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arXiv:cond-mat/9601020 · Physical Review Letters

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

Yuval Oreg, Alexander M. Finkel’stein

Published May 27, 1996• 36 citations
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Abstract

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.

DOI
10.1103/physrevlett.76.4230

Related papers

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

Michele Fabrizio, Alexander O. Gogolin

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.

arXiv:cond-mat/9702080•Physical Review Letters•Jun 9, 1997•30 citations

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).

arXiv:1502.02774•Physical Review B•Jul 27, 2015•11 citations

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

Amulya Ratnakar, Sourin Das

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.

arXiv:2012.13414•Physical review. B./Physical review. B•Jul 1, 2021•2 citations

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

Tunneling density of states in a Y junction of Tomonaga-Luttinger liquid wires: A density matrix renormalization group study

Monalisa Singh Roy, Manoranjan Kumar, Sourin Das

It is well known that the pristine bulk of an interacting one-dimensional system in Tomonaga-Luttinger liquid (TLL) phase shows power law suppression of quasiparticle tunneling amplitude for all values of TLL parameter $g$, in the zero-energy limit. We perform a density matrix renormalization group (DMRG) study of a fully symmetric Y junction of TLL wires and observe an anomalous enhancement of the tunneling density of states (TDOS) in the vicinity of the junction for both (a) interacting bosons case and (b) interacting fermions case, when $g>1$. We also observe suppression of TDOS for $g<1$ for both bosonic and fermionic cases. We find that the TDOS enhancements follow different power laws for bosonic and fermionic cases which suggests that these represent distinct fixed points, owing to statistical correlations that play an important role at the Y junction. Analysis of static conductance for the junction indicates that the fixed point for $1<g<3$ resembles the mysterious $M$ fixed point of Y junction predicted by Oshikawa, Chamon, and Affleck [J. Stat. Mech. (2006) P02008]. We also show that the TDOS enhancement spans over a length scale of $\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}1}$ from the junction, for $1<g<3$.

arXiv:1912.13040•Physical review. B./Physical review. B•Jul 17, 2020•3 citations

Multichannel impurity scattering in a Tomonaga-Luttinger liquid

Yu-Liang Liu

Using an elementary method, we demonstrate that (1) the duality of the correlation exponents near impurity site $x=0$ between ultraviolet and infrared fixed points is also valid for channel number larger than one; (2) the infrared fixed points ${\ensuremath{\delta}}_{c}^{i}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ do not correspond to two real half-infinity Tomonaga-Luttinger liquids even if the conductance is zero; (3) the electron's density of state at $x=0$ is enhanced compared with its neighbor ones; (4) as channel number is larger than (or equal to) two, the Fermi-edge singularity induced by backward scattering will be swept off by even small repulsive interaction of the electrons.

Physical review. B, Condensed matter•May 15, 1998•0 citations
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.
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.
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).
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.
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.
It is well known that the pristine bulk of an interacting one-dimensional system in Tomonaga-Luttinger liquid (TLL) phase shows power law suppression of quasiparticle tunneling amplitude for all values of TLL parameter ggg, in the zero-energy limit. We perform a density matrix renormalization group (DMRG) study of a fully symmetric Y junction of TLL wires and observe an anomalous enhancement of the tunneling density of states (TDOS) in the vicinity of the junction for both (a) interacting bosons case and (b) interacting fermions case, when g>1g>1g>1. We also observe suppression of TDOS for g<1g<1g<1 for both bosonic and fermionic cases. We find that the TDOS enhancements follow different power laws for bosonic and fermionic cases which suggests that these represent distinct fixed points, owing to statistical correlations that play an important role at the Y junction. Analysis of static conductance for the junction indicates that the fixed point for 1<g<31<g<31<g<3 resembles the mysterious MMM fixed point of Y junction predicted by Oshikawa, Chamon, and Affleck [J. Stat. Mech. (2006) P02008]. We also show that the TDOS enhancement spans over a length scale of $\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}1}$ from the junction, for 1<g<31<g<31<g<3.
Using an elementary method, we demonstrate that (1) the duality of the correlation exponents near impurity site x=0x=0x=0 between ultraviolet and infrared fixed points is also valid for channel number larger than one; (2) the infrared fixed points ${\ensuremath{\delta}}_{c}^{i}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ do not correspond to two real half-infinity Tomonaga-Luttinger liquids even if the conductance is zero; (3) the electron's density of state at x=0x=0x=0 is enhanced compared with its neighbor ones; (4) as channel number is larger than (or equal to) two, the Fermi-edge singularity induced by backward scattering will be swept off by even small repulsive interaction of the electrons.