Fermion Pairs Research Articles

Pairing of holes by confining strings in antiferromagnets

In strongly correlated quantum materials, the behavior of charge carriers is dominated by strong electron-electron interactions. These can lead to insulating states with spin order, and upon doping to competing ordered states including unconventional superconductivity. The underlying pairing mechanism remains poorly understood however, even in strongly simplified theoretical models. Recent advances in quantum simulation allow to study pairing in paradigmatic settings, e.g. in the t-Jt−J and t-J_zt−Jz Hamiltonians. Even there, the most basic properties of paired states of only two dopants, such as their dispersion relation and excitation spectra, remain poorly studied in many cases. Here we provide new analytical insights into a possible string-based pairing mechanism of mobile holes in an antiferromagnet. We analyze an effective model of partons connected by a confining string and calculate the spectral properties of bound states. Our model is equally relevant for understanding Hubbard-Mott excitons consisting of a bound doublon-hole pair or confined states of dynamical matter in lattice gauge theories, which motivates our study of different parton statistics. Although an accurate semi-analytic estimation of binding energies is challenging, our theory provides a detailed understanding of the internal structure of pairs. For example, in a range of settings we predict heavy states of immobile pairs with flat-band dispersions - including for the lowest-energy dd-wave pair of fermions. Our findings shed new light on the long-standing question about the origin of pairing and competing orders in high-temperature superconductors.

The validity of the BCS-like theory of Fermi-liquid superconductivity in overdoped cuprates

In this paper, we study the key and challenging issues arising in the physics of doped cuprate superconductors, which depending on the doping level (or the Fermi energy [Formula: see text]) and the characteristic energy [Formula: see text] of the attractive interaction between the charge carriers (holes or electrons) might be either in the limit of fermionic (weakly-bound) Cooper pairs just like in ordinary metals or in the limit of bosonic (tightly-bound) Cooper pairs. We argue that the underlying mechanism of superconductivity in doped cuprates depends on the fermionic or bosonic nature of Cooper pairs. We examine the validity criterion of the Bardeen–Cooper–Schrieffer (BCS)-like theory of Fermi-liquid superconductivity in these materials and determine the doping level at which this criterion is well satisfied. We find that the specific overdoped cuprates (with [Formula: see text] or [Formula: see text][Formula: see text]eV) can become the BCS-type superconductors. Using a pertinent BCS-like pairing theory, we calculate the superconducting order parameter (defined as a BCS-like gap [Formula: see text]) and the critical temperature [Formula: see text] of the superconducting transition and the doping dependences of [Formula: see text] and [Formula: see text] in various overdoped cuprates. Our results for [Formula: see text] and [Formula: see text] in specific overdoped cuprates are in fair agreement with the experimental findings reported for these systems.

Ground state of composite bosons in low-dimensional graphs

We consider a system of composite bosons given by strongly bound fermion pairs tunneling through sites that form a low-dimensional network. It has been shown that the ground state of this system can have condensatelike properties in the very dilute regime for two-dimensional lattices but displays fermionization for one-dimensional lattices. Studying graphs with fractal dimensions, we explore intermediate situations between these two cases and observe a correlation between increasing dimension and increasing condensatelike character. However, this is only the case for graphs for which the average path length grows with power smaller than 1 in the number of sites and which have an unbounded circuit rank. We thus conjecture that these two conditions are relevant for condensation of composite bosons in arbitrary networks and should be considered jointly with the well-established criterion of high entanglement between constituents.

