May 23, 2024
One-dimensional Luttinger liquids in a two-dimensional moiré lattice – Nature

One-dimensional Luttinger liquids in a two-dimensional moiré lattice – Nature

  • Giamarchi, T. Quantum Physics in One Dimension (Oxford Univ. Press, 2003).

  • Wen, X. G. Metallic non-Fermi-liquid fixed point in two and higher dimensions. Phys. Rev. B 42, 6623–6630 (1990).

    ADS 
    CAS 

    Google Scholar
     

  • Emery, V. J., Fradkin, E., Kivelson, S. A. & Lubensky, T. C. Quantum theory of the smectic metal state in stripe phases. Phys. Rev. Lett. 85, 2160–2163 (2000).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Sondhi, S. L. & Yang, K. Sliding phases via magnetic fields. Phys. Rev. B 63, 054430 (2001).

    ADS 

    Google Scholar
     

  • Vishwanath, A. & Carpentier, D. Two-dimensional anisotropic non-Fermi-liquid phase of coupled Luttinger liquids. Phys. Rev. Lett. 86, 676–679 (2001).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Mukhopadhyay, R., Kane, C. L. & Lubensky, T. C. Sliding Luttinger liquid phases. Phys. Rev. B 64, 045120 (2001).

    ADS 

    Google Scholar
     

  • Kane, C. L., Mukhopadhyay, R. & Lubensky, T. C. Fractional quantum Hall effect in an array of quantum wires. Phys. Rev. Lett. 88, 036401 (2002).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Teo, J. C. Y. & Kane, C. L. From Luttinger liquid to non-Abelian quantum Hall states. Phys. Rev. B 89, 085101 (2014).

    ADS 

    Google Scholar
     

  • Tam, P. M. & Kane, C. L. Nondiagonal anisotropic quantum Hall states. Phys. Rev. B 103, 035142 (2021).

    ADS 
    CAS 

    Google Scholar
     

  • Neupert, T., Chamon, C., Mudry, C. & Thomale, R. Wire deconstructionism of two-dimensional topological phases. Phys. Rev. B 90, 205101 (2014).

    ADS 

    Google Scholar
     

  • Iadecola, T., Neupert, T., Chamon, C. & Mudry, C. Wire constructions of Abelian topological phases in three or more dimensions. Phys. Rev. B 93, 195136 (2016).

    ADS 

    Google Scholar
     

  • Meng, T., Neupert, T., Greiter, M. & Thomale, R. Coupled-wire construction of chiral spin liquids. Phys. Rev. B 91, 241106 (2015).

    ADS 

    Google Scholar
     

  • Patel, A. A. & Chowdhury, D. Two-dimensional spin liquids with Z2 topological order in an array of quantum wires. Phys. Rev. B 94, 195130 (2016).

    ADS 

    Google Scholar
     

  • Kennes, D. M., Xian, L., Claassen, M. & Rubio, A. One-dimensional flat bands in twisted bilayer germanium selenide. Nat. Commun. 11, 1124 (2020).

    ADS 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Ali, M. N. et al. Large, non-saturating magnetoresistance in WTe2. Nature 514, 205–208 (2014).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Wang, P. et al. Landau quantization and highly mobile fermions in an insulator. Nature 589, 225–229 (2021).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Jia, Y. et al. Evidence for a monolayer excitonic insulator. Nat. Phys. 18, 87–93 (2022).

    CAS 

    Google Scholar
     

  • Bockrath, M. et al. Luttinger-liquid behaviour in carbon nanotubes. Nature 397, 598–601 (1999).

    ADS 
    CAS 

    Google Scholar
     

  • Yao, Z., Postma, H. W. C., Balents, L. & Dekker, C. Carbon nanotube intramolecular junctions. Nature 402, 273–276 (1999).

    ADS 
    CAS 

    Google Scholar
     

  • Qian, X., Liu, J., Fu, L. & Li, J. Quantum spin Hall effect in two-dimensional transition metal dichalcogenides. Science 346, 1344–1347 (2014).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Fei, Z. et al. Edge conduction in monolayer WTe2. Nat. Phys. 13, 677–682 (2017).

    CAS 

    Google Scholar
     

  • Tang, S. et al. Quantum spin Hall state in monolayer 1T′-WTe2. Nat. Phys. 13, 683–687 (2017).

    CAS 

    Google Scholar
     

  • Wu, S. et al. Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal. Science 359, 76–79 (2018).

    ADS 
    MathSciNet 
    CAS 
    PubMed 
    MATH 

    Google Scholar
     

  • Sajadi, E. et al. Gate-induced superconductivity in a monolayer topological insulator. Science 362, 922–925 (2018).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Fatemi, V. et al. Electrically tunable low-density superconductivity in a monolayer topological insulator. Science 362, 926–929 (2018).

