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Influence of topological degeneracy on the boundary Berezinskii-Kosterlitz-Thouless quantum phase transition of a dissipative resonant level (2303.11152v2)

Published 20 Mar 2023 in cond-mat.mes-hall

Abstract: The interplay between a topological degeneracy and the residue degeneracy (also known as the residue entropy) of quantum criticality remains as an important but not thoroughly understood topic. We find that this topological degeneracy, provided by a Majorana zero mode pair, relaxes the otherwise strictly requested symmetry requirement, to observe the boundary Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition (QPT) of a dissipative resonant level. Our work indicates that the topological degeneracy can be potentially viewed as an auxiliary symmetry that realizes a robust boundary QPT. The relaxation of the symmetry requirement extends the transition from a point to a finite area, thus greatly reducing the difficulty to experimentally observe the QPT. This topology-involved exotic BKT phase diagram, on the other hand, provides another piece of evidence that can further confirm the existence of a Majorana zero mode.

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References (86)
  1. Matthias Vojta, “Impurity quantum phase transitions,” Philosophical Magazine 86, 1807–1846 (2006), https://doi.org/10.1080/14786430500070396 .
  2. Ian Affleck, “Quantum impurity problems in condensed matter physics,”  (2008).
  3. Ian Affleck and Andreas W.W. Ludwig, “Critical theory of overscreened Kondo fixed points,” Nuclear Physics B 360, 641–696 (1991a).
  4. Ian Affleck, Andreas W. W. Ludwig, H.-B. Pang,  and D. L. Cox, “Relevance of anisotropy in the multichannel Kondo effect: Comparison of conformal field theory and numerical renormalization-group results,” Phys. Rev. B 45, 7918–7935 (1992).
  5. V. J. Emery and S. Kivelson, “Mapping of the two-channel Kondo problem to a resonant-level model,” Phys. Rev. B 46, 10812–10817 (1992).
  6. A. K. Mitchell, L. A. Landau, L. Fritz,  and E. Sela, “Universality and scaling in a charge two-channel Kondo device,” Phys. Rev. Lett. 116, 157202 (2016).
  7. Pedro L. S. Lopes, I. Affleck,  and E. Sela, “Anyons in multichannel Kondo systems,” Phys. Rev. B 101, 085141 (2020a).
  8. A. Komnik and A. O. Gogolin, “Resonant tunneling between Luttinger liquids: A solvable case,” Phys. Rev. Lett. 90, 246403 (2003).
  9. B. A. Jones and C. M. Varma, “Study of two magnetic impurities in a fermi gas,” Phys. Rev. Lett. 58, 843–846 (1987).
  10. B. A. Jones, B. G. Kotliar,  and A. J. Millis, “Mean-field analysis of two antiferromagnetically coupled Anderson impurities,” Phys. Rev. B 39, 3415–3418 (1989).
  11. Ian Affleck and Andreas W. W. Ludwig, “Exact critical theory of the two-impurity Kondo model,” Phys. Rev. Lett. 68, 1046–1049 (1992).
  12. Clément Sire, Chandra M. Varma,  and H. R. Krishnamurthy, “Theory of the non-fermi-liquid transition point in the two-impurity Kondo model,” Phys. Rev. B 48, 13833–13839 (1993).
  13. M. Garst, S. Kehrein, T. Pruschke, A. Rosch,  and M. Vojta, “Quantum phase transition of Ising-coupled Kondo impurities,” Phys. Rev. B 69, 214413 (2004).
  14. R. Žitko and J. Bonča, “Multiple-impurity Anderson model for quantum dots coupled in parallel,” Phys. Rev. B 74, 045312 (2006).
  15. Rok Žitko, Jernej Mravlje,  and Kristjan Haule, “Ground state of the parallel double quantum dot system,” Phys. Rev. Lett. 108, 066602 (2012).
