Residual conductance of correlated one-dimensional nanosystems: A numerical approach

Molina, Rafael A.; Schmitteckert, Peter; Weinmann, Dietmar; Jalabert, Rodolfo A.; Ingold, Gert‐Ludwig; Pichard, Jean‐Louis

doi:10.1140/epjb/e2004-00176-y

Cited by 23 publications

(46 citation statements)

References 44 publications

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“…Having always free fermions as t d varies means that the T = 0 scattering properties of an interacting region embedded inside an infinite non-interacting lattice are those of an effective non-interacting system with renormalized parameters, in agreement with the DMRG study of the persistent current given in Ref. 2. We underline that those effective non-interacting spectra describe the T = 0 limit, while a description of the low-temperature dependence of the conductance requires effective Hamiltonians of Landau quasiparticles with residual quasiparticle interactions.…”

Section: Role Of the Internal Hopping At T =supporting

confidence: 81%

Universal scaling of the quantum conductance of an inversion-symmetric interacting model

Freyn

Pichard

2010

Phys. Rev. B

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We consider quantum transport of spinless fermions in a 1D lattice embedding an interacting region (two sites with inter-site repulsion U and inter-site hopping t d , coupled to leads by hopping terms tc). Using the numerical renormalization group for the particle-hole symmetric case, we study the quantum conductance g as a function of the inter-site hopping t d . The interacting region, which is perfectly reflecting when t d → 0 or t d → ∞, becomes perfectly transmitting if t d takes an intermediate value τ (U, tc) which defines the characteristic energy of this interacting model. When t d < tc √ U , g is given by a universal function of the dimensionless ratio X = t d /τ . This universality characterizes the non-interacting regime where τ = t 2 c , the perturbative regime (U < t 2 c ) where τ can be obtained using Hartree-Fock theory, and the non-perturbative regime (U > t 2 c ) where τ is twice the characteristic temperature TK of an orbital Kondo effect induced by the inversion symmetry. When t d < τ , the expression g(X) = 4(X + X −1 ) −2 valid without interaction describes also the conductance in the presence of the interaction. To obtain those results, we map this spinless model onto an Anderson model with spins, where the quantum impurity is at the end point of a semi-infinite 1D lead and where t d plays the role of a magnetic field h. This allows us to describe g(t d ) using exact results obtained for the magnetization m(h) of the Anderson model at zero temperature. We expect this universal scaling to be valid also in models with 2D leads, and observable using 2D semi-conductor heterostructures and an interacting region made of two identical quantum dots with strong capacitive inter-dot coupling and connected via a tunable quantum point contact.

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Section: Role Of the Internal Hopping At T =supporting

confidence: 81%

Universal scaling of the quantum conductance of an inversion-symmetric interacting model

Freyn

Pichard

2010

Phys. Rev. B

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“…This task will be hopeless for an isolated system where electrons interact with a large interaction strength U , but becomes possible when leads where electrons do not interact are attached to it. This has been numerically demonstrated in previous works [5,6] using the embedding method, which allows to extract [5,6,7,8,9,10,11] the effective coefficient |t(E F , U )| 2 from the persistent current of a large noninteracting ring embedding the many-body scatterer. Using the same method, we show that it is not the region where the electrons interact which acts as an effective one-body scatterer with renormalized parameters, but a larger region where the many-body scatterer induces correlations.…”

Section: Introductionmentioning

confidence: 68%

Interacting electron systems between Fermi leads: effective one-body transmissions and correlation clouds

2005

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In order to extend the Landauer formulation of quantum transport to correlated fermions, we consider a spinless system in which charge carriers interact, connected to two reservoirs by non-interacting one-dimensional leads. We show that the mapping of the embedded many-body scatterer onto an effective one-body scatterer with interaction-dependent parameters requires to include parts of the attached leads where the interacting region induces power law correlations. Physically, this gives a dependence of the conductance of a mesoscopic scatterer upon the nature of the used leads which is due to electron interactions inside the scatterer. To show this, we consider two identical correlated systems connected by a noninteracting lead of length LC. We demonstrate that the effective one-body transmission of the ensemble deviates by an amount A/LC from the behavior obtained assuming an effective one-body description for each element and the combination law of scatterers in series. A is maximum for the interaction strength U around which the Luttinger liquid becomes a Mott insulator in the used model, and vanishes when U → 0 and U → ∞. Analogies with the Kondo problem are pointed out.

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“…We underline that this non local effect is a pure many-body effect that one neglects when one takes non interacting models for describing quantum transport. This non local effect was first numerically discovered in a previous work [8], using the embedding method [9,10,11,12,13,14,15,16] and the DMRG algorithm [17,18] valid for one dimensional fermions. In this work, we give a simple theory of this effect based on the HF approximation, which turns out to qualitatively describe this non local effect for all values of U , including its suppression in the limit when U → ∞.…”

Section: Introductionmentioning

confidence: 80%

“…Exact values of the conductance of a one dimensional scatterer in which electrons interact can be obtained using the embedding method and the DMRG algorithm, as explained in previous works [8,9,10,11]. We have compared in Fig.…”

Section: Comparison With Exact Dmrg Resultsmentioning

confidence: 99%

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Conductance of nano-systems with interactions coupled via conduction electrons: effect of indirect exchange interactions

2006

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Abstract. A nano-system in which electrons interact and in contact with Fermi leads gives rise to an effective one-body scattering which depends on the presence of other scatterers in the attached leads. This non local effect is a pure many-body effect that one neglects when one takes non interacting models for describing quantum transport. This enhances the non-local character of the quantum conductance by exchange interactions of a type similar to the RKKY-interaction between local magnetic moments. A theoretical study of this effect is given assuming the Hartree-Fock approximation for spinless fermions of Fermi momentum kF in an infinite chain embedding two scatterers separated by a segment of length Lc. The fermions interact only inside the two scatterers. The dependence of one scatterer onto the other exhibits oscillations of period π/kF which decay as 1/Lc and which are suppressed when Lc exceeds the thermal length LT.

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Residual conductance of correlated one-dimensional nanosystems: A numerical approach

Cited by 23 publications

References 44 publications

Universal scaling of the quantum conductance of an inversion-symmetric interacting model

Universal scaling of the quantum conductance of an inversion-symmetric interacting model

Interacting electron systems between Fermi leads: effective one-body transmissions and correlation clouds

Conductance of nano-systems with interactions coupled via conduction electrons: effect of indirect exchange interactions

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