    ADS 
    MathSciNet 
    CAS 
    PubMed 

    Google Scholar
     

  • Jung, J., Raoux, A., Qiao, Z. & MacDonald, A. H. Ab initio theory of moiré superlattice bands in layered two-dimensional materials. Phys. Rev. B 89, 205414 (2014).

    ADS 

    Google Scholar
     

  • Levitov, S. & Shytov, A. V. Semiclassical theory of the Coulomb anomaly. J. Exp. Theor. Phys. Lett. 66, 214–221 (1997).


    Google Scholar
     

  • Bartosch, L. & Kopietz, P. Zero bias anomaly in the density of states of low-dimensional metals. Eur. Phys. J. B 28, 29–36 (2002).

    ADS 
    CAS 

    Google Scholar
     

  • Rodin, A. S. & Fogler, M. M. Apparent power-law behavior of conductance in disordered quasi-one-dimensional systems. Phys. Rev. Lett. 105, 106801 (2010).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Ishii, H. et al. Direct observation of Tomonaga–Luttinger-liquid state in carbon nanotubes at low temperatures. Nature 426, 540–544 (2003).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Deshpande, V. V., Bockrath, M., Glazman, L. I. & Yacoby, A. Electron liquids and solids in one dimension. Nature 464, 209–216 (2010).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Auslaender, O. M. et al. Spin-charge separation and localization in one dimension. Science 308, 88–92 (2005).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Sato, Y. et al. Strong electron-electron interactions of a Tomonaga-Luttinger liquid observed in InAs quantum wires. Phys. Rev. B 99, 155304 (2019).

    ADS 
    CAS 

    Google Scholar
     

  • Glattli, D. C. In The Quantum Hall Effect: Poincaré Seminar 2004 (eds. Douçot, B. et al.) 163–197 (Birkhäuser, 2005); https://doi.org/10.1007/3-7643-7393-8_5.

  • Li, T. et al. Observation of a helical Luttinger liquid in InAs/GaSb quantum spin Hall edges. Phys. Rev. Lett. 115, 136804 (2015).

    ADS 
    PubMed 

    Google Scholar
     

  • Stühler, R. et al. Tomonaga–Luttinger liquid in the edge channels of a quantum spin Hall insulator. Nat. Phys. 16, 47–51 (2020).


    Google Scholar
     

  • Biermann, S., Georges, A., Giamarchi, T. & Lichtenstein, A. In Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems (eds. Lerner, I. V et al.) 81–102 (Springer, 2002); https://doi.org/10.1007/978-94-010-0530-2_5.

  • Dudy, L., Aulbach, J., Wagner, T., Schäfer, J. & Claessen, R. One-dimensional quantum matter: gold-induced nanowires on semiconductor surfaces. J. Phys. Condens. Matter 29, 433001 (2017).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Clarke, D. G., Strong, S. P. & Anderson, P. W. Incoherence of single particle hopping between Luttinger liquids. Phys. Rev. Lett. 72, 3218–3221 (1994).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Georges, A., Giamarchi, T. & Sandler, N. Interchain conductivity of coupled Luttinger liquids and organic conductors. Phys. Rev. B 61, 16393–16396 (2000).

    ADS 
    CAS 

    Google Scholar
     

  • Ali, M. N. et al. Correlation of crystal quality and extreme magnetoresistance of WTe2. Europhys. Lett. 110, 67002 (2015).

    ADS 

    Google Scholar
     

  • Kim, K. et al. Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene. Proc. Natl Acad. Sci. USA 114, 3364–3369 (2017).

    ADS 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Ponomarenko, L. A. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Simon, S. H. Comment on “Evidence for an anisotropic state of two-dimensional electrons in high Landau levels”. Phys. Rev. Lett. 83, 4223–4223 (1999).

    ADS 
    CAS 

    Google Scholar
     

  • Lopatin, A., Georges, A. & Giamarchi, T. Hall effect and interchain magneto-optical properties of coupled Luttinger liquids. Phys. Rev. B 63, 075109 (2001).

    ADS 

    Google Scholar
     

  • Giannozzi, P. et al. Advanced capabilities for materials modelling with Quantum ESPRESSO. J. Phys. Condens. Matter 29, 465901 (2017).

    CAS 
    PubMed 

    Google Scholar
     

  • van Setten, M. J. et al. The PseudoDojo: training and grading a 85 element optimized norm-conserving pseudopotential table. Comput. Phys. Commun. 226, 39–54 (2018).

    ADS 

    Google Scholar
     

  • Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).

    ADS 
    PubMed 

    Google Scholar
     

  • Naik, M. H. & Jain, M. Ultraflatbands and shear solitons in moiré patterns of twisted bilayer transition metal dichalcogenides. Phys. Rev. Lett. 121, 266401 (2018).

    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Nam, N. N. T. & Koshino, M. Lattice relaxation and energy band modulation in twisted bilayer graphene. Phys. Rev. B 96, 075311 (2017).

    ADS 

    Google Scholar
     

  • Source link