Nonzero Momentum Research Articles

Toward the global fit of the TMD gluon density in the proton from the LHC data

We propose a new analytical expression for the transverse-momentum-dependent (TMD, or unintegrated) gluon density in the proton. Essential phenomenological parameters are extracted from the LHC data on inclusive hadron production in $pp$ collisions at low transverse momenta ${p}_{T}\ensuremath{\le}1\text{ }\text{ }\mathrm{GeV}$. The latter are described in the framework of a modified soft quark-gluon string model, where the gluonic state and nonzero transverse momentum of partons inside the proton are taken into account. To determine the parameters important at moderate and large $x$, we use the measurements of inclusive $b$-jet and Higgs boson production at the LHC as well as the latest HERA data on proton structure functions ${F}_{2}^{c}(x,{Q}^{2})$ and ${F}_{2}^{b}(x,{Q}^{2})$ and reduced cross sections ${\ensuremath{\sigma}}_{\mathrm{red}}^{c}(x,{Q}^{2})$ and ${\ensuremath{\sigma}}_{\mathrm{red}}^{b}(x,{Q}^{2})$. The Catani-Ciafaloni-Fiorani-Marchesini evolution equation is applied to extend the initial gluon distribution to the whole kinematical region. We achieve a simultaneous description of all considered processes with ${\ensuremath{\chi}}^{2}/\mathrm{d}.\mathrm{o}.\mathrm{f}.=2.2$, thus moving toward the global fit of the TMD gluon density from collider data. The obtained TMD gluon distribution in a proton is available for public usage and implemented in the tmdlib package and Monte Carlo event generator pegasus.

Interplay between extended s -wave symmetry of the gap and spin-orbit coupling in the low electron concentration regime of quasi-two-dimensional superconductors

We analyze the real-space paired state with the $\mathbf{k}$-dependent superconducting gap in the presence of Rashba type spin-orbit coupling and external magnetic field. We show that the $extended$ $s$-$wave$ pairing symmetry is the most probable scenario to appear in the low-electron concentration regime. According to our study, the van Hove singularity induced by the spin-orbit coupling may lead to a significant enhancement of the superconducting gap, critical temperature and critical magnetic field. Moreover, the combined effect of the spin-orbit coupling and the external magnetic field results in a non-zero total momentum of the Cooper pairs, which is a characteristic feature of the so-called helical state. In such situation, due to the C$_4$ symmetry breaking, a small $d$-$wave$ and $p$-$wave$ contributions to the pairing appear, which significantly change the character of the helical state. The obtained results are discussed in the context of the experimental data related with the unconventional superconducting features of the transition metal oxide interfaces as well as the recently reported supercurrent diode effect.

Rotating bi-electron in two-dimensional systems with mexican-hat single-electron energy dispersion

A number of novel two-dimensional materials and nanostructures demonstrate complex single-electron energy dispersion, which is called the mexican-hat dispersion. In this paper, we analyze interaction of a pair of electrons with such an energy dispersion. We show that relative motion of the electron pair is of a very peculiar character. For example, the real space trajectories corresponding to electron-electron scattering can have three reversal points, reversal points at non-zero radial momentum and other unusual features. Despite the repulsive Coulomb interaction, two electrons can be coupled forming a composite quasi-particle – the bi-electron. The bi-electron corresponds to excited states of the two-electron system. Because the bi-electron coupled states exist in continuum of extended (free) states of the electron pair, these states are quasi-resonant and have finite times of life. We found that rotating bi-electron is a long-living composite quasi-particle. The rotating bi-electrons can be in motion. For slowly moving bi-electrons, we have determined the kinetic energy and the effective mass. Due to strongly nonparabolic energy dispersion, the translational motion of the bi-electron is coupled to its internal motion. This results in effective masses dependent on quantum states of the bi-electron. In the paper, properties of the bi-electron have been illustrated for the example of bigraphene in a transverse electric field. We have suggested that investigation of rotating bi-electrons at the mexican-hat single-electron energy dispersion may bring new interesting effects in low-dimensional and low-temperature physics.

Analytic expansions of multi-hadron finite-volume energies. I. Two-particle states

We derive analytic expansions for the finite-volume energies of weakly-interacting two-particle systems, using the general relations between scattering amplitudes and energies derived by Lüscher and others. The relations hold for ground and excited states with both zero and non-zero total momentum in the finite-volume frame. A number of instructive aspects arise in the derivation, including the role of accidental degeneracies and the importance of defining a power-counting scheme in the expansions. The results give intuition concerning the imprint of perturbative interactions on the energy spectrum, while also providing a useful basis for the analogous results concerning three-particle excited states, to appear. We have also developed a Mathematica notebook that automates the expansions described in this work.

Local Volume Conservation in Concentrated Electrolytes Is Governing Charge Transport in Electric Fields.

While ion transport processes in concentrated electrolytes, e.g., based on ionic liquids (IL), are a subject of intense research, the role of conservation laws and reference frames is still a matter of debate. Employing electrophoretic NMR, we show that momentum conservation, a typical prerequisite in molecular dynamics (MD) simulations, is not governing ion transport. Involving density measurements to determine molar volumes of distinct ion species, we propose that conservation of local molar species volumes is the governing constraint for ion transport. The experimentally quantified net volume flux is found to be zero, implying a nonzero local momentum flux, as tested in pure ILs and IL-based electrolytes for a broad variety of concentrations and chemical compositions. This constraint is consistent with incompressibility, but not with a local application of momentum conservation. The constraint affects the calculation of transference numbers as well as comparisons of MD results to experimental findings.

Quantum theory of statistical radiation pressure in free space

Light is known to exert radiation pressure on any surface it is incident upon, via the transfer of momentum from the light to the surface. In general, this force is assumed to be pushing or repulsive in nature. In this paper, we present a quantum treatment of radiation pressure. We show that the interaction of an atom with light can lead to both repulsive and attractive forces due to absorption and emission of photons, respectively. An atom prepared in the excited state initially will experience a pulling force when interacting with light. On the other hand, if the atom is prepared in the ground state then the force will be repulsive, while having the same magnitude as in the earlier case. Therefore, for an ensemble of atoms, the direction of the net force will be decided by the excited and ground state populations. In the semi-classical treatment of light-matter interaction the absorption and emission processes have the same probability, therefore the magnitudes of the force in the two processes turn out to be the same. We obtain the effective emission profile for an excited atom interacting with quantum electromagnetic field, and show that in the quantum treatment, despite these probabilities being different, the magnitudes of the statistical force remain the same. This can be explained by noting that the extra contribution in the emission process is due to the interaction of the atom with the vacuum modes of electromagnetic field, results in symmetric emission profile, contributing to a net zero force on the atoms in an ensemble. We further identify the set of states of electromagnetic field which give rise to non-zero momentum transfer to the atom.

Combined effects of crab dispersion and momentum dispersion in colliders with local crab crossing scheme

In this paper, we present the effects of linear transverse-longitudinal coupling on beam size at the interaction point (IP) of a collider with a local crab crossing scheme, when time-dependent transverse deflection (crab kicks) and dispersive orbit intertwine near IP. The analytic propagation formula and the closed orbit form of the crab dispersion and momentum dispersion are derived. The nonzero momentum dispersion at crab cavities and the nonideal phase from crab cavities to IP are detailed with the derived propagation formula to predict the beam size distortion at IP with or without the beam-beam interaction. The linear results are compared with nonlinear simulation using the weak-strong beam-beam code.

Nonzero Momentum Requires Long-Range Entanglement

We show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has nonzero lattice momentum, i.e., if it is an eigenstate of the translation symmetry with eigenvalue eiP≠1. Equivalently, any state that can be connected with a nonzero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. Some nontrivial consequences follow immediately from our theorem: (i) Several different types of Lieb-Schultz-Mattis-Oshikawa-Hastings theorems, including a previously unknown version involving only a discrete Zn symmetry, can be derived in a simple manner from our result; (ii) a gapped topological order (in space dimension d>1) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum—this generalizes the familiar physics of Tao-Thouless; (iii) our result provides further evidence of the “smoothness” assumption widely used in the classification of crystalline symmetry-protected topological phases.Received 22 December 2021Revised 2 May 2022Accepted 26 May 2022DOI:https://doi.org/10.1103/PhysRevX.12.031007Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCharge density wavesCrystal symmetryExotic phases of matterQuantum entanglementQuantum gatesTopological phases of matterCondensed Matter, Materials & Applied PhysicsQuantum Information

Magnetic field induces spatially varying superconductivity

Strontium ruthenate may exhibit an exotic superconducting state composed of electron pairs with nonzero momentum.

Role of spin-orbit coupling in canted ferromagnetism and spin-wave dynamics of SrRuO3

A canted ferromagnetic arrangement with a long-range-ordered antiferromagnetic component is predicted for the metallic ${\mathrm{SrRuO}}_{3}$ orthoperovskite based on local-density-approximation-type electronic-structure calculation including on-site Coulomb repulsion $U$ and spin-orbit coupling. The electronic state of ${\mathrm{Ru}}^{4+}$ ions and the nature of nonzero orbital momentum are analyzed in detail. With regard to the density of states at the Fermi level, the value of the magnetic moment, and the easy axis along the $a$-axis in a Pbnm setting, a good agreement with the experimental data is achieved for $U=1$ eV. The calculated parameters of magnetic exchange, including the anisotropic and antisymmetric terms, are used to determine the magnon spectra. It is shown that notable anisotropic exchange in ${\mathrm{SrRuO}}_{3}$ is responsible for a gap of 1.7 meV at the $\mathrm{\ensuremath{\Gamma}}$ point of the magnon spectra, found previously by inelastic neutron diffraction. The origin of the spin canting that is confined within the $ab$-plane follows from the presence of the Dzyaloshinskii-Moriya interaction associated with the antisymmetric exchange.

Chiral germanium micro-gears for tuning orbital angular momentum.

Group IV light sources with vertical emission and non-zero orbital-angular momentum (OAM) promise to unlock many novel applications. In this report, we demonstrate cylindrically symmetrical germanium micro-gear cavities, fabricated by etching a grating around the circumference of standard micro-disks, with periods ranging from 14 to 22. Photoluminescence (PL) measurements were done to identify the confined whispering-gallery modes (WGM). Finite-difference time-domain (FDTD) simulations were conducted to map the resonant modes to their modal profiles and characteristics. Vertical emission of WGMs with non-zero OAM was demonstrated, with a clear dependence of the OAM order (ell) on the WGM azimuthal order and the number of micro-gear grating periods. As the chirality, or the direction of rotation, is not controlled in a symmetrical cavity, we propose introducing staircase or triangular-shaped gear periods resulting in an asymmetry. By choosing the diameter, number of periods, and the asymmetrical direction of the gear-teeth, it is possible to generate OAM signals with certain wavelength, OAM order and chirality.

Electron Number Density and Coherence Length of Boson-Fermion Pair in HTSC

A Bose-Einstein Condensate (BEC) of a nonzero momentum Cooper pair constitutes a composite boson or simply a boson. Previously, it has been shown that the quantum coherence of the two-component BEC (boson and fermion condensates) is controlled by plasmons where < 1 % of plasmon energy mediates the charge pairing but most of the plasmon energy is used to overcome the modes that compete against superconductivity such as phonons, charge density waves, antiferromagnetism, and damping effects. The dependence of plasmon frequency on the material of a superconductor reveals that modes within a specific range of frequency enhance superconductivity and therefore affect the critical temperature of a particular superconducting material. Against this background, we study the effect on doping on boson-fermion pairing energy and hence the critical temperature. While most hole doping agents are atoms lighter than copper, many of the electron doping agents are materials heavier than copper. This property defines the doping effect on the plasma frequency. Heavier dopants lower the critical temperature while lighter dopants increase the critical temperature of a superconductor. The number density of electrons is also found to be proportional to the square of critical temperature T c while the size of a boson-fermion pair condensate (BFPC) is proportional to T c − 2 / 3 . The size of a BFPC particle is less than boson-fermion (BF) coherence length by almost an order.

Higher order finite volume quantization conditions for two spinless particles

Lattice QCD calculations of scattering phaseshifts and resonance parameters in the two-body sector are becoming precision studies. Early calculations employed L\"uscher's formula for extracting these quantities at lowest order. As the calculations become more ambitious, higher-order relations are required. In this study we present a way to validate the higher-order quantization conditions. This is an important step given the involved derivations of these formulae. We derive and validate quantization conditions up to $\ell=5$ partial waves in both cubic and elongated geometries, and for states zero and non-zero total momentum. For all 45 quantization conditions we considered (22 in cubic box, 23 in elongated box) we find perfect agreement.

Fulde-Ferrell-Larkin-Ovchinnikov pairing induced by a Weyl nodal line in an Ising superconductor with a high critical field

Superconducting and topological states are two quantum phenomena attracting much interest. Their coexistence may lead to topological superconductivity sought-after for Majorana-based quantum computing. However, there is no causal relationship between the two, since superconductivity is a many-body effect due to electron-electron interaction while topology is a single-particle manifestation of electron band structure. Here, we demonstrate a novel form of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing, induced by topological Weyl nodal lines in Ising Bardeen-Cooper-Schrieffer (IBCS) superconductors. Based on first-principles calculations and analyses, we predict that the nonmagnetic metals of MA$_2$Z$_4$ family, including ${\alpha}_1$-TaSi$_2$P$_4$, ${\alpha}_1$-TaSi$_2$N$_4$, ${\alpha}_1$-NbSi$_2$P$_4$, ${\alpha}_2$-TaGe$_2$P$_4$, and ${\alpha}_2$-NbGe$_2$P$_4$ monolayers, are all superconductors. While the intrinsic IBCS paring arises in these non-centrosymmetric systems, the extrinsic FFLO pairing is revealed to be evoked by the Weyl nodal lines under magnetic field, facilitating the formation of Cooper pairs with nonzero momentum in their vicinity. Moreover, we show that the IBCS pairing alone will enhance the in-plane critical field $B_c$ to ~10-50 times of Pauli paramagnetic limit $B_p$, and additional FFLO pairing can further triple the $B_c/B_p$ ratio. It therefore affords an effective approach to enhance the robustness of superconductivity. Also, the topology induced superconductivity renders naturally the possible existence of topological superconducting state.

Initial longitudinal velocity resolved spiderlike photoelectron momentum distributions in hydrogen

Tunneling ionization of atoms is the basis of many phenomena and techniques, which requires people to be able to comprehensively understand this crucial physical process. Recent experiments have demonstrated the existence of the nonzero initial longitudinal momentum spread at the tunnel exit. However, the initial longitudinal velocity is usually set to be zero in the adiabatic regime. In this work, we numerically study that the initial longitudinal velocity of ionized-out electrons plays the role in the spiderlike photoelectron momentum distributions in hydrogen atom by using the semiclassical rescattering model and the time-dependent Schrödinger equation. Nonzero longitudinal initial velocity, no matter whether it is an offset or an offset distribution, is considered in the semiclassical rescattering model. Longitudinal cut-plot and transverse cut-plot of the photoelectron momentum distribution are discussed. The final longitudinal momentum of the electron is found to be sensitive to the initial longitudinal velocity, which offers us a method of determining the information about the initial longitudinal velocity from a photoelectron momentum distribution according to this linear relationship. We unveil that either an offset or an offset distribution for the initial longitudinal velocity can perfectly reproduce the same spiderlike photoelectron momentum distributions. The semiclassical results are backed by the full quantum simulation. It is expected that more precise research is required to deepen the knowledge of the initial longitudinal velocity in strong field ionization of atoms.

Plasmon Mediation of Charge Pairing in High Temperature Superconductors

A Bose-Einstein condensate (BEC) of a nonzero momentum Cooper pair constitutes a composite boson or simply a boson. We demonstrated that the quantum coherence of the two-component BEC (boson and fermion condensates) is controlled by plasmons. It has been proposed that plasmons, observed in both electron-doped and hole-doped cuprates, originates from the long-range Coulomb screening, where the transfer momentum q ⟶ 0 . We further show that the screening mediates boson-fermion pairing at condensate state. While only about 1 % of plasmon energy mediates the charge pairing, most of the plasmon energy is used to overcome the modes that compete against superconductivity such as phonons, charge density waves, antiferromagnetism, and damping effects. Additionally, the dependence of frequency of plasmons on the material of a superconductor is also explored. This study gives a quantum explanation of the modes that enhance and those that inhibit superconductivity. The study informs the nature of electromagnetic radiations (EMR) that can enhance the critical temperature of such materials.

Constraints on Pseudo-Nambu-Goldstone dark matter from direct detection experiment and neutron star reheating temperature

Pseudo-Nambu-Goldstone dark matter can interact with Standard Model fermion through the Higgs portal, and some models can emerge a cancellation mechanism that helps to escape the stringent constraints from direct detection experiments. In this paper we explore new constraints of these cancellation models on parameter space of non-zero momentum transfer, from both the current direct detection experiment and the neutron star temperature via the dark matter reheating mechanism.

Nucleon helicity generalized parton distribution at physical pion mass from lattice QCD

The generalized parton distributions (GPDs) offer a window on three-dimensional imaging of the nucleon, providing understanding of how the fundamental properties of the nucleon, such as its mass and spin, arise from the underlying quark and gluon degrees of freedom. In this work, we present the first lattice calculation of the nucleon isovector helicity GPD at physical pion mass, using an a≈0.09 fm lattice ensemble with 2+1+1 flavors of highly improved staggered quarks generated by MILC Collaboration. We perform the GPD calculation in Breit frame using averaged nucleon boost momentum Pz≈2.2 GeV with nonzero momentum transfers in [0.2,1.0] GeV2. Nonperturbative renormalization in RI/MOM scheme is used to obtain the quasi-distribution before matching to the lightcone GPDs. The three-dimensional distribution H˜(x,Q2) is presented, along with the three-dimensional nucleon tomography and impact-parameter–dependent distribution for selected Bjorken x at μ=3 GeV in MS‾ scheme.

One-loop structure of parton distribution for the gluon condensate and \u201czero modes\u201d

We present results for one-loop corrections to the recently introduced “gluon condensate” PDF F(x). In particular, we give expression for the gg-part of its evolution kernel. To enforce strict compliance with the gauge invariance requirements, we have used on-shell states for external gluons, and have obtained identical results both in Feynman and light-cone gauges. No “zero mode” δ(x) terms were found for the twist-4 gluon PDF F(x). However a q2δ(x) term was found for the ξ = 0 GPD F(x, q2) at nonzero momentum transfer q. Overall, our results do not agree with the original attempt of one-loop calculations of F(x) for gluon states, which sets alarm warning for calculations that use matrix elements with virtual external gluons and for lattice renormalization procedures based on their results.

Nucleon Tomography and Generalized Parton Distribution at Physical Pion Mass from Lattice QCD.

We present the first lattice calculation of the nucleon isovector unpolarized generalized parton distribution at the physical pion mass using a lattice ensemble with 2+1+1 flavors of highly improved staggered quarks generated by the MILC Collaboration, with lattice spacing a≈0.09 fm and volume 64^{3}×96. We use momentum-smeared sources to improve the signal at nucleon boost momentum P_{z}≈2.2 GeV and report results at nonzero momentum transfers in [0.2,1.0] GeV^{2}. Nonperturbative renormalization in a regularization-independent momentum-subtraction scheme is used to obtain the quasidistribution before matching to the light-cone generalized parton distributions. The three-dimensional distributions H(x,Q^{2}) and E(x,Q^{2}) at ξ=0 are presented, along with the three-dimensional nucleon tomography and impact parameter-dependent distribution for selected Bjorken x at μ=3 GeV in a modified minimal subtraction scheme.