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arXiv:2307.12857 · Journal of Physics Condensed Matter

Coincidence detection probability of ( γ , 2 e ) photoemission measurement

Yuehua Su, Kun Cao, Chao Zhang

Published Sep 23, 2024• 1 citation
arXivHTMLPDF

Abstract

In the study of strongly correlated electrons, one of the challenging core tasks is to develop the potential techniques for direct detection of the many-body correlations of strongly correlated electrons. The(γ,2e)photoemission technique has been developed to investigate the two-body correlations of the target correlated electrons. In this article, we will focus on this technique for the correlated electrons near the Fermi energy in condensed matter. The coincidence detection probability of the two emitted electrons in the(γ,2e)photoemission measurement is shown to be relevant to a two-body Bethe-Salpeter wave function, which describes the dynamical two-body correlations of the target correlated electrons near the Fermi energy. As the coincidence detection probability involves an electron-electron interaction matrix element, the arbitrary momentum and/or energy transfer due to this electron-electron interaction makes the(γ,2e)photoemission technique fail to reveal the inner-pair structures of the two-body Bethe-Salpeter wave function. However, the center-of-mass momentum and energy of the two-body Bethe-Salpeter wave function can be distinctly resolved. Thus, the(γ,2e)photoemission technique can provide the center-of-mass physics of the two-body correlations of the target correlated electrons. It will be one potential technique to study the center-of-mass physics of the Cooper pairs in superconductor.

DOI
10.1088/1361-648x/ad7e74

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In the study of strongly correlated electrons, one of the challenging core tasks is to develop the potential techniques for direct detection of the many-body correlations of strongly correlated electrons. The(γ,2e)photoemission technique has been developed to investigate the two-body correlations of the target correlated electrons. In this article, we will focus on this technique for the correlated electrons near the Fermi energy in condensed matter. The coincidence detection probability of the two emitted electrons in the(γ,2e)photoemission measurement is shown to be relevant to a two-body Bethe-Salpeter wave function, which describes the dynamical two-body correlations of the target correlated electrons near the Fermi energy. As the coincidence detection probability involves an electron-electron interaction matrix element, the arbitrary momentum and/or energy transfer due to this electron-electron interaction makes the(γ,2e)photoemission technique fail to reveal the inner-pair structures of the two-body Bethe-Salpeter wave function. However, the center-of-mass momentum and energy of the two-body Bethe-Salpeter wave function can be distinctly resolved. Thus, the(γ,2e)photoemission technique can provide the center-of-mass physics of the two-body correlations of the target correlated electrons. It will be one potential technique to study the center-of-mass physics of the Cooper pairs in superconductor.
Abstract It is one challenge to develop experimental techniques for direct detection of the many-body correlations of strongly correlated electrons, which exhibit a variety of unsolved mysteries. In this article, we present a post-experiment coincidence counting method and propose two post-experiment coincidence detection techniques, post-experiment coincidence angle-resolved photoemission spectroscopy and post-experiment coincidence inelastic neutron scattering. By coincidence detection of two photoelectric processes or two neutron-scattering processes, the post-experiment coincidence detection techniques can detect directly the two-body correlations of strongly correlated electrons in particle-particle channel or two-spin channel. The post-experiment coincidence detection techniques can be implemented upon the pulse -resolved angle-resolved photoemission spectroscopy or inelastic neutron scattering experimental apparatus with pulse photon or neutron source. When implemented experimentally, they will be powerful techniques to study the highly esoteric high-temperature superconductivity and the highly coveted quantum spin liquids.
Research on strongly correlated electron systems faces a fundamental challenge due to the complex nature of intrinsic many-body correlations. A key strategy to address this challenge lies in advancing experimental methods that can directly probe and elucidate the underlying many-body correlations. In this perspective article, we discuss the theoretically proposed coincidence detection techniques, which are designed to directly measure two-body correlations in various particle-particle and particle-hole channels, with momentum, energy, and/or spatial resolution. We also explore the prospects of these coincidence detection techniques for future theoretical and experimental developments. The successful implementation and refinement of these coincidence detection techniques promise to deliver powerful new approaches for unraveling long-standing puzzles in strongly correlated electron systems, such as the enigmatic mechanism of unconventional superconductivity and the long-sought quantum spin liquids. Furthermore, these coincidence detection techniques will offer powerful new methods to investigate novel phenomena like itinerant magnetism and electronic nematicity in quantum materials.
Describing correlated electron systems has been a major challenge in computational condensed-matter physics. Quantum Monte Carlo, a powerful computational tool for the study of correlated systems, solves electron correlation problems explicitly. It has been taken as a benchmark method for understanding the correlated systems. Instead of making approximations to Hamiltonian, QMC methods work with the wave functions, and the computational cost scales well with the system size. With the development of parallel computing, QMC calculations on large systems are becoming more and more feasible. We have investigated two correlated systems with highly accurate fixed node QMC techniques. The first system is a correlated hydrogen model system near the metal to insulator transition. We have successfully identified the transition point by calculating spin and charge properties and analyzing the low energy Hilbert space. The second one is a strongly correlated Fe/O system. Calculations on the Fe atoms, O atoms, and FeO molecules are conducted with multiple highly accurate many-body techniques. The source of errors has been disentangled by comparing the results of the many body techniques with the experimental results. For the Fe and O atoms, the calculated properties coincide well with previous experimental results. For the basis-based techniques, the performance is mainly limited by the basis set. The calculated equilibrium bond length, excitation energy and vibrational frequency of the FeO molecules are also in close agreement with the known values from previous experiments.
In time-resolved photoemission experiments, more than one electron can be emitted from the solid by a single ultrashort pulse. We theoretically demonstrate how correlations between the momenta of outgoing electrons relate to time-dependent two-particle correlations in the solid. This can extend the scope of time- and angle-resolved photoemission spectroscopy to probe superconducting and charge density fluctuations in systems without long-range order, and to reveal their dynamics independent of the electronic gap and thus unrestricted by the energy-time uncertainty. The proposal is illustrated for superconductivity in a BCS model. An impulsive perturbation can quench the gap on ultrafast timescales, while nonequilibrium pairing correlations persist much longer, even when electron-electron scattering beyond mean-field theory is taken into account. There is thus a clear distinction between a dephasing of the Cooper pairs and the thermalization into the normal state. While a measurement of the gap would be blind to such pairing correlations, they can be revealed by the angular correlations in photoemission.
Relation between the binding energy of a pair of electrons in Cooper's configuration and the magnitude of the attractive interaction between them is investigated theoretically for a two-dimensional electron gas when the electron pair has (a) zero and (b) finite center of mass momentum (CMM) first (i) in the background of a passive Fermi sea and (ii) with inclusion of the effect of Pauli exclusion principle in the presence of an active Fermi sea, at zero temperature. In the Cooper's approach (Cooper 1956 Phys. Rev. 104 1189) two pairing electrons are considered above the Fermi sea. Due to Pauli exclusion principle, these two electrons are forbidden to go into the states whose energies are less than the Fermi energy. Consequently, the role of the electrons which form the Fermi sea is passive in formation of electron pair (Fujita and Godoy 2001 Theory of High Temperature Superconductivity (Kluwer Academic Publishers)). However, in the case of an active Fermi sea, implying possible presence of multiple pairs of electrons coming out of the Fermi sea, the two electrons will have less available region in the momentum space for pair formation due to the Pauli blocking effect. In both the situations, threshold values of attractive interaction are found to exist to bind the electrons having finite CMM even with respect to the Fermi energy while with arbitrarily small value of attractive interaction they can be bound only in the case of zero CMM and that too in the presence of a passive Fermi sea. However, the presence of an active Fermi sea strongly opposes the pair formation having lower CMM. Furthermore, raising the range of the attractive interaction below and above the Fermi surface makes the pair formation more difficult due to enhanced Pauli blocking in this case. In the case of a passive Fermi sea however, with the increase in the range of the attractive interaction it becomes easier for the electron pairs to be in both Cooper pair state (CP) and true bound state (TB). These results are totally distinct from those obtained by Randeria et al (1989 Phys. Rev. Lett. 62 981, 1990 Phys. Rev. B 41 327) that a fermionic bound state in true vacuum is a necessary and sufficient condition for the Cooper pairing instability in the presence of a passive Fermi sea, independent of attractive interaction strength implying that for a potential which is attractive everywhere in two dimension, a two-body bound state exists for an arbitrarily weak attraction. Our calculations show, in the mean field approximation, that co-existence of TB state and CP state with various CMMs can occur only beyond a critical attractive interaction strength. This could lead to the formation of incoherent pairs even under strong coupling situation, which may hint onto the pseudo gap formation leading to some of the exotic features in the anomalous normal state seen in some of the exotic superconductors.
The Hubbard Hamiltonian is projected onto a representation consisting of electron pairs characterised by the momentum of their centre of mass.Within this approximation the electron gas can be viewed as a collection of subsets, each of which contains a constant number of electron pairs, all having the same centre of mass momentum.As these subsets are decoupled, the Hubbard Hamiltonian is diagonalised to give two types of many-body eigenstates: correlated and uncorrelated.The uncorrelated pairs build up an ideal Fermi gas.Excellent agreement is found for the uncorrelated energy calculated at zero temperature in one dimension between this model and the Bethe ansatz, for arbitrary electron concentration and magnitude of the electron interaction.The correlated states turn out to be of the BCS type.