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arXiv:cond-mat/9702080 · Physical Review Letters

Comment on ``Enhancement of the Tunneling Density of States in Tomonaga-Luttinger Liquids''

Michele Fabrizio, Alexander O. Gogolin

Published Jun 9, 1997• 30 citations
arXivHTMLPDF

Abstract

In a recent Physical Review Letter, Oreg and Finkel'stein (OF) have calculated the electron density of states (DOS) for tunneling into a repulsive Luttinger liquid close to the location of an impurity. The result of their calculation is a DOS which is enhanced with respect to the pure system, and moreover diverging for not too strong repulsion. In this Comment we intend to show that OF's calculation suffers from a subtle flaw which, being corrected, results into a DOS not only vanishing at zero frequency but in fact suppressed in comparison with the DOS of a pure Luttinger liquid.

DOI
10.1103/physrevlett.78.4527

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Oreg and Finkel'stein Reply:

Yuval Oreg, Alexander M. Finkel’stein

In their comment Fabrizio and Gogolin dispute our result of the enhancement of the tunneling density of states in a Tomonaga-Luttinger liquid at the location of a backward scattering defect [Phys. Rev. Lett. 76, 4230(1996); cond-mat/9601020]. They state that the anticommutativity of the fermion operators of the left and right moving electrons was not considered properly in the Letter. We show in the Reply that the result of the Letter can be reproduced following the Comment when its calculations are performed correctly. This clearly indicates that the question about the anticommutation relations was raised by Fabrizio and Gogolin without serious grounds.

arXiv:cond-mat/9707161•Physical Review Letters•Jun 9, 1997•10 citations

Enhancement of the Tunneling Density of States in Tomonaga-Luttinger Liquids

Yuval Oreg, Alexander M. Finkel’stein

We have calculated the tunneling density of states (DOS) at the location of a backward scattering defect for quantum wires and for edge state electrons in quantum Hall systems. A singular enhancement of the DOS arises as a result of the combined effect of multiple backward scattering together with a repulsive electron-electron interaction.

arXiv:cond-mat/9601020•Physical Review Letters•May 27, 1996•36 citations

Enhancement in tunneling density of states in a Luttinger liquid: Role of nonlocal interaction

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Power-law suppression of local electronic tunneling density of states (TDOS) in the zero-energy limit is a hallmark of the Luttinger liquid (LL) phase of the interacting one-dimensional electron system. We present a theoretical model which hosts the LL state with the surprising feature of enhancement rather than suppression in local TDOS originating from nonlocal and repulsive density-density interactions. Importantly, we find enhancement of TDOS in the manifold of parameter space where the system is stable in the renormalization group (RG) sense. We argue that enhancement of TDOS along with RG stability is possible only when the system has broken parity symmetry about the position of local TDOS enhancement. Such a model could be realized on the edge states of a bilayer quantum Hall system where both intralayer and interlayer density-density interactions are present mimicking the role of local and nonlocal interactions, respectively.

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Enhancement of tunneling density of states at a Y junction of spin- 12 Tomonaga–Luttinger liquid wires

Sougata Mardanya, Amit Agarwal

We calculate the tunneling density of states (TDOS) in a dissipationless three-wire junction of interacting spin-1/2 electrons, and find an anomalous enhancement of the TDOS in the zero-bias limit, even for repulsive interactions for several bosonic fixed points. This enhancement is physically related to the reflection of holes from the junction for incident electrons, and it occurs only in the vicinity of the junction ($x<{v}_{\mathrm{min}}/2\ensuremath{\omega}$, where ${v}_{\mathrm{min}}$ is the minimum of the velocity of charge or spin excitations and $\ensuremath{\omega}$ is the bias frequency), crossing over to the bulk value, which is always suppressed at larger distances. The TDOS exponent can be directly probed in an STM experiment by measuring the differential tunneling conductance as a function of either the bias voltage or temperature as done in C. Blumenstein et al., Nat. Phys. 7, 776 (2011).