Modified general relativity and dark matter

Modified General Relativity (MGR) is the natural extension of General Relativity (GR). MGR explicitly uses the smooth regular line element vector field [Formula: see text], which exists in all Lorentzian spacetimes, to construct a connection-independent symmetric tensor that represents the energy–momentum of the gravitational field. It solves the problem of the nonlocalization of gravitational energy–momentum in GR, preserves the ontology of the Einstein equation, and maintains the equivalence principle. The line element field provides MGR with the extra freedom required to describe dark energy and dark matter. An extended Schwarzschild solution for the matter-free Einstein equation of MGR is developed, from which the Tully–Fisher relation is derived, and the gravitational energy density is calculated. The mass of the invisible matter halo of galaxy NGC 3198 calculated with MGR is identical to the result obtained from GR using a dark matter profile. Although dark matter in MGR is described geometrically, it has an equivalent representation as a particle with the property of a vector boson or a pair of fermions; the geometry of spacetime and the quantum nature of matter are linked together by the unit line element covectors that belong to both the Lorentzian metric and the spin-1 Klein–Gordon wave equation. The three classic tests of GR provide a comparison of the theories in the solar system and several parts of the cosmos. MGR provides the flexibility to describe inflation after the Big Bang and galactic anisotropies.

Dihedral twist liquid models from emergent Majorana fermions

We present a family of electron-based coupled-wire models of bosonic orbifold topological phases, referred to as twist liquids, in two spatial dimensions. All local fermion degrees of freedom are gapped and removed from the topological order by many-body interactions. Bosonic chiral spin liquids and anyonic superconductors are constructed on an array of interacting wires, each supports emergent massless Majorana fermions that are non-local (fractional) and constitute theSO(N)Kac-Moody Wess-Zumino-Witten algebra at level 1. We focus on the dihedralDksymmetry ofSO(2n)1, and its promotion to a gauge symmetry by manipulating the locality of fermion pairs. Gauging the symmetry (sub)group generates theC/Gtwist liquids, whereG=Z2forC=U(1)l,SU(n)1, andG=Z2,Zk,DkforC=SO(2n)1. We construct exactly solvable models for all of these topological states. We prove the presence of a bulk excitation energy gap and demonstrate the appearance of edge orbifold conformal field theories corresponding to the twist liquid topological orders. We analyze the statistical properties of the anyon excitations, including the non-Abelian metaplectic anyons and a new class of quasiparticles referred to as Ising-fluxons. We show an eight-fold periodic gauging pattern inSO(2n)1/Gby identifying the non-chiral components of the twist liquids with discrete gauge theories.

Fractional Quantum Hall Effect with Unconventional Pairing in Monolayer Graphene.

Motivated by the observation of even denominator fractional quantum Hall effect in the n=3 Landau level of monolayer graphene [Kim etal., Nat. Phys. 15, 154 (2019)NPAHAX1745-247310.1038/s41567-018-0355-x], we consider a Bardeen-Cooper-Schrieffer variational state for composite fermions and find that the composite-fermion Fermi sea in this Landau level is unstable to an f-wave pairing. Analogous calculation suggests the possibility of a p-wave pairing of composite fermions at half filling in the n=2 graphene Landau level, whereas no pairing instability is found at half filling in the n=0 and n=1 graphene Landau levels. The relevance of these results to experiments is discussed.

Meson content of entanglement spectra after integrable and nonintegrable quantum quenches

We use tensor network simulations to calculate the time evolution of the lower part of the entanglement spectrum and return rate functions after global quantum quenches in the Ising model. We consider ground state quenches towards mesonic parameter ranges with confined fermion pairs as nonperturbative bound states in a semiclassical regime and the relativistic E$_8$ theory. We find that in both cases only the dominant eigenvalue of the modular Hamiltonian fully encodes the meson content of the quantum many-body system or quantum field theory, giving rise to nearly identical entanglement oscillations in the entanglement entropy. When the initial state is prepared in the paramagnetic phase, the return rate density exhibits regular cusps at unequally spaced positions, signaling the appearance of dynamical quantum phase transitions, at which the entanglement spectrum remains gapped. Our analyses provide a deeper understanding on the role of quantum information quantities for the dynamics of emergent phenomena reminiscent of systems in high-energy physics.

