Completing the emergent-localized-state/Kondo picture of quantum point contacts: predictive microscopic control, higher-spin Kondo regimes, integrated transport theory, and discrimination from hybrid-device zero-bias anomalies

Quantum point contacts (QPCs) — short, gate-defined one-dimensional channels — display the long-standing 0.7 conductance anomaly and zero-bias anomalies (ZBAs) that Iqbal et al. (Nature 501, 79 (2013)) attributed to emergent localized states (ELSs) formed by Friedel oscillations, with odd- or even-parity Kondo effects matching the number of ELSs. The unresolved issues and outlook directions identified by that paper are: (i) predicting and controlling ELS positions, energies, couplings, and Kondo temperatures from device fabrication parameters, including the role of residual disorder and remote dopant imperfections; (ii) establishing and characterizing the higher-spin ($S=1$, $S=3/2$) Kondo regimes that spin-density-functional theory suggests may develop for multiple overlapping ELSs; (iii) building a transport theory that integrates the Kondo contribution with the experimentally observed non-Kondo background conductance rather than modeling the Kondo part alone; and (iv) supplying quantitative criteria by which QPC-origin many-body ZBAs can be excluded when interpreting zero-bias peaks in semiconductor–superconductor hybrid devices.

Background

A quantum point contact (QPC) is a narrow, gate-controlled constriction connecting two electron reservoirs in a semiconductor heterostructure; at low temperature its two-terminal conductance is quantized in units of $2e^2/h$ as transverse modes are opened one by one. Even in the cleanest devices, a shoulder near $0.7\cdot 2e^2/h$ (the '0.7 anomaly') and zero-bias anomalies (ZBAs — enhanced differential conductance at vanishing source–drain voltage) appear generically and are widely believed to reflect electron–electron interactions. The Kondo effect is the many-body screening of a localized electron spin by conduction electrons; in transport it produces a zero-bias conductance resonance below a characteristic Kondo temperature $T_K$, which depends exponentially on the coupling of the localized state to the leads. Iqbal et al. (2013) argued that in length-tunable QPCs the many-body physics arises from 'emergent localized states' (ELSs): quasi-bound, roughly one-electron charge states that self-consistently form out of Friedel oscillations (oscillations of the electron density near a scattering potential) rather than from any atomic impurity, and are therefore an interaction effect in a nominally open channel. They observed the ZBA parity alternating between single- and double-peak character as the channel lengthened by one Friedel period, matching odd versus even ELS number, and reproduced trends with a two-impurity Anderson model (two coupled localized levels coupled to reservoirs, including a Kondo singlet and an inter-impurity singlet) solved in the slave-boson non-crossing approximation. Supporting spin-density-functional theory (SDFT — density-functional theory with spin-dependent potentials, here generalized to variable channel length) predicted ELSs forming one at a time as the channel lengthens and, for overlapping ELSs, total-spin states $S=1$ or $S=3/2$, i.e. underscreened Kondo regimes in which conduction electrons cannot fully screen a spin larger than 1/2. The same paper cautioned that essentially identical ZBAs appear in semiconductor–superconductor hybrid nanowires proposed to host Majorana zero modes (zero-energy quasiparticles at the ends of a topological superconductor), so QPC-type alternative explanations must be excluded before a zero-bias peak is read as a Majorana signature. Five limitations of this picture, stated by the authors themselves, remain the frontier: ELS positions, couplings, and resulting $T_K$ vary strongly from device to device because of parameter sensitivity and remote dopant imperfections, so no predictive microscopic control exists; the predicted higher-spin Kondo regimes have not been experimentally demonstrated or characterized; the theory computes only the Kondo contribution to current and omits the non-Kondo background conductance (experimentally finite, not Coulomb-blockade suppressed); quantitative criteria for separating QPC-origin many-body ZBAs from putative Majorana signatures are missing; and the roles of residual disorder, dopant-charge instabilities, and electrostatic asymmetry in selecting particular ELS configurations (e.g. producing asymmetric double-peak ZBAs via unequal ELS–lead couplings) are uncharacterized. Later work frames these issues within a still-unsettled controversy about the anomaly mechanism: statistical studies of hundreds of QPCs report that Kondo and spontaneous-polarization models do not fit their data, and alternative non-Kondo ZBA mechanisms (e.g. coherent scattering from frozen phonon disorder, and interaction-induced Friedel-oscillation corrections in partially open adiabatic channels) continue to appear, so the microscopic picture itself, not merely its refinement, remains to be settled.