  16. H. T. Mebrahtu, I. V. Borzenets, Dong E. Liu, Huaixiu Zheng, Yu. V. Bomze, A. I. Smirnov, H. U. Baranger,  and G. Finkelstein, “Quantum phase transition in a resonant level coupled to interacting leads,” Nature 488, 61–64 (2012).
  17. H. T. Mebrahtu, I. V. Borzenets, H. Zheng, Yu. V. Bomze, A. I. Smirnov, S. Florens, H. U. Baranger,  and G. Finkelstein, “Observation of Majorana quantum critical behavior in a resonant level coupled to a dissipative environment,” Nat. Phys. 9, 732–737 (2013).
  18. Dong E. Liu, Huaixiu Zheng, Gleb Finkelstein,  and Harold U. Baranger, “Tunable quantum phase transitions in a resonant level coupled to two dissipative baths,” Phys. Rev. B 89, 085116 (2014).
  19. Eyal Cornfeld, L. Aviad Landau, Kirill Shtengel,  and Eran Sela, “Entanglement spectroscopy of non-abelian anyons: Reading off quantum dimensions of individual anyons,” Phys. Rev. B 99, 115429 (2019).
  20. Pedro L. S. Lopes, I. Affleck,  and E. Sela, “Anyons in multichannel Kondo systems,” Phys. Rev. B 101, 085141 (2020b).
  21. Yashar Komijani, “Isolating Kondo anyons for topological quantum computation,” Phys. Rev. B 101, 235131 (2020).
  22. Matan Lotem, Eran Sela,  and Moshe Goldstein, “Manipulating non-abelian anyons in a chiral multichannel Kondo model,” Phys. Rev. Lett. 129, 227703 (2022).
  23. Dor Gabay, Cheolhee Han, Pedro L. S. Lopes, Ian Affleck,  and Eran Sela, “Multi-impurity chiral Kondo model: Correlation functions and anyon fusion rules,” Phys. Rev. B 105, 035151 (2022).
  24. Gu Zhang and Christian Spånslätt, “Distinguishing between topological and quasi Majorana zero modes with a dissipative resonant level,” Phys. Rev. B 102, 045111 (2020).
  25. Chung-Hou Chung, Karyn Le Hur, Matthias Vojta,  and Peter Wölfle, “Nonequilibrium transport at a dissipative quantum phase transition,” Phys. Rev. Lett. 102, 216803 (2009).
  26. A Yu Kitaev, “Unpaired Majorana fermions in quantum wires,”  44, 131–136 (2001).
  27. Roman M. Lutchyn, Jay D. Sau,  and S. Das Sarma, “Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures,” Phys. Rev. Lett. 105, 077001 (2010).
  28. Yuval Oreg, Gil Refael,  and Felix von Oppen, “Helical liquids and Majorana bound states in quantum wires,” Phys. Rev. Lett. 105, 177002 (2010).
  29. N. Read and Dmitry Green, “Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect,” Phys. Rev. B 61, 10267–10297 (2000).
  30. Liang Fu and C. L. Kane, “Superconducting proximity effect and Majorana fermions at the surface of a topological insulator,” Phys. Rev. Lett. 100, 096407 (2008).
  31. Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman,  and Sankar Das Sarma, “Non-abelian anyons and topological quantum computation,” Rev. Mod. Phys. 80, 1083–1159 (2008).
  32. I. Affleck and A. W. Ludwig, “Universal noninteger "ground-state degeneracy" in critical quantum systems.” Phys. Rev. Lett. 67, 161 – 164 (1991b).
  33. Ian Affleck and Andreas W. W. Ludwig, “Exact conformal-field-theory results on the multichannel Kondo effect: Single-fermion green’s function, self-energy, and resistivity,” Phys. Rev. B 48, 7297–7321 (1993).
  34. Daniel Friedan and Anatoly Konechny, “Boundary entropy of one-dimensional quantum systems at low temperature,” Phys. Rev. Lett. 93, 030402 (2004).
  35. A. Schiller and K. Ingersent, “Renormalization-group study of a magnetic impurity in a Luttinger liquid,” Europhysics Letters 39, 645 (1997).
  36. Gert-Ludwig Ingold and Yu V. Nazarov, “Charge tunneling rates in ultrasmall junctions,” in Single Charge Tunneling: Coulomb Blockade Phenomena In Nanostructures, edited by Hermann Grabert and Michel H. Devoret (Springer US, Boston, MA, 1992) pp. 21–107.
  37. F. D. Parmentier, A. Anthore, S. Jezouin, H. le Sueur, U. Gennser, A. Cavanna, D. Mailly,  and F. Pierre, “Strong back-action of a linear circuit on a single electronic quantum channel,” Nature Physics 7, 935–938 (2011).
  38. S. Jezouin, M. Albert, F. D. Parmentier, A. Anthore, U. Gennser, A. Cavanna, I. Safi,  and F. Pierre, “Tomonaga-Luttinger physics in electronic quantum circuits,” Nat. Commun. 4, 1802 (2013).
  39. Yu V. Nazarov, “Anomalous current-voltage characteristics of tunnel junctions,” Sov. Phys. JETP 68, 561 (1989).
  40. I. Safi and H. Saleur, “One-channel conductor in an Ohmic environment: Mapping to a Tomonaga-Luttinger liquid and full counting statistics,” Phys. Rev. Lett. 93, 126602 (2004).
  41. Serge Florens, Pascal Simon, Sabine Andergassen,  and Denis Feinberg, “Interplay of electromagnetic noise and Kondo effect in quantum dots,” Phys. Rev. B 75, 155321 (2007).
  42. C. L. Kane and Matthew P. A. Fisher, “Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas,” Phys. Rev. B 46, 15233–15262 (1992).
  43. T. Giamarchi, Quantum Physics in One Dimension (Oxford Univ. Press, Oxford UK, 2004).
  44. The QPT is not of BKT-type when r<2𝑟2r<2italic_r < 2 Mebrahtu et al. (2012). When r>3𝑟3r>3italic_r > 3, the dot is always isolated.
  45. See Supplemental Information for more details.
  46. Dong E. Liu and Harold U. Baranger, “Detecting a Majorana-fermion zero mode using a quantum dot,” Phys. Rev. B 84, 201308 (2011).
  47. E. Vernek, P. H. Penteado, A. C. Seridonio,  and J. C. Egues, “Subtle leakage of a Majorana mode into a quantum dot,” Phys. Rev. B 89, 165314 (2014).
  48. I. Safi and H. J. Schulz, “Transport in an inhomogeneous interacting one-dimensional system,” Phys. Rev. B 52, R17040–R17043 (1995).
  49. Dmitrii L. Maslov and Michael Stone, “Landauer conductance of Luttinger liquids with leads,” Phys. Rev. B 52, R5539–R5542 (1995).
  50. V. V. Ponomarenko, “Renormalization of the one-dimensional conductance in the Luttinger-liquid model,” Phys. Rev. B 52, R8666–R8667 (1995).
  51. Arisato Kawabata, “On the renormalization of conductance in Tomonaga-Luttinger liquid,” Journal of the Physical Society of Japan 65, 30–32 (1996), https://doi.org/10.1143/JPSJ.65.30 .
  52. Claudio de C. Chamon and Eduardo Fradkin, “Distinct universal conductances in tunneling to quantum Hall states: The role of contacts,” Phys. Rev. B 56, 2012–2025 (1997).
  53. Yichen Hu and C. L. Kane, “Universal symmetry-protected resonances in a spinful Luttinger liquid,”  (2016), arXiv:1604.08280.
  54. VL314399 Berezinskii, “Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. classical systems,” Sov. Phys. JETP 32, 493–500 (1971).
  55. JM Kosterlitz, “The critical properties of the two-dimensional xy model,” Journal of Physics C: Solid State Physics 7, 1046 (1974).
