Reorganization of Edge Modes: Quantum Phase Transitions and Textures

• Applicant: Professor Dr. Bernd Rosenow
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2018 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 406252756

• Final Report Year: 2024

Final Report Abstract

Notwithstanding earlier attempts at describing quantum phase transitions on the edge of quantum Hall systems, our project obtained significant new results. The results can be grouped into two main thrusts: On the one hand, novel classes of naturally occurring (or induced) quantum phase transitions (QPTs) on the edge (e.g., spin switching transitions; spontaneous time reversal symmetry breaking) have been studied. Beyond the basic physics importance of discovering and analyzing new classes of phase transitions in topological systems, the latter have implications on charge and spin transport through such setups. Moreover, the fact that spontaneous breakdown of time reversal symmetry may take place in otherwise time reversal invariant systems, implies that renewed attention was given to "topological protection" (e.g., in TRI topological insulators), necessary for quantum computation. On the other hand, there has been much interest into the prospects of engineered edge structures. On the experimental side, novel heterostructure designs have allowed to engineer devices with a screened Coulomb interaction and sharp edge states. This edge physics allows to observe signatures of a quantum transition between a phase with constant chemical potential and a phase with constant density, allowing to find signatures of anyonic statistics. Engineering of the interaction among edge states on the other hand allows to find superconducting correlations arising exclusively due to repulsive Coulomb interaction. In a confined geometry, the repulsive Coulomb interaction was found to give rise to electron pairing in the time domain.

Publications

• Interaction-induced charge transfer in a mesoscopic electron spectrometer. Physical Review B, 100(19).
  Fischer, Stefan G.; Park, Jinhong; Meir, Yigal & Gefen, Yuval
  
• Superconducting Correlations Out of Repulsive Interactions on a Fractional Quantum Hall Edge. Physical Review Letters, 122(23).
  Väyrynen, Jukka I.; Goldstein, Moshe & Gefen, Yuval
  
• Topological Classification of Shot Noise on Fractional Quantum Hall Edges. Physical Review Letters, 123(13).
  Spånslätt, Christian; Park, Jinhong; Gefen, Yuval & Mirlin, Alexander D.
  
• Detection of Quantum Interference without an Interference Pattern. Physical Review Letters, 125(2).
  Esin, Iliya; Romito, Alessandro & Gefen, Yuval
  
• Electron pairing in the quantum Hall regime due to neutralon exchange. Physical Review Research, 2(4).
  Frigeri, Giovanni A. & Rosenow, Bernd
  
• Flux Superperiods and Periodicity Transitions in Quantum Hall Interferometers. Physical Review Letters, 124(10).
  Rosenow, Bernd & Stern, Ady
  
• Noise on the Non-Abelian ν = 5/ 2 Fractional Quantum Hall Edge. Phys. Rev. Lett. 125, 157702.
  Park, Jinhong; Spånslätt, Christian; Gefen, Yuval & Mirlin, Alexander D.
  
• Observation of quantum Hall interferometer phase jumps due to a change in the number of bulk quasiparticles. Physical Review B, 101(12).
  Röösli, Marc P.; Brem, Lars; Kratochwil, Benedikt; Nicolí, Giorgio; Braem, Beat A.; Hennel, Szymon; Märki, Peter; Berl, Matthias; Reichl, Christian; Wegscheider, Werner; Ensslin, Klaus; Ihn, Thomas & Rosenow, Bernd
  
• Emergence of spin-active channels at a quantum Hall interface. Physical Review B, 103(8).
  Saha, Amartya; De Suman, Jyoti; Rao, Sumathi; Gefen, Yuval & Murthy, Ganpathy
  
• Exponentially growing bulk Green functions as signature of nontrivial non-Hermitian winding number in one dimension. Physical Review B, 103(19).
  Zirnstein, Heinrich-Gregor & Rosenow, Bernd
  
• Fractional Coulomb blockade for quasi-particle tunneling between edge channels. Science Advances, 7(19).
  Röösli, Marc P.; Hug, Michael; Nicolí, Giorgio; Märki, Peter; Reichl, Christian; Rosenow, Bernd; Wegscheider, Werner; Ensslin, Klaus & Ihn, Thomas
  
• Fractional edge reconstruction in integer quantum Hall phases. Physical Review B, 103(12).
  Khanna, Udit; Goldstein, Moshe & Gefen, Yuval
  
• Symmetry-related transport on a fractional quantum Hall edge. Physical Review Research, 3(2).
  Park, Jinhong; Rosenow, Bernd & Gefen, Yuval
  
• Transmission amplitude through a Coulomb blockaded Majorana wire. Physical Review Research, 3(2).
  Thamm, Matthias & Rosenow, Bernd
  
• Tunable topological states hosted by unconventional superconductors with adatoms. Physical Review Research, 3(3).
  Kreisel, Andreas; Hyart, Timo & Rosenow, Bernd
  
• Edge Reconstruction of a Time-Reversal Invariant Insulator: Compressible-Incompressible Stripes. Physical Review Letters, 128(18).
  Khanna, Udit; Gefen, Yuval; Entin-Wohlman, Ora & Aharony, Amnon
  
• Emergence of Neutral Modes in Laughlin-like Fractional Quantum Hall Phases. Physical Review Letters, 129(14).
  Khanna, Udit; Goldstein, Moshe & Gefen, Yuval
  
• One-particle entanglement for one-dimensional spinless fermions after an interaction quantum quench. Physical Review B, 106(16).
  Thamm, Matthias; Radhakrishnan, Harini; Barghathi, Hatem; Rosenow, Bernd & Del, Maestro Adrian
  
• Optimized steering: Quantum state engineering and exceptional points. Physical Review A, 105(1).
  Kumar, Parveen; Snizhko, Kyrylo; Gefen, Yuval & Rosenow, Bernd
  
• Robustness of helical edge states under edge reconstruction. Europhysics Letters, 140(2), 26002.
  John, Niels; Del Maestro, Adrian & Rosenow, Bernd
  
• Superconductivity of neutral modes in quantum Hall edges. Physical Review B, 105(8).
  Väyrynen, Jukka I.; Goldstein, Moshe & Gefen, Yuval
  
• Machine Learning Optimization of Majorana Hybrid Nanowires. Physical Review Letters, 130(11).
  Thamm, Matthias & Rosenow, Bernd
  
• Near-frozen nonequilibrium state at high energy in an integrable system. Physical Review B, 108(8).
  Fischer, Stefan G.; Meir, Yigal; Gefen, Yuval & Rosenow, Bernd
  
• Conductance based machine learning of optimal gate voltages for disordered Majorana wires. Physical Review B, 109(4).
  Thamm, Matthias & Rosenow, Bernd
  
• Dynamical breaking of electron-hole symmetry in nonequilibrium chiral quantum channels. Physical Review B, 109(8).
  Puster, Felix; Fischer, Stefan G. & Rosenow, Bernd
  
• Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise. Phys. Rev. Lett. 132, 136502.
  Manna, Sourav; Das, Ankur; Goldstein, Moshe & Gefen, Yuval