Problem Statement

The problem is to turn the emergent-localized-state (ELS)/Kondo picture of many-body anomalies in quantum point contacts from a qualitative, post-hoc consistency argument into a predictive and quantitatively validated microscopic account, together with its downstream discrimination consequence. Concretely, as identified by Iqbal et al. (Nature 501, 79 (2013)): (1) predict, for given fabrication and gate parameters, the number, positions, energies, and inter-state/lead couplings of emergent localized states and the resulting Kondo temperatures — including the effect of residual disorder, dopant-layer charge instabilities, and electrostatic asymmetries that currently produce strong device-to-device variability and asymmetric double-peak zero-bias anomalies — so that many-body configurations can be engineered reproducibly rather than found empirically; (2) establish whether the higher-spin regimes suggested by spin-density-functional theory for multiple overlapping ELSs — total-spin $S=1$ and $S=3/2$ states with their expected underscreened-Kondo transport fingerprints — develop in QPCs, and quantitatively characterize their stability and signatures; (3) construct a transport theory that integrates the Kondo contribution with a microscopic description of the non-Kondo background conductance (the experimentally observed finite conductance at high temperature, which the two-impurity Anderson modeling of 2013 omitted), yielding full conductance versus gate voltage, bias, temperature, and magnetic field that can be compared quantitatively to measured devices; and (4) derive and validate quantitative criteria by which zero-bias anomalies originating from QPC-type many-body physics can be distinguished from, and excluded as explanations of, zero-bias peaks measured in semiconductor–superconductor hybrid devices proposed to host Majorana modes. Components (1)–(3) concern the predictive microscopic theory and component (4) is the explicit application of that theory to hybrid-device interpretation. All four are jointly required for a resolution of the task, and each has a checkable outcome: (1) is resolved by a calculable microscopic criterion that, for stated fabrication and gate parameters, returns the ELS number, positions, energies, inter-state and lead couplings and the resulting $T_K$ and reproduces the measured device-to-device variation — including the single-peak versus asymmetric double-peak ZBA alternation — without per-device fitting; (2) is resolved by a determination of which total spin (if any above $1/2$) forms for overlapping ELSs, with its stability and transport fingerprints characterized, so that the existence question is settled whether the higher-spin regimes are found or excluded; (3) is resolved by a combined Kondo-plus-background conductance whose predictions match the measured conductance versus gate voltage, bias, temperature and magnetic field of Iqbal et al. (2013) and of subsequent devices, within experimental uncertainty; and (4) is resolved by discrimination criteria whose scaling in temperature and magnetic field separates QPC-origin many-body ZBAs from hybrid zero-bias peaks when applied to measured data. A well-supported refutation of the ELS/Kondo premise resolves components (1)–(3) as a negative result; component (4) is resolved by operative exclusion criteria whether or not that premise holds.