  56. John Michael Kosterlitz and David James Thouless, “Ordering, metastability and phase transitions in two-dimensional systems,” in Basic Notions Of Condensed Matter Physics (CRC Press, 2018) pp. 493–515.
  57. Alexander Altland and Ben D. Simons, Condensed Matter Field Theory, 2nd ed. (Cambridge University Press, 2010).
  58. P. W. Anderson, G. Yuval,  and D. R. Hamann, “Exact results in the Kondo problem. II. scaling theory, qualitatively correct solution, and some new results on one-dimensional classical statistical models,” Phys. Rev. B 1, 4464–4473 (1970).
  59. Henrik Bruus and Karsten Flensberg,  Many-body quantum theory in condensed matter physics - an introduction (Oxford University Press, United States, 2004).
  60. Huaixiu Zheng, Serge Florens,  and Harold U. Baranger, “Transport signatures of Majorana quantum criticality realized by dissipative resonant tunneling,” Phys. Rev. B 89, 235135 (2014).
  61. Paul Ginsparg, “Applied conformal field theory,” arXiv preprint hep-th/9108028  (1988).
  62. Ian Affleck, Andreas W. W. Ludwig,  and Barbara A. Jones, “Conformal-field-theory approach to the two-impurity Kondo problem: Comparison with numerical renormalization-group results,” Phys. Rev. B 52, 9528–9546 (1995).
  63. Vincent Mourik, Kun Zuo, Sergey M Frolov, SR Plissard, Erik PAM Bakkers,  and Leo P Kouwenhoven, “Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices,” Science 336, 1003–1007 (2012).
  64. M. T. Deng, S. Vaitiekėnas, E. B. Hansen, J. Danon, M. Leijnse, K. Flensberg, J. Nygård, P. Krogstrup,  and C. M. Marcus, “Majorana bound state in a coupled quantum-dot hybrid-nanowire system,” Science 354, 1557 (2016).
  65. S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup,  and C. M. Marcus, “Exponential protection of zero modes in Majorana islands,” Nature 531, 206 (2016).
  66. A. Fornieri, A. M. Whiticar, F. Setiawan, E. Portolés, A. C. Drachmann, A. Keselman, S. Gronin, C. Thomas, T. Wang, R. Kallaher, et al., “Evidence of topological superconductivity in planar Josephson junctions,” Nature 569, 89 (2019).
  67. H. Ren, F. Pientka, S. Hart, A. T. Pierce, M. Kosowsky, L. Lunczer, R. Schlereth, B. Scharf, E. M. Hankiewicz, L. W. Molenkamp, et al., “Topological superconductivity in a phase-controlled Josephson junction,” Nature 569, 93 (2019).
  68. S. Vaitiekėnas, Y. Liu, P. Krogstrup,  and C. Marcus, “Zero-bias peaks at zero magnetic field in ferromagnetic hybrid nanowires,” Nat. Phys. 17, 43 (2021).
  69. H. Song, Z. Zhang, D. Pan, D. Liu, Z. Wang, Z. Cao, L. Liu, L. Wen, D. Liao, R. Zhuo, D. E. Liu, R. Shang, J. Zhao,  and H. Zhang, “Large zero bias peaks and dips in a four-terminal thin InAs-Al nanowire device,” Phys. Rev. Research 4, 033235 (2022).
  70. Z. Wang, H. Song, D. Pan, Z. Zhang, W. Miao, R. Li, Z. Cao, G. Zhang, L. Liu, L. Wen, R. Zhuo, D. E. Liu, K. He, R. Shang, J. Zhao,  and H. Zhang, “Plateau Regions for Zero-Bias Peaks within 5%percent\%% of the Quantized Conductance Value 2⁢e2/h2superscript𝑒2ℎ2e^{2}/h2 italic_e start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT / italic_h ,” Phys. Rev. Lett. 129, 167702 (2022a).
