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arXiv:cond-mat/9806136 · Physical Review Letters

Fractional Charge in Transport through a 1D Correlated Insulator of Finite Length

Vadim V. Ponomarenko, Naoto Nagaosa

Published Aug 30, 1999• 10 citations
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Abstract

Transport between two Fermi liquid reservoirs through a one channel wire of length $L$ is examined when the 1D electron system has an energy gap $2M\ensuremath{\gg}{v}_{c}/L$ ( ${v}_{c}$ is the charge velocity in the wire). In the spinless case transformation of reservoir electrons into solitons of fractional charge entails a crossover from a Fermi liquid regime of integer charge transfer below the crossover energy ${T}_{x}\ensuremath{\ll}{T}_{L}$ to an insulating regime of the fractional charge transfer in the current vs voltage, conductance vs temperature, and the shot noise. Similar behavior is predicted for a spin Mott insulator of filling factor $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}n/({2m}^{\ensuremath{'}})$ ( ${n,m}^{\ensuremath{'}}$ are positive integers).

DOI
10.1103/physrevlett.83.1822

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Transport between two Fermi liquid reservoirs through a one channel wire of length LLL is examined when the 1D electron system has an energy gap 2M\ensuremath≫vc/L2M\ensuremath{\gg}{v}_{c}/L2M\ensuremath≫vc​/L ( vc{v}_{c}vc​ is the charge velocity in the wire). In the spinless case transformation of reservoir electrons into solitons of fractional charge entails a crossover from a Fermi liquid regime of integer charge transfer below the crossover energy Tx\ensuremath≪TL{T}_{x}\ensuremath{\ll}{T}_{L}Tx​\ensuremath≪TL​ to an insulating regime of the fractional charge transfer in the current vs voltage, conductance vs temperature, and the shot noise. Similar behavior is predicted for a spin Mott insulator of filling factor \ensuremathν=n/(2m\ensuremath′)\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}n/({2m}^{\ensuremath{'}})\ensuremathν=n/(2m\ensuremath′) ( n,m\ensuremath′{n,m}^{\ensuremath{'}}n,m\ensuremath′ are positive integers).
We study low-energy spin and charge transport through a 1D Mott-Hubbard insulator of finite length L attached to Fermi liquid reservoirs, which, in the presence of spin accumulation, are characterized by different electrochemical potentials for electrons of opposite spin polarizations. At temperatures less than ( v c : charge velocity in the wire) and under the assumption that the Hubbard gap 2 M is large enough, M > T L , we calculate the average currents (charge and spin) and their zero-frequency correlators. The average spin (charge) current depends only on the difference (sum) of the spin-dependent voltages and even a weak electron backscattering of low rate leads to the spin current suppression at smaller than . The spin current recovers its free mode behavior at spin voltage or temperature larger than Γ. Suppression of the spin-charge correlator suggesting the appearance of spin-charge separation needs both to be larger than Γ. In the absence of the average charge current at its shot noise is proportional to the average spin backscattered current defined by V s and can be used to measure the spin accumulation in the reservoirs. The relation of these results to Kondo dot transport in the Toulouse limit is also clarified.
We study low energy spin and charge transport through a 1D Mott-Hubbard insulator of finite length LLL attached to Fermi liquid reservoirs characterized by different chemical potentials for electrons of opposite spin polarizations as it happens in quantum spin Hall insulators. We calculate the average currents (charge and spin) and their correlators and demonstrate how a transition induced by the reservoirs to the low energy Fermi liquid regime results in breakdown of the spin-charge separation, which is visible in the presence of the spin dependent voltages and a weak one electron scattering in the system. These calculations are carried out under assumption that the Hubbard gap 2M is large enough: M>TL≡vc/LM > T_L \equiv v_c/LM>TL​≡vc​/L (vcv_cvc​: charge velocity in the wire) and the scattering rate Γs≪TLΓ_s \ll T_LΓs​≪TL​. Relation of these results to Kondo dot transport in the Toulouse limit is also clarified.
We theoretically investigate transport in a spin-incoherent one-dimensional electron system, which may be realized in quantum wires at low-electron density and finite temperature. Both the pure and disordered cases are considered, both in finite wires and in the thermodynamic limit. The effect of Fermi-liquid leads attached to the finite-length system is also addressed. In the infinite system, we find a phase diagram identical to that obtained for a spinless Luttinger liquid, provided we make the identification g=2gcg=2{g}_{c}g=2gc​, where ggg is the interaction parameter in a spinless Luttinger liquid and gc{g}_{c}gc​ is the interaction parameter of the charge sector of a Luttinger-liquid theory for electrons with spin. For a finite-length wire attached to Fermi-liquid leads, the transport depends on the details of the disorder in the wire. A simple picture for the crossover from the spin-incoherent regime to the spin-coherent regime as the temperature is varied is also discussed, as well as some physical implications.
Transport through a 1D Mott-Hubbard insulator of a finite length LLL is studied beyond the perturbative approach. At a special value of the low-energy constant of the interaction we have mapped the problem onto exactly solvable models and found current vs voltage at a high temperature T>max(m,TL)T>\mathrm{max}({m,T}_{L})T>max(m,TL​) and at a low energy T,V<TLT,V<{T}_{L}T,V<TL​ ( TL=vc/L{T}_{L}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}v}_{c}/LTL​=vc​/L; vc{v}_{c}vc​: charge velocity). The result shows that for the strong interaction creating a large Mott-Hubbard gap $2m\ensuremath{\gg}{T}_{L}$ inside the wire, the transport is suppressed near half filling everywhere inside the gap except for a small region where $V,T<{T}_{L}\mathrm{exp}(\ensuremath{-}2m/{T}_{L})$.
Suppression of electron current $ ΔI$ through a 1D channel of length LLL connecting two Fermi liquid reservoirs is studied taking into account the Umklapp interaction induced by a periodic potential. This interaction opens band gaps at the integer fillings and Hubbard gaps 2m2m2m at some rational fillings in the infinite wire: L→∞L \to \inftyL→∞. In the perturbative regime where m≪vc/Lm \ll v_c/Lm≪vc​/L (vc:v_c:vc​: charge velocity), and for small deviations δnδnδn of the electron density from its commensurate values −ΔI/V- ΔI/V−ΔI/V can diverge with some exponent as voltage or temperature V,TV,TV,T decreases above Ec=max(vc/L,vcδn)E_c=max(v_c/L,v_c δn)Ec​=max(vc​/L,vc​δn), while it goes to zero below EcE_cEc​. This results in a non-monotonous behavior of the conductance. In the case when the Umklapp interaction creates a large Mott-Hubbard gap $2m \gg T_L $ inside the wire, the transport is suppressed near half-filling everywhere inside the gap except for an exponentially small region of V,T<TLexp(−2m/TL)V,T < T_L exp(-2m/T_L)V,T<TL​exp(−2m/TL​).
The phenomenon of charge fractionalization describes the emergence of novel excitations with fractional quantum numbers, as predicted in strongly correlated systems such as spin liquids. We elucidate that precisely such an unusual effect may occur in the simplest possible non-Fermi liquid, the two-channel Kondo effect. To bring this concept down to experimental test, we study nonequilibrium transport through a device realizing the charge two-channel Kondo critical point in a recent experiment by Iftikhar et al. [Nature (London) 526, 233 (2015)NATUAS0028-083610.1038/nature15384]. The shot noise at low voltages is predicted to result in a universal Fano factor e^{*}/e=1/2. This allows us to experimentally identify elementary transport processes of emergent fermions carrying half-integer charge.