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Physica Scripta

Interaction mediated electron transport within the many-body tunnelling Hamiltonian

Kelly R. Patton

Published May 17, 2023• 0 citations
Publisher

Abstract

Abstract For a non-superconducting system and in the spirit of the transfer or tunnelling Hamiltonian formalism, an expression for the electronic tunnelling current through an insulating barrier is calculated, explicitly taking into account the effects of electron-electron interactions that can persist across the barrier. In the presence of a single tunnelling barrier, the exact Hamiltonian is projected onto the subspaces of the ‘left’ and ‘right’ conducting leads. In the weak-tunnelling limit, the well-known tunnelling Hamiltonian is recovered, along with an additional term. This additional term originates from the projection of the electron-electron interaction onto each subspace and corresponds to a correlated or interaction-mediated tunnelling. It is shown that the tunnelling current in this approximation is related to—in addition to the single-particle density of states—the two-particle spin-spin and density-density susceptibilities. The signatures of these terms have been observed in scanning tunnelling microscope experiments on atomic spin chains.

DOI
10.1088/1402-4896/acd667

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arXiv:2307.16737•Physical review. B./Physical review. B•May 10, 2024•2 citations
Abstract For a non-superconducting system and in the spirit of the transfer or tunnelling Hamiltonian formalism, an expression for the electronic tunnelling current through an insulating barrier is calculated, explicitly taking into account the effects of electron-electron interactions that can persist across the barrier. In the presence of a single tunnelling barrier, the exact Hamiltonian is projected onto the subspaces of the ‘left’ and ‘right’ conducting leads. In the weak-tunnelling limit, the well-known tunnelling Hamiltonian is recovered, along with an additional term. This additional term originates from the projection of the electron-electron interaction onto each subspace and corresponds to a correlated or interaction-mediated tunnelling. It is shown that the tunnelling current in this approximation is related to—in addition to the single-particle density of states—the two-particle spin-spin and density-density susceptibilities. The signatures of these terms have been observed in scanning tunnelling microscope experiments on atomic spin chains.
We consider two one-dimensional interacting electron systems that are coupled via interchain tunneling to calculate transport properties in the presence of impurities or a single barrier by using the bosonization formalisms for the non-Luttinger-liquid phases on the phase diagram obtained by Fabrizio [Phys. Rev. B 48, 15 838 (1993)]. We find for the weak- and strong-interaction phases, where the superconducting correlation dominates in the ground state, that the interchain transfer enhances the conductivity and the Anderson localization is suppressed. This shows that multichain systems can have unique transport properties.
We derive tunneling Hamiltonians from a microscopic model of ultracold atoms separated by an external potential barrier. Not only usual one-body tunneling but also pair- and spin-tunneling processes naturally arise from a well-known microscopic model without any empirical parameters, where the tunneling process occurs via local transfer in the overlapped region of the many-body wave functions around the potential barrier. Applying the Schwinger-Keldysh formalism to the effective model in the momentum space, we demonstrate how anomalous tunneling currents occur via the tunneling Hamiltonians in strongly interacting systems. Our formulation is useful for various junction systems as well as sheds light on a clear connection between atomtronics and spintronics.
Motivated by recent developments in measurements of electron spin resonances of individual atoms and molecules with a scanning tunneling microscope (ESR-STM), we study electron transport through an impurity under periodic driving as a function of the transport parameters in a model junction. The model consists of a single-orbital quantum impurity connected to two electrodes via time-dependent hopping terms. The hopping terms are treated at the lowest order in perturbation theory to recover a Lindblad-like quantum master equation with electron transport. As in the experiment, the ESR-STM signal is given by the variation of the long-time DC current with the driving frequency. The density-matrix coherences play an important role in the evaluation of the ESR-STM signal. Electron correlation is included in our impurity mode. The charging energy UUU has significant influence on the spin dynamics depending on the sign and magnitude of the applied DC bias. Our model allows direct insight into the origin of the ESR signal from the many-body dynamics of the impurity.
