Spectral properties of Luttinger liquids: A comparative analysis of regular, helical, and spiral Luttinger liquids

Braunecker, Bernd; Bena, Cristina; Simon, Pascal

doi:10.1103/physrevb.85.035136

Cited by 39 publications

(61 citation statements)

References 118 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, {·, ·} denotes the anticommutator. The gap seen in A ψ (k, ω) would also be visible in the d.c. conductance of the wire, and the tunneling density of states, 30,31 …”

Section: Resultsmentioning

confidence: 99%

Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields

et al. 2016

View full text Add to dashboard Cite

A partially gapped spectrum due to the application of a magnetic field is one of the main probes of Rashba spin-orbit coupling in nanowires. Such a "helical gap" manifests itself in the linear conductance, as well as in dynamic response functions such as the spectral function, the structure factor, or the tunnelling density of states. In this paper, we investigate theoretically the signature of the helical gap in these observables with a particular focus on the interplay between Rashba spin-orbit coupling and electron-electron interactions. We show that in a quasi-one-dimensional wire, interactions can open a helical gap even without magnetic field. We calculate the dynamic response functions using bosonization, a renormalization group analysis, and the exact form factors of the emerging sine-Gordon model. For special interaction strengths, we verify our results by refermionization. We show how the two types of helical gaps, caused by magnetic fields or interactions, can be distinguished in experiments.

show abstract

“…Moreover, {·, ·} denotes the anticommutator. The gap seen in A ψ (k, ω) would also be visible in the d.c. conductance of the wire, and the tunneling density of states, 30,31 …”

Section: Resultsmentioning

confidence: 99%

Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields

et al. 2016

View full text Add to dashboard Cite

show abstract

“…For instance, Luttinger liquids are expected to exhibit spin-charge separation, where charge and spin degrees of freedom act independently 8 ; spin-charge separation has been convincingly observed via photoemission experiments in artificially created one-dimensional structures 9 . Likewise, the density of states around the Fermi level is predicted to show a distinctive power law behavior 10 ; this was also observed in an artificially created 1D chain 11 . Other observations of Luttinger liquid-like behavior, however, have been made not on actual one-dimensional chains but rather on two-dimensional collections of one-dimensional systems such as in the polymer films that motivated this work 1 or on highly anisotropic three-dimensional crystals [12][13][14] ; it is not immediately clear that the results of these experiments should be directly compared to theories of single Luttinger liquids.…”

Section: Introductionmentioning

confidence: 60%

Electrical and thermal transport in the quasiatomic limit of coupled Luttinger liquids

2017

View full text Add to dashboard Cite

We introduce a new model for quasi one-dimensional materials, motivated by intriguing but not yet well-understood experiments that have shown two-dimensional polymer films to be promising materials for thermoelectric devices. We consider a two-dimensional material consisting of many one-dimensional systems, each treated as a Luttinger liquid, with weak (incoherent) coupling between them. This approximation of strong interactions within each one-dimensional chain and weak coupling between them is the "quasi-atomic limit." We find integral expressions for the (interchain) transport coefficients, including the electrical and thermal conductivities and the thermopower, and we extract their power law dependencies on temperature. Luttinger liquid physics is manifested in a violation of the Wiedemann-Franz law; the Lorenz number is larger than the Fermi liquid value by a factor between γ 2 and γ 4 , where γ ≥ 1 is a measure of the electron-electron interaction strength in the system.

show abstract

“…Note that in the conventional spinful Luttinger liquids where K s = 1, the above correlation functions get modified accordingly 19,32,33 .…”

Section: The Topological Edge States (Ti) Phasementioning

confidence: 99%

“…14 via Quantum Monte Carlo and dynamical mean-field approaches, the helical edge states are stable up to a finite Hubbard interaction, and a gaped spin-liquid phase was predicted in the phase diagram of the KM Hubbard model at half filling for small to intermediate range of U . Moreover, the 1D Luttinger liquid physics with power-law correlations for the helical edge states has been studied numerically 16 as well as analytically 19 in the framework of the KM Hubbard model. Meanwhile, the doping effect on the KM Hubbard model was addressed in Ref.…”

mentioning

confidence: 99%

Kane-Mele Hubbard model on a zigzag ribbon: Stability of the topological edge states and quantum phase transitions

2014

View full text Add to dashboard Cite

We study the quantum phases and phase transitions of the Kane-Mele Hubbard (KMH) model on a zigzag ribbon of honeycomb lattice at a finite size via the weak-coupling renormalization group (RG) approach. In the non-interacting limit, the KM model is known to support topological edge states where electrons show helical property with orientations of the spin and momentum being locked. The effective inter-edge hopping terms are generated due to finite-size effect. In the presence of an on-site Coulomb repulsive interaction and the inter-edge hoppings, special focus is put on the stability of the topological edge states (TI phase) in the KMH model against (i) the charge and spin gaped (II) phase, (ii) the charge gaped but spin gapless (IC) phase and (iii) the spin gaped but charge gapless (CI) phase depending on the number (even/odd) of the zigzag ribbons, doping level (electron filling factor) and the ratio of the Coulomb interaction to the inter-edge tunneling. We discuss different phase diagrams for even and odd numbers of zigzag ribbons. We find the TI-CI, II-IC, and II-CI quantum phase transitions are of the Kosterlitz-Thouless (KT) type. By computing various correlation functions, we further analyze the nature and leading instabilities of these phases.

show abstract

Spectral properties of Luttinger liquids: A comparative analysis of regular, helical, and spiral Luttinger liquids

Cited by 39 publications

References 118 publications

Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields

Dynamic response functions and helical gaps in interacting Rashba nanowires with and without magnetic fields

Electrical and thermal transport in the quasiatomic limit of coupled Luttinger liquids

Kane-Mele Hubbard model on a zigzag ribbon: Stability of the topological edge states and quantum phase transitions

Contact Info

Product

Resources

About