  71. M. Aghaee, A. Akkala, Z. Alam, R. Ali, A. A. Ramirez, M. Andrzejczuk, A. E. Antipov, M. Astafev, B. Bauer, J. Becker, et al., “InAs-Al Hybrid Devices Passing the Topological Gap Protocol,” Phys. Rev. B 107, 245423 (2023a).
  72. T. Dvir, G. Wang, N. van Loo, C.-X. Liu, G. P. Mazur, A. Bordin, S. L. D. ten Haaf, J.-Y. Wang, D. van Driel, F. Zatelli, X. Li, F. K. Malinowski, S. Gazibegovic, G. Badawy, E. P. A. M. Bakkers, M. Wimmer,  and L. P. Kouwenhoven, “Realization of a minimal Kitaev chain in coupled quantum dots,” Nature 614, 445 (2023).
  73. D. E. Liu, “Proposed Method for Tunneling Spectroscopy with Ohmic Dissipation Using Resistive Electrodes: A Possible Majorana Filter ,” Phys. Rev. Lett. 111, 207003 (2013).
  74. D. Liu, G. Zhang, Z. Cao, H. Zhang,  and D. E. Liu, “Universal Conductance Scaling of Andreev Reflections Using a Dissipative Probe,” Phys. Rev. Lett. 128, 076802 (2022).
  75. S. Zhang, Z. Wang, D. Pan, H. Li, S. Lu, Z. Li, G. Zhang, D. Liu, Z. Cao, L. Liu, L. Wen, D. Liao, R. Zhuo, R. Shang, D. E. Liu, J. Zhao,  and H. Zhang, “Suppressing Andreev Bound State Zero Bias Peaks Using a Strongly Dissipative Lead ,” Phys. Rev. Lett. 128, 076803 (2022a).
  76. Z. Wang, S. Zhang, D. Pan, G. Zhang, Z. Xia, Z. Li, D. Liu, Z. Cao, L. Liu, L. Wen, D. Liao, R. Zhuo, Y. Li, D. E. Liu, R. Shang, J. Zhao,  and H. Zhang, “Large Andreev bound state zero-bias peaks in a weakly dissipative environment,” Phys. Rev. B 106, 205421 (2022b).
  77. S. Zhang, Z. Wang, D. Pan, Z. Wang, Z. Li, Z. Zhang, Y. Gao, Z. Cao, G. Zhang, L. Liu, et al., “In situ tuning of dynamical Coulomb blockade on Andreev bound states in hybrid nanowire devices,” Phys. Rev. B 108, 235416 (2022b).
  78. G. W. Semenoff and P. Sodano, “Teleportation by a Majorana Medium,” arXiv e-prints , cond-mat/0601261 (2006), arXiv:cond-mat/0601261 [cond-mat.other] .
  79. L. Fu, “Electron Teleportation via Majorana Bound States in a Mesoscopic Superconductor,” Phys. Rev. Lett. 104, 056402 (2010).
  80. B. Béri and N. R. Cooper, “Topological Kondo Effect with Majorana Fermions ,” Phys. Rev. Lett. 109, 156803 (2012).
  81. A. Altland and R. Egger, “Multiterminal Coulomb-Majorana Junction ,” Phys. Rev. Lett. 110, 196401 (2013).
  82. B. Béri, “Majorana-Klein Hybridization in Topological Superconductor Junctions,” Phys. Rev. Lett. 110, 216803 (2013).
  83. A. Altland, B. Béri, R. Egger,  and A. M. Tsvelik, “Multichannel Kondo Impurity Dynamics in a Majorana Device ,” Phys. Rev. Lett. 113, 076401 (2014).
  84. Y. Hao, G. Zhang, D. Liu,  and D. E. Liu, “Anomalous universal conductance as a hallmark of non-locality in a Majorana-hosted superconducting island,” Nature Communications 13, 6699 (2022).
  85. A. C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge Univ. Press, Cambridge UK, 1993).
  86. A. Schiller and K. Ingersent, “Renormalization-group study of a magnetic impurity in a luttinger liquid,” Europhysics Letters 39, 645 (1997).
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