Correction: Composite-boson formalism applied to strongly bound fermion pairs in a one-dimensional trap

Correction: Composite-boson formalism applied to strongly bound fermion pairs in a one-dimensional trap

Composite-boson formalism applied to strongly bound fermion pairs in a one-dimensional trap

We analyze a system of fermions in a one dimensional harmonic trap with attractive delta-interactions between different fermions species, as an approximate description of experiments involving atomic dimers. We solve the problem of two fermion pairs numerically using the so-called "coboson formalism" as an alternative to techniques which are based on the single-particle basis. This allows us to explore the strongly bound regime, approaching the limit of infinite attraction in which the composite particles behave as hard-core bosons. Our procedure is computationally inexpensive and illustrates how the coboson toolbox is useful for ultracold atom systems even in absence of condensation.

Topological superfluid of s -wave-interacting fermions by engineered orbital hybridization in an optical lattice

Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for exploring quantum many-body states of matter that had not been accessible previously. Here we report that a topological fermionic superfluid with higher Chern number emerges spontaneously from $s$-wave spin-singlet pairing in an orbital optical lattice when its geometry is tuned to explicitly break reflection symmetry. Qualitatively distinct from the conventional scheme that relies on higher partial-wave pairing, the crucial ingredient of our model is topology originating from mixing higher Wannier orbitals. It leads to unexpected changes in the topological band structure at the single-particle level, i.e., the bands are transformed from possessing two flux-$\ensuremath{\pi}$ Dirac points into a single quadratic touching point with flux $2\ensuremath{\pi}$. Based on such engineered single-particle bands, spin-singlet pairing of ultracold fermions arising from standard $s$-wave attractive interaction is found to induce higher Chern number (Chern number of 2) and topologically protected chiral edge modes, all occurring at a higher critical temperatures in relative scales, potentially circumventing one of the major obstacle for its realization in ultracold gases.

From edge to bulk: Cavity-induced displacement of topological nonlocal qubits

We investigate the ability of selective cavity coupling to a topological chain for tailoring the connectivity of Majorana fermions. We show how topological qubits (TQs), associated with nonlocal Majorana fermion pairing, can be displaced from the edges to the bulk of a topological chain through selective access to light-matter interaction with specific physical sites. In particular, we present a comprehensive density matrix renormalization group study of ground-state features in different chain-cavity coupling geometries, and we validate analytical insights in the strong-coupling regime. This type of Majorana fermion correlation generation process comes with emergent cavity photon features. Moreover, by considering the time evolution after a sudden quench of the cavity-matter coupling strength, we show that the development of high nontrivial matter (Majorana) correlations leaves behind measurable nonclassical photon imprints in the cavity. Innovative ways to dynamically generate TQ nonlocal correlations in topological chains of arbitrary length are thus provided, opening alternative routes to controllable long-range entanglement in hybrid photonic solid-state systems.

Local pairs in high-temperature superconductors: The concept of pseudogap

The origin of the high-temperature superconductivity of cuprates remains a subject of debate after almost four decades of investigation. One of the main questions — what is the physics behind the mechanism of superconducting pairing, which makes it possible to obtain real Cooper pairs at temperatures much higher than 100 K, remains open. It is believed that the answer can be obtained by the studying the properties of cuprates in the normal state above Tc, where the pseudogap (PG) opens at T* >> Tc. The number of papers devoted to the study of PG is extraordinarily large, but its physics also remains in question. In cuprates, the question arises whether the pseudogap phase arises exclusively due to antiferromagnetic fluctuations, spin or charge density waves, or whether it can be explained by the formation below T* of specific paired fermions, the so-called local pairs. We review studies on both approaches to PG that should clarify this issue. In addition to theoretical considerations, we analyze and discuss various experimental results of fluctuation conductivity and PG measurements, as well as magnetic measurements, in an attempt to prove the decisive role of local pairs in the formation of the PG state. Accordingly, various types of supposed magnetic interactions can be considered as possible mechanisms of superconducting pairing in high-temperature superconductors.

Observation of highly anisotropic bulk dispersion and spin-polarized topological surface states in CoTe2

We present CoTe2 as a new type-II Dirac semimetal supporting Lorentz symmetry violating Dirac fermions in the vicinity of the Fermi energy. By combining first principle ab-initio calculations with experimental angle-resolved photo-emission spectroscopy results, we show the CoTe2 hosts a pair of type-II Dirac fermions around 90 meV above the Fermi energy. In addition to the bulk Dirac fermions, we find several topological band inversions in bulk CoTe2, which gives rise to a ladder of spin-polarized surface states over a wide range of energies. In contrast to the surface states which typically display Rashba-type in-plane spin splitting, we find that CoTe2 hosts novel out-of-plane spin polarization as well. Our work establishes CoTe2 as a potential candidate for the exploration of Dirac fermiology and applications in spintronic devices, infrared plasmonics, and ultrafast optoelectronics.

Angular momentum inheritance from the Schwinger effect in (chromo)electromagnetic fields

Abstract The angular momentum of fermion pairs generated by the Schwinger effect is studied in homogeneous (chromo)electromagnetic fields, mimicking the early stages of a heavy-ion collision. It is demonstrated that the angular momentum density of produced pairs is proportional to that of the background fields. This is argued both heuristically in a virtual breaking condensate model by evaluating Wong’s equations, and out-of-equilibrium to one-loop using the in–in formalism.

Relativistic Fermion and Boson Fields: Bose-Einstein Condensate as a Time Crystal

In a basis of the space-time coordinate frame four quaternions discovered by Hamilton can be used. For subsequent reproduction of the coordinate frame these four quaternions are expanded to four 4 × 4 matrices with real-valued matrix coefficients −0 and 1. This group set is isomorphic to the SU(2) group. Such a matrix basis introduces extra six degrees of freedom of matter motion in space-time. There are three rotations about three space axes and three boosts along these axes. Next one declares the differential generating operators acting on the energy-momentum density tensor written in the above quaternion basis. The subsequent actions of this operator together with its transposed one on the above tensor lead to the emergence of the gravitomagnetic equations that are like the Maxwell equations. Wave equations extracted from the gravitomagnetic ones describe the propagation of energy density waves and their vortices through space. The Dirac equations and their reduction to two equations with real-valued functions, the quantum Hamilton-Jacobi equations and the continuity equations, are considered. The Klein-Gordon equations arising on the mass shell hints to the alternation of the paired fermion fields and boson ones. As an example, a Feynman diagram of an electron–positron time crystal is illustrated.

Interacting second-order topological insulators in one-dimensional fermions with correlated hopping

Higher-order topological crystalline phases in low-dimensional interacting quantum systems represent a challenging and largely unexplored research topic. Here, we derive a Hamiltonian describing fermions interacting through correlated hopping processes that break chiral invariance, but preserve both inversion and time-reversal symmetries. In this way, we show that our one-dimensional model gives rise to an interacting second-order topological insulating phase that supports gapped edge states. The topological nature of such interacting phase turns out to be revealed by both long-range order of a non-local string correlation function and by even degeneracy of the entanglement spectrum. For strong interactions we instead find that the topological crystalline phase is destroyed and replaced by a singlet superconducting phase. The latter, characterized by local fermionic pairing, turns out to appear both in a homogeneous and in a phase separated form. Relevantly, the derived one-dimensional model and the second-order topological insulator can be explored and investigated in atomic quantum simulators.

Pairing of fermions under spin-orbit coupling in two dimensions

We present a theoretical approach to the problem of two-dimensional fermion pairing under spin-orbit (SO) coupling and Zeeman interaction with an external magnetic field. We introduce a generic pairing Hamiltonian operating in the Hilbert space spanning free pairs and bare two-body bound states. The SO coupling of Rashba or Dresselhaus type provides $p$-wave dressing of an $s$-wave spin-singlet bound state by continua in the triplet scattering channels. In the strong-coupling (Bose-Einstein condensate) limit of the many-body fermion system at zero temperature our theory maps onto the two-channel Fano-Anderson model of a spinless resonant $p$-wave superfluid.