References

1. M. J. Iqbal, R. Levy, E. J. Koop, J. B. Dekker, J. P. de Jong, J. H. M. van der Velde, D. Reuter, A. D. Wieck, R. Aguado, Y. Meir, C. H. van der Wal, 'Odd and even Kondo effects from emergent localization in quantum point contacts', Nature 501, 79–83 (2013). DOI: 10.1038/nature12491, https://doi.org/10.1038/nature12491 (preprint arXiv:1307.7167, https://arxiv.org/abs/1307.7167)
2. Hao Zhang, Phillip M. Wu, Albert M. Chang, 'Quasibound states and evidence for a spin-1 Kondo effect in asymmetric quantum point contacts', Physical Review B 88, 075311 (2013). DOI: 10.1103/PhysRevB.88.075311, https://doi.org/10.1103/PhysRevB.88.075311
3. Jan Heyder, Florian Bauer, Enrico Schubert, David Borowsky, Dieter Schuh, Werner Wegscheider, Jan von Delft, Stefan Ludwig, 'Relation between the 0.7 anomaly and the Kondo effect: Geometric crossover between a quantum point contact and a Kondo quantum dot', Physical Review B 92, 195401 (2015). DOI: 10.1103/PhysRevB.92.195401, https://doi.org/10.1103/PhysRevB.92.195401
4. Luke W. Smith, Hong-Bin Chen, Che-Wei Chang, Chien-Wei Wu, Shun-Tsung Lo, Shih-Hsiang Chao, I. Farrer, H. E. Beere, J. P. Griffiths, G. A. C. Jones, D. A. Ritchie, Yueh-Nan Chen, Tse-Ming Chen, 'Electrically Controllable Kondo Correlation in Spin-Orbit-Coupled Quantum Point Contacts', Physical Review Letters 128, 027701 (2022). DOI: 10.1103/PhysRevLett.128.027701, https://doi.org/10.1103/PhysRevLett.128.027701
5. Shun-Tsung Lo, Che-Cheng Wang, Sheng-Chin Ho, Jun-Hao Chang, Ming-Wei Chen, G. L. Creeth, L. W. Smith, Shih-Hsiang Chao, Yu-Chiang Hsieh, Pei-Tzu Wu, Yi-Cheng Wu, Chi-Te Liang, M. Pepper, J. P. Griffiths, I. Farrer, G. A. C. Jones, D. A. Ritchie, Tse-Ming Chen, 'On-Chip Quantum Sensing of Kondo Spins in a High-Mobility Quasi-One-Dimensional Nanoconstriction', Nano Letters 25, 7740–7747 (2025). DOI: 10.1021/acs.nanolett.5c00560, https://doi.org/10.1021/acs.nanolett.5c00560
6. Josep Ingla-Aynés, S. Volosheniuk, Talieh S. Ghiasi, Angelika Knothe, Kenji Watanabe, T. Taniguchi, V. I. Fal'ko, H. S. J. van der Zant, 'Tunable Kondo effect in a bilayer graphene quantum channel' (2025). arXiv:2511.17188, https://arxiv.org/abs/2511.17188
7. Pengcheng Ma, Kaveh Delfanazari, Reuben K. Puddy, Jiahui Li, Moda Cao, Teng Yi, Jonathan P. Griffiths, Harvey E. Beere, David A. Ritchie, Michael J. Kelly, Charles G. Smith, 'Statistical evaluation of 571 GaAs quantum point contact transistors showing the 0.7 anomaly in quantized conductance using cryogenic on-chip multiplexing', Chip 3, 100095 (2024). DOI: 10.1016/j.chip.2024.100095, https://doi.org/10.1016/j.chip.2024.100095 (preprint arXiv:2404.06784 under the slightly longer preprint title '...using millikelvin cryogenic on-chip multiplexing', https://arxiv.org/abs/2404.06784)
8. Y.-H. Lee, S. Xiao, K. W. Kim, J. L. Reno, J. P. Bird, J. E. Han, 'Giant Zero Bias Anomaly due to Coherent Scattering from Frozen Phonon Disorder in Quantum Point Contacts', Physical Review Letters 123, 056802 (2019). DOI: 10.1103/PhysRevLett.123.056802, https://doi.org/10.1103/PhysRevLett.123.056802
9. J. Chen, B. D. Woods, P. Yu, M. Hocevar, D. Car, S. R. Plissard, E. P. A. M. Bakkers, T. D. Stanescu, S. M. Frolov, 'Ubiquitous Non-Majorana Zero-Bias Conductance Peaks in Nanowