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arXiv:2110.11983 · Physical Review Letters

Temperature-Dependent Periodicity of the Persistent Current in Strongly Interacting Systems

Ovidiu I. Pâţu, D. V. Averin

Published Mar 4, 2022• 16 citations
arXivHTMLPDF

Abstract

The persistent current in small isolated rings enclosing magnetic flux is the current circulating in equilibrium in the absence of an external excitation. While initially studied in superconducting and normal metals, recently, atomic persistent currents have been generated in ultracold gases spurring a new wave of theoretical investigations. Nevertheless, our understanding of the persistent currents in interacting systems is far from complete, especially at finite temperatures. Here we consider the fermionic one-dimensional Hubbard model and show that in the strong-interacting limit, the current can change its flux period and sign (diamagnetic or paramagnetic) as a function of temperature, features that cannot be explained within the single-particle or Luttinger liquid techniques. Also, the magnitude of the current can counterintuitively increase with temperature, in addition to presenting different rates of decay depending on the polarization of the system. Our work highlights the properties of the strongly interacting multicomponent systems that are missed by conventional approximation techniques, but can be important for the interpretation of experiments on persistent currents in ultracold gases.

DOI
10.1103/physrevlett.128.096801

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The persistent current in small isolated rings enclosing magnetic flux is the current circulating in equilibrium in the absence of an external excitation. While initially studied in superconducting and normal metals, recently, atomic persistent currents have been generated in ultracold gases spurring a new wave of theoretical investigations. Nevertheless, our understanding of the persistent currents in interacting systems is far from complete, especially at finite temperatures. Here we consider the fermionic one-dimensional Hubbard model and show that in the strong-interacting limit, the current can change its flux period and sign (diamagnetic or paramagnetic) as a function of temperature, features that cannot be explained within the single-particle or Luttinger liquid techniques. Also, the magnitude of the current can counterintuitively increase with temperature, in addition to presenting different rates of decay depending on the polarization of the system. Our work highlights the properties of the strongly interacting multicomponent systems that are missed by conventional approximation techniques, but can be important for the interpretation of experiments on persistent currents in ultracold gases.
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Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study the persistent current of the interacting electron gas in a one-dimensional continuous ring containing a single δδδ barrier. We calculate the persistent current as a function of the ring circumference, magnetic flux threading the ring, barrier strength, etc. We compare our results with the results of correlated models like the Luttinger liquid model and the Hubbard model solved by means of the renormalization group. A good agreement is found. First, the persistent current decays with the increasing ring circumference (LLL) faster than L−1L^{-1}L−1 and eventually like L−α−1L^{-α-1}L−α−1, where α>0α>0α>0 depends only on the electron-electron interaction. Second, the persistent current is a sine-shaped function of magnetic flux. This sine-like dependence and in particular the universal power law L−α−1L^{-α-1}L−α−1 have sofar been believed to arise only in the correlated many-body models. Observation of these features within the Hartree-Fock model is a surprising result.
The persistent current and spin-charge separation are studied in a one-dimensional (1D) Hubbard ring with side sites connected to the even sites of the ring. At half filling, the persistent current is always paramagnetic and has a period of flux quantum. Away from half filling, as the onsite repulsion UUU increases, the sign of the current may oscillate depending on the total number of electrons Ne{N}_{e}Ne​ and the hopping ttt between the ring site and the side site. For small hopping ttt, the number of electrons ${N}_{e}^{\ensuremath{'}}$ in the ring sites plays an important role in determining the sign of the current. In contrast to the 1D Hubbard model, a weak or a moderate UUU can strongly enhance the persistent current while the hopping ttt always suppresses the current. The study on the transmittance of the ring with two connected leads indicates that in the large UUU and small ttt case, the transmittance varies with a period $1∕{N}_{e}^{\ensuremath{'}}$ of a flux quantum, demonstrating a spin-charge separation in this system.
Within the basic assumption that oxygen orbitals may play a fundamental role in the superconductive properties of Cu-O high-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials, exact calculations of the ground-state energy and thermodynamic properties of strongly interacting fermions in small oxygen rings have been performed. Persistent currents (mesoscopic effect) and supercurrents have been computed for several microscopic models including repulsive and attractive Hubbard and the occupation-dependent hopping Hamiltonians. It is shown that for a given range of parameters the latter model exhibits features reminiscent of superconductivity: a maximum in the temperature dependence of the specific heat, whose position correlates with the temperature at which the superelectron concentration vanishes and exact hc/2e-periodic dependence of the free energy as a function of magnetic flux.
Theoretical studies suggest that an interacting one-dimensional electron system does not behave as a Fermi liquid. Instead, it is predicted to form a Luttinger liquid characterized e.g. by the absence of fermionic quasiparticles and interaction-dependent power-laws for transport quantities. So far, however, only a limited number of experiments have provided evidence for Luttinger liquid behavior. In this thesis we consider alternative methods to detect electronic correlations in one-dimensional electron systems based on our calculations of persistent currents and quantization of charge in ballistic single channel rings. The persistent current in an isolated impurity-free Luttinger liquid ring is found to be the same as for a system of non-interacting electrons. In contrast, a Luttinger liquid behavior is revealed if the ring is weakly connected to an electron reservoir and capacitively coupled to a gate electrode. The persistent current and the average charge in the ring are shown to change in a stepwise manner with the gate voltage at low temperatures. Both the step positions and the crossover temperatures are determined by the Luttinger liquid correlation parameter .alpha.(.alpha.c) which therefore can be measured. When a potential barrier is incorporated into the ring, the presence of strong interactions between electrons leads to a suppression of the persistent current and a change in its temperature dependence. A sharp maximum of the current is predicted to occur as a function of temperature. When two barriers are introduced into the ring, the possibility of resonant tunneling for the persistent current opens up. Two kinds of resonant behavior are discovered in the closed geometry: a current independent of the barrier transparency and a current analogous to the one with a single potential barrier. The persistent current in a ring containing a gas of fractionally charged excitations obeying fractional exclusion statistics is also studied. At finite temperatures, anomalous oscillations of the current are predicted as a manifestation of the statistics of the quasiparticles.
Persistent currents in disordered mesoscopic rings threaded by a magnetic flux are calculated using exact diagonalization methods in the one-dimensional (1D) case and self-consistent Hartree-Fock treatments for two dimensional (2D) systems. For multichannel systems, a comparative study between models of spinless or spinfull (Hubbard) fermions has been done. First, it is shown that a purely one-dimensional model can not reproduce the correct order of magnitude of the observed currents. For 2D systems, going beyond first order pertubative calculations, we show that the second harmonic of the current is {\it strongly suppressed} in the case of spinless fermion models but {\it significantly enhanced} for the Hubbard model. This reduction (resp. increase) of the second harmonic is related to a strong increase (resp. reduction) of the spacial charge density fluctuations. Our work underlines the important role of the spin degrees of freedom in the persistent currents.