Unavoidable Higgs coupling deviations in the Z2 -symmetric Georgi-Machacek model

The $Z_{2}$-symmetric version of the Georgi-Machacek model does not possess a decoupling limit in which all the new particles can be made arbitrarily heavy, opening the possibility that the model can be entirely excluded if experiments reveal no deviations from the Standard Model. We explore this model, focusing on the part of parameter space in which the vacuum expectation value of the triplets, $\nu_\chi$, is small. In the small-$\nu_\chi$ limit, the second custodial-singlet scalar field $S$ necessarily becomes very light and can contribute to the total width of the 125 GeV Higgs boson $h$ via $h \to SS$. We show that this process, together with LHC measurements of the $h \to \gamma\gamma$ rate, entirely excludes masses $m_S < m_h/2$ and thereby severely constrains the parameter space, setting an experimental lower bound $\nu_\chi \gtrsim 12.5$ GeV on the vacuum expectation value of the triplets. This lower bound makes it impossible to avoid deviations from the Standard Model in the couplings of $h$ to fermion and vector boson pairs. We study the remaining parameter space after imposing constraints from direct searches for the additional Higgs bosons, and show that it is on the edge of being fully excluded at $95\%$ confidence level by LHC measurements of the 125 GeV Higgs boson's couplings. Measurements of these couplings at the future high-luminosity run of the LHC will have sufficient precision to entirely exclude the model at $5\sigma$ if no deviations from the Standard Model are observed.

Excitation spectra of one-dimensional spin-1/2 Fermi gas with an attraction

Using an exact Bethe ansatz solution, we rigorously study excitation spectra of the spin-1/2 Fermi gas (called Yang–Gaudin model) with an attractive interaction. Elementary excitations of this model involve particle-hole excitation, hole excitation and adding particles in the Fermi seas of pairs and unpaired fermions. The gapped magnon excitations in the spin sector show a ferromagnetic coupling to the Fermi sea of the single fermions. By numerically and analytically solving the Bethe ansatz equations and the thermodynamic Bethe ansatz equations of this model, we obtain excitation energies for various polarizations in the phase of the Fulde–Ferrell–Larkin–Ovchinnikov-like state. For a small momentum (long-wavelength limit) and in the strong interaction regime, we analytically obtained their linear dispersions with curvature corrections, effective masses as well as velocities in particle-hole excitations of pairs and unpaired fermions. Such a type of particle-hole excitations display a novel separation of collective motions of bosonic modes within paired and unpaired fermions. Finally, we also discuss magnon excitations in the spin sector and the application of Bragg spectroscopy for testing such separated charge excitation modes of pairs and single fermions.

Vortex dynamics in the two-dimensional BCS-BEC crossover

The Bardeen–Cooper–Schrieffer (BCS) condensation and Bose–Einstein condensation (BEC) are the two limiting ground states of paired Fermion systems, and the crossover between these two limits has been a source of excitement for both fields of high temperature superconductivity and cold atom superfluidity. For superconductors, ultra-low doping systems like graphene and LixZrNCl successfully approached the crossover starting from the BCS-side. These superconductors offer new opportunities to clarify the nature of charged-particles transport towards the BEC regime. Here we report the study of vortex dynamics within the crossover using their Hall effect as a probe in LixZrNCl. We observed a systematic enhancement of the Hall angle towards the BCS-BEC crossover, which was qualitatively reproduced by the phenomenological time-dependent Ginzburg-Landau (TDGL) theory. LixZrNCl exhibits a band structure free from various electronic instabilities, allowing us to achieve a comprehensive understanding of the vortex Hall effect and thereby propose a global picture of vortex dynamics within the crossover. These results demonstrate that gate-controlled superconductors are ideal platforms towards investigations of unexplored properties in BEC superconductors.