of the PV observables with these two sets, is found to be ${10}^{\ensuremath{-}6}$ to ${10}^{\ensuremath{-}7}$ which indicates that the expected order is achieved in this energy range. The cutoff independent results support the validity of our approach.

Dipole Spin Polarizabilities and Gyrations of Spin-One Particles in the Duffin–Kemmer–Petiau Formalism

In this paper relativistic-invariant phenomenological Lagrangians of interaction between spin-1 particles and electromagnetic field were obtained in the Duffin-Kemmer-Petiau formalism on the basis of the covariant model that takes into account both spin polarizabilities and gyrations of the above-mentioned particles. It was shown that in the suggested covariant model with regard to the crossing symmetry, spatial parity and gauge invariance conservation laws, definite spin polarizabilities and gyrations of spin-1 particles contribute to the expansion of Compton scattering amplitude, starting from the corresponding orders on energy of pfotons that is in the agreement with low-energy theorems for that process.

Production ofJ/ψ+χcandJ/ψ+J/ψwith real gluon emission at the LHC

In the present work we study production of $J/\psi + \chi_c$ and $J/\psi + J/\psi$ in LHC. The first process is forbidden at the leading order in gluon fusion due to the $C$-parity conservation, and the first non-vanishing contribution is given by the process with additional emission of real gluon. Considering the direct production of $J/\psi + J/\psi$, where the leading order is allowed, we have found that the contribution from the higher order process with real gluon emission is comparable and even more significant than the leading order. Moreover, account of this higher order effect dramatically changes kinematical distributions. Through the present paper we study in details different channels of paired $J/\psi + J/\psi$ production: direct $J/\psi + J/\psi$ production, feed-down from $J/\psi + \chi_c$ channel, double parton scattering. We also try to find kinematical distributions that are most suitable to separate these different channels.

Revisiting on-shell renormalization conditions in theories with flavor mixing

In this review, we present a derivation of the on-shell renormalization conditions for scalar and fermionic fields in theories with and without parity conservation. We also discuss the specifics of Majorana fermions. Our approach only assumes a canonical form for the renormalized propagators and exploits the fact that the inverse propagators are nonsingular in [Formula: see text], where [Formula: see text] is the external four-momentum and [Formula: see text] is a pole mass. In this way, we obtain full agreement with commonly used on-shell conditions. We also discuss how they are implemented in renormalization.

Probing Fractional Josephson Junction with a Quantum Dot

We consider theoretically a junction between two topological superconducting wires, mediated by a quantum dot. The wires are modelled by the Kitaev chains tuned into topological phase, which possess unpaired Majorana states at their ends. We derive the low energy Hamiltonian of the model. The Majorana states closer to the dot convert into the Dirac fermion inside the dot, forming fractional Josephson junction. The dot is additionally weakly coupled to the normal tunneling probe allowing transport measurement through the dot. When the topological wires are short, the unpaired Majorana end-states can hybridize inside the wire forming an extended Dirac fermionic state. It yields the destruction of the extended state in the dot. We discuss the dependence of the spectral density of the dot and its conductance on superconducting phase. We show that the conservation of parity of the junction, crucial for successful measurement of the fractional effect, can be assured by the gate voltage manipulation of the dot level position and that in case of an unpaired Majorana state in the junction a half conductance quantum can be observed.