Wednesday, November 27, 2024
No menu items!
HomeNatureDirect visualization of relativistic quantum scars in graphene quantum dots

Direct visualization of relativistic quantum scars in graphene quantum dots

  • Heller, E. J. Bound-state eigenfunctions of classically chaotic Hamiltonian systems: scars of periodic orbits. Phys. Rev. Lett. 53, 1515–1518 (1984).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Stöckmann, H.-J. Quantum Chaos: An Introduction (American Association of Physics Teachers, 2000).

  • Gutzwiller, M. C. Chaos in Classical and Quantum Mechanics Vol. 1 (Springer Science & Business Media, 2013).

  • Heller, E., Crommie, M., Lutz, C. & Eigler, D. Scattering and absorption of surface electron waves in quantum corrals. Nature 369, 464–466 (1994).

    Article 
    ADS 

    Google Scholar
     

  • Crook, R. et al. Imaging fractal conductance fluctuations and scarred wave functions in a quantum billiard. Phys. Rev. Lett. 91, 246803 (2003).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Martins, F. et al. Imaging electron wave functions inside open quantum rings. Phys. Rev. Lett. 99, 136807 (2007).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Burke, A. et al. Periodic scarred states in open quantum dots as evidence of quantum Darwinism. Phys. Rev. Lett. 104, 176801 (2010).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Aoki, N. et al. Direct imaging of electron states in open quantum dots. Phys. Rev. Lett. 108, 136804 (2012).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Cabosart, D. et al. Recurrent quantum scars in a mesoscopic graphene ring. Nano Lett. 17, 1344–1349 (2017).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Ge, Z. et al. Imaging quantum interference in stadium-shaped monolayer and bilayer graphene quantum dots. Nano Lett. 21, 8993–8998 (2021).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Lee, J. et al. Imaging electrostatically confined Dirac fermions in graphene quantum dots. Nat. Phys. 12, 1032–1036 (2016).

    Article 
    CAS 

    Google Scholar
     

  • Ge, Z. et al. Visualization and manipulation of bilayer graphene quantum dots with broken rotational symmetry and nontrivial topology. Nano Lett. 20, 8682–8688 (2020).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Huang, L., Lai, Y.-C., Ferry, D. K., Goodnick, S. M. & Akis, R. Relativistic quantum scars. Phys. Rev. Lett. 103, 054101 (2009).

    Article 
    ADS 
    PubMed 

    Google Scholar
     

  • Huang, L., Xu, H.-Y., Grebogi, C. & Lai, Y.-C. Relativistic quantum chaos. Phys. Rep. 753, 1–128 (2018).

    Article 
    ADS 
    MathSciNet 
    CAS 

    Google Scholar
     

  • Luukko, P. J. et al. Strong quantum scarring by local impurities. Sci. Rep. 6, 37656 (2016).

    Article 
    ADS 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Keski-Rahkonen, J., Luukko, P. J., Kaplan, L., Heller, E. & Räsänen, E. Controllable quantum scars in semiconductor quantum dots. Phys. Rev. B 96, 094204 (2017).

    Article 
    ADS 

    Google Scholar
     

  • Keski-Rahkonen, J., Ruhanen, A., Heller, E. & Räsänen, E. Quantum Lissajous scars. Phys. Rev. Lett. 123, 214101 (2019).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Xu, H., Huang, L., Lai, Y.-C. & Grebogi, C. Chiral scars in chaotic dirac fermion systems. Phys. Rev. Lett. 110, 064102 (2013).

    Article 
    ADS 
    PubMed 

    Google Scholar
     

  • Song, M.-Y., Li, Z.-Y., Xu, H.-Y., Huang, L. & Lai, Y.-C. Quantization of massive Dirac billiards and unification of nonrelativistic and relativistic chiral quantum scars. Phys. Rev. Res. 1, 033008 (2019).

    Article 
    CAS 

    Google Scholar
     

  • Keski-Rahkonen, J., Graf, A. & Heller, E. Antiscarring in chaotic quantum wells. Preprint at https://arxiv.org/abs/2403.18081 (2024).

  • Berry, M. Quantum chaology, not quantum chaos. Phys. Scr. 40, 335 (1989).

    Article 
    ADS 
    MathSciNet 
    CAS 

    Google Scholar
     

  • Einstein, A. Zum quantensatz von Sommerfeld und Epstein. Verh. Dtsch. Phys. Ges. 19, 82–92 (1917).

  • Stone, A. D. Einstein’s unknown insight and the problem of quantizing chaos. Phys. Today 58, 37 (2005).

    Article 

    Google Scholar
     

  • Pilatowsky-Cameo, S. et al. Ubiquitous quantum scarring does not prevent ergodicity. Nat. Commun. 12, 852 (2021).

    Article 
    ADS 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Hummel, Q., Richter, K. & Schlagheck, P. Genuine many-body quantum scars along unstable modes in Bose–Hubbard systems. Phys. Rev. Lett. 130, 250402 (2023).

    Article 
    ADS 
    MathSciNet 
    CAS 
    PubMed 

    Google Scholar
     

  • Evrard, B., Pizzi, A., Mistakidis, S. I. & Dag, C. B. Quantum scars and regular eigenstates in a chaotic spinor condensate. Phys. Rev. Lett. 132, 020401 (2024).

    Article 
    ADS 
    MathSciNet 
    CAS 
    PubMed 

    Google Scholar
     

  • Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Heller, E. J. The Semiclassical Way to Dynamics and Spectroscopy (Princeton Univ. Press, 2018).

  • Zelditch, S. Uniform distribution of eigenfunctions on compact hyperbolic surfaces. Duke Math. J. 55, 919–941 (1987).

    Article 
    MathSciNet 

    Google Scholar
     

  • Bohigas, O., Giannoni, M.-J. & Schmit, C. Characterization of chaotic quantum spectra and universality of level fluctuation laws. Phys. Rev. Lett. 52, 1 (1984).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Sridhar, S. Experimental observation of scarred eigenfunctions of chaotic microwave cavities. Phys. Rev. Lett. 67, 785 (1991).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Stein, J. & Stöckmann, H.-J. Experimental determination of billiard wave functions. Phys. Rev. Lett. 68, 2867 (1992).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Chinnery, P. A. & Humphrey, V. F. Experimental visualization of acoustic resonances within a stadium-shaped cavity. Phys. Rev. E 53, 272 (1996).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Kudrolli, A., Abraham, M. C. & Gollub, J. P. Scarred patterns in surface waves. Phys. Rev. E 63, 026208 (2001).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Manoharan, H., Lutz, C. & Eigler, D. Quantum mirages formed by coherent projection of electronic structure. Nature 403, 512–515 (2000).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Crommie, M. F., Lutz, C. P. & Eigler, D. M. Confinement of electrons to quantum corrals on a metal surface. Science 262, 218–220 (1993).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Ghahari, F. et al. An on/off Berry phase switch in circular graphene resonators. Science 356, 845–849 (2017).

    Article 
    ADS 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Behn, W. A. et al. Measuring and tuning the potential landscape of electrostatically defined quantum dots in graphene. Nano Lett. 21, 5013–5020 (2021).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Ge, Z. et al. Giant orbital magnetic moments and paramagnetic shift in artificial relativistic atoms and molecules. Nat. Nanotechnol. 18, 250–256 (2023).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Zhao, Y. et al. Creating and probing electron whispering-gallery modes in graphene. Science 348, 672–675 (2015).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Gutiérrez, C., Brown, L., Kim, C.-J., Park, J. & Pasupathy, A. N. Klein tunnelling and electron trapping in nanometre-scale graphene quantum dots. Nat. Phys. 12, 1069–1075 (2016).

    Article 

    Google Scholar
     

  • Zheng, Q., Zhuang, Y.-C., Sun, Q.-F. & He, L. Coexistence of electron whispering-gallery modes and atomic collapse states in graphene/WSe2 heterostructure quantum dots. Nat. Commun. 13, 1597 (2022).

    Article 
    ADS 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Akis, R., Ferry, D. & Bird, J. Wave function scarring effects in open stadium shaped quantum dots. Phys. Rev. Lett. 79, 123 (1997).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Katsnelson, M. I., Novoselov, K. S. & Geim, A. K. Chiral tunnelling and the Klein paradox in graphene. Nat. Phys. 2, 620–625 (2006).

    Article 
    CAS 

    Google Scholar
     

  • Berry, M. V. & Mondragon, R. Neutrino billiards: time-reversal symmetry-breaking without magnetic fields. Proc. R. Soc. Lond. A 412, 53–74 (1987).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Chen, S. et al. Electron optics with pn junctions in ballistic graphene. Science 353, 1522–1525 (2016).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Cao, H. & Wiersig, J. Dielectric microcavities: model systems for wave chaos and non-Hermitian physics. Rev. Mod. Phys. 87, 61–111 (2015).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Young, A. F. & Kim, P. Quantum interference and Klein tunnelling in graphene heterojunctions. Nat. Phys. 5, 222–226 (2009).

    Article 
    CAS 

    Google Scholar
     

  • Ge, Z. Wavefunction Mapping and Magnetic Field Response of Electrostatically Defined Graphene Quantum Dots. PhD thesis, Univ. California, Santa Cruz (2023).

  • Zomer, P., Dash, S., Tombros, N. & Van Wees, B. A transfer technique for high mobility graphene devices on commercially available hexagonal boron nitride. Appl. Phys. Lett. 99, 232104 (2011).

    Article 
    ADS 

    Google Scholar
     

  • Goossens, A. et al. Mechanical cleaning of graphene. Appl. Phys. Lett. 100, 073110 (2012).

    Article 
    ADS 

    Google Scholar
     

  • Ge, Z. et al. Source data for “Direct visualization of relativistic quantum scars”. Zenodo. https://doi.org/10.5281/zenodo.13751637 (2024).

  • RELATED ARTICLES

    Most Popular

    Recent Comments