"A microscopic theory of impurity-assisted tunneling is constructed in which the current-carrying (extended) eigenstates of the average one electron potential in a tunnel junction are utilized as the basis functions which are mixed by the Hamiltonian associated with the presence of a static or dynamic impurity anywhere in the system. In such a system, the one-electron propagator and its concomitant current across the junction easily can be calculated at zero bias by standard techniques for manipulating temperature Green's functions, The presence of a finite bias across the junction is incorporated into the theory via the principle of rigid-occupancy; i.e, the equilibrium occupation of the (current-carrying) many-body eigenstates of the system is taken to be unaffected by the presence of the bias. Therefore the rigid occupancy hypothesis relates the non-equilibrium current flow to the equilibrium (zero-bias) properties of the junction system so that we obtain a theory of nonequilibrium current flow which is not based on linear-response theory, The hypothesis is incorporated into the Matsubara perturbation theory by treating the chemical potentials of the left and right-hand electrodes as separate Lagrangian multipliers determined after the completion of all Matsubara sums to be related by ~=~L-eV. Therefore, for purposes of constructing and solving Dyson's equations for the renormalized one-electron propagators, the theory reduces to the conventional equilibrium theory defined using distorted-wave (i,e. non-plane-wave) states. The usual transfer Hamiltonian results are recovered by expanding the transmission probability. Using this theory, we have constructed and solved the Dysonis equations associated with bare vertex functions for both a static delta-function impurity and dynamic delta-function impurity vibrating at a (Einstein) local mode frequency, All electron-impurity (l~cal-mode-phonon) interactions appear in this formalism as self-energy corrections to the extended-basis electronic wave functions, The position of the impurity relative to the junction-region determines both the sign and magnitude of these corrections, Therefore, the asymmetries in the tunnel characteristics which can be traced to the position of the impurities enter the theory via the asymmetry in the impurity-induced self-energy of the two (i,e, left ~right and right ~ left) linearly-independent current-carrying basis states. Resonant elastic tunneling through impurity states of energy Er near the zero-bias Fermi energy, ,~ causes conductance minima(maxima) for E > r ,(E <'). Zero-bias anomalies in photosensitive GaAs:Au p-n tunnel diodes have been identified with this mechanism. The major new prediction is that resonant elastic impurity-assisted tunneling strongly affects inelastic impurity-assisted tunneling: e,g., if an ""impurity"" state is localized near the oxide in a M-O-S junction then large cusp-like phonon structure in the conductance appears only for majority carrier tunneling from the semiconductor into the metal, This prediction, and its correlation with a zero-bias anomaly is borne out in III-V tunnel diodes and metal-Si:B3P junctions."
Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study tunneling of the interacting electron gas through a single δ barrier in a finite one-dimensional wire connected to contacts.Our results exhibit features known from correlated many-body models.In particular, the conductance decays with the wire length as ∝ L -2α , where the power α is universal.We also show that a similar result for a wire conductance can be extracted from the persistent current (I) through the δ barrier in a one-dimensional ring, where it is known that I ∝ L -1-α .
We present a nonstandard Hubbard model applicable to arbitrary single-particle potential profiles and interparticle interactions. Our approach involves a treatment of Wannier functions, free from the ambiguities of conventional methods and applicable to finite systems without periodicity constraints. To ensure the consistent evaluation of Wannier functions, we develop a perturbative approach, utilizing the barrier penetration coefficient as a perturbation parameter. With the defined Wannier functions as a basis, we derive the Hubbard Hamiltonian, revealing the emergence of density-induced and pair tunneling terms alongside standard contributions. Our investigation demonstrates that long-range interparticle interactions can induce a mechanism for repulsive particle pairing. This mechanism relies on the effective suppression of single-particle tunneling due to density-induced tunneling. Contrary to expectations based on the standard Hubbard model, an increase in interparticle interaction does not lead to an insulating state. Instead, our proposed mechanism implies the coherent motion of correlated electron pairs, similar to bound states within a multiwell system, resistant to decay from single-electron tunneling transitions. These findings carry significant implications for various phenomena, including the formation of flat bands, the emergence of superconductivity in twisted bilayer graphene, and the possibility of a metal-insulator transition.