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Reply to Skorik's Comment

Paul Fendley, Ludwig, A. W. W., Hubert Saleur

In a series of papers we combined the Bethe ansatz with a kinetic (Boltzmann) equation in order to compute exactly transport properties in a Luttinger liquid with an impurity. In a recent comment [cond-mat/9708163], Skorik claimed that while our results were correct in linear response, there was a ``serious flaw'' in our calculation at finite voltage. We explain here why Skorik's arguments are inappropriate, and that there is no flaw in our work [cond-mat/9408068; cond-mat/9505031; cond-mat/9503172].

arXiv:cond-mat/9710205•Oct 20, 1997•0 citations

Tunnel density of states in a Luttinger constriction

Yuli V. Nazarov, A. A. Odintsov, D. V. Averin

We study Luttinger constriction that is a finite region of interacting electrons adiabatically connected to the reservoirs of non-interacting electrons. We have shown that, in contrast to an infinite Luttinger liquid, the density of states (DOS) remains finite at the Fermi surface although it is strongly suppressed in comparison with the non-interacting value. The finite-size effects give rise to an additional staircase structure in the energy dependence of the DOS at higher energies.

Europhysics Letters (EPL)•Jan 20, 1997•13 citations
In a recent Physical Review Letter, Oreg and Finkel'stein (OF) have calculated the electron density of states (DOS) for tunneling into a repulsive Luttinger liquid close to the location of an impurity. The result of their calculation is a DOS which is enhanced with respect to the pure system, and moreover diverging for not too strong repulsion. In this Comment we intend to show that OF's calculation suffers from a subtle flaw which, being corrected, results into a DOS not only vanishing at zero frequency but in fact suppressed in comparison with the DOS of a pure Luttinger liquid.
In their comment Fabrizio and Gogolin dispute our result of the enhancement of the tunneling density of states in a Tomonaga-Luttinger liquid at the location of a backward scattering defect [Phys. Rev. Lett. 76, 4230(1996); cond-mat/9601020]. They state that the anticommutativity of the fermion operators of the left and right moving electrons was not considered properly in the Letter. We show in the Reply that the result of the Letter can be reproduced following the Comment when its calculations are performed correctly. This clearly indicates that the question about the anticommutation relations was raised by Fabrizio and Gogolin without serious grounds.
Power-law suppression of local electronic tunneling density of states (TDOS) in the zero-energy limit is a hallmark of the Luttinger liquid (LL) phase of the interacting one-dimensional electron system. We present a theoretical model which hosts the LL state with the surprising feature of enhancement rather than suppression in local TDOS originating from nonlocal and repulsive density-density interactions. Importantly, we find enhancement of TDOS in the manifold of parameter space where the system is stable in the renormalization group (RG) sense. We argue that enhancement of TDOS along with RG stability is possible only when the system has broken parity symmetry about the position of local TDOS enhancement. Such a model could be realized on the edge states of a bilayer quantum Hall system where both intralayer and interlayer density-density interactions are present mimicking the role of local and nonlocal interactions, respectively.
We calculate the tunneling density of states (TDOS) in a dissipationless three-wire junction of interacting spin-1/2 electrons, and find an anomalous enhancement of the TDOS in the zero-bias limit, even for repulsive interactions for several bosonic fixed points. This enhancement is physically related to the reflection of holes from the junction for incident electrons, and it occurs only in the vicinity of the junction ($x<{v}_{\mathrm{min}}/2\ensuremath{\omega}$, where vmin{v}_{\mathrm{min}}vmin​ is the minimum of the velocity of charge or spin excitations and $\ensuremath{\omega}$ is the bias frequency), crossing over to the bulk value, which is always suppressed at larger distances. The TDOS exponent can be directly probed in an STM experiment by measuring the differential tunneling conductance as a function of either the bias voltage or temperature as done in C. Blumenstein et al., Nat. Phys. 7, 776 (2011).
In a series of papers we combined the Bethe ansatz with a kinetic (Boltzmann) equation in order to compute exactly transport properties in a Luttinger liquid with an impurity. In a recent comment [cond-mat/9708163], Skorik claimed that while our results were correct in linear response, there was a ``serious flaw'' in our calculation at finite voltage. We explain here why Skorik's arguments are inappropriate, and that there is no flaw in our work [cond-mat/9408068; cond-mat/9505031; cond-mat/9503172].