Transport properties of a Luttinger liquid with a cluster of impurities

Das, Joy Prakash; Setlur, Girish S.

doi:10.1016/j.physe.2019.02.003

Cited by 3 publications

(4 citation statements)

References 30 publications

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“…and obtained to be D(ω)∼ω. Recalculating the exponent in equation(18) for the spinless case (double of this exponent) and strong impurity (| | = R agreement with the works of Delft and Schoeller[3], Fabrizio and Gogolin[44], Furusaki[45], etc.…”

supporting

confidence: 77%

“…Consider the Luttinger parameter g (also called K ρ in the literature) which in the present work is equal to v F /v h . From equation (18), the DDOS exponent for points far away from the impurity can be written in terms of g as…”

Section: Far Away From the Impuritymentioning

confidence: 99%

“…Once the Green function of a given system is obtained, it may be used to predict different physical phenomena occurring in the system. Typical physical phenomena studied in Luttinger liquids with impurities includes Friedel oscillations [15], conductance [16][17][18][19][20][21], Kondo effect [22,23] and so on. In the famous work by Kane and Fisher [24], it has been shown how impurities can cause extreme effects in the transport properties of constituent particles based on the nature of mutual interaction between them, viz., attractive or repulsive.…”

Section: Introductionmentioning

confidence: 99%

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Friedel oscillations and dynamical density of states of an inhomogeneous Luttinger liquid

2020

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In this work, the four-point Green functions relevant to the study of Friedel oscillations are calculated for a Luttinger liquid with a cluster of impurities around an origin using the powerful Non chiral bosonization technique (NCBT). The two-point functions obtained using the same method are used to calculate the dynamical density of states (DDOS), which exhibits a power law in energy and closed analytical expressions for the DDOS exponent is calculated. These results interpolates between the weak barrier and weak link cases which are typically studied in the literature. The dependence of the DDOS on the nature of interactions and the strength of the impurity clusters are highlighted. Finally the special case of the Luttinger parameter g=1/2 is studied and compared with existing results.

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supporting

confidence: 77%

Section: Far Away From the Impuritymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Friedel oscillations and dynamical density of states of an inhomogeneous Luttinger liquid

2020

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“…Also it is unlikely that such numerical methods are able to capture the most singular parts of the Greenʼs functions that NCBT provides. The NCBT results have already been validated analytically using the Schwinger-Dyson equation [22] and a host of other ways as shown in our group's published works [21,23,[42][43][44][45].…”

Section: Introductionmentioning

confidence: 76%

Density-density correlation function of strongly inhomogeneous Luttinger liquids

Babu¹,

Das²,

Setlur³

2020

Phys. Scr.

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In this work, we show in pedagogical detail that the most singular contributions to the slow part of the asymptotic density-density correlation function of Luttinger liquids with fermions interacting mutually with only short-range forward scattering and also with localised scalar static impurities (where backward scattering takes place) has a compact analytical expression in terms of simple functions that have second order poles and involve only the scale-independent bare transmission and reflection coefficients. This proof uses conventional fermionic perturbation theory resummed to all orders, together with the idea that for such systems, the (connected) moments of the density operator all vanish beyond the second order—the odd ones vanish identically and the higher order even moments are less singular than the second order moment which is the only one included. This important result is the crucial input to the recently introduced ‘Non-Chiral Bosonization Technique’ (NCBT) to study such systems. The results of NCBT cannot be easily compared with the results obtained using conventional bosonization as the former only extracts the most singular parts of the correlation functions albeit for arbitrary impurity strengths and mutual interactions. The latter, ambitiously attempts to study all the parts of the asymptotic correlation functions and is thereby unable to find simple analytical expressions and is forced to operate in the vicinity of the homogeneous system or the half line (the opposite extreme). For a fully homogeneous system or its antithesis viz. the half-line, all the higher order connected moments of the density vanish identically which means the results of chiral bosonization and NCBT ought to be the same and indeed they are.

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Conductance of inhomogeneous Luttinger liquids with a finite bandwidth

Das

Setlur

2019

Physics Letters A

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The finite-bandwidth conductance of a Luttinger liquid (LL) with a cluster of impurities is studied and its variation with respect to temperature is shown. The calculations are done using the correlation functions obtained using the powerful non-chiral bosonization technique (NCBT) . The results are compared with those obtained by Matveev, Yue and Glazman [K. Matveev et al., Phys. Rev. Lett. 71, 3351 (1993)] who deal with a weakly interacting LL. By contrast, NCBT correctly provides the conductance for all values of the interaction strength (as well as the sign). In addition to finding perfect agreement with the results of Matveev et al. for both weakly repulsive and weakly attractive mutual interactions, we are also able to probe novel physics seen when the repulsion is strong -in the form of a weakly temperature dependent conductance when there is a definite relationship between the transmission amplitude of the non-interacting system and the holon velocity. Secondly, an unusual high conductance for strongly repulsive mutual interactions is observed for a weak barrier at low temperatures. Lastly, inclusion of backward scattering leads to the non-monotonic temperature dependence of conductance when dealing with fermions with spin. This work is also important as a validation of the NCBT itself. arXiv:1809.05484v3 [cond-mat.str-el]

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Transport properties of a Luttinger liquid with a cluster of impurities

Cited by 3 publications

References 30 publications

Friedel oscillations and dynamical density of states of an inhomogeneous Luttinger liquid

Friedel oscillations and dynamical density of states of an inhomogeneous Luttinger liquid

Density-density correlation function of strongly inhomogeneous Luttinger liquids

Conductance of inhomogeneous Luttinger liquids with a finite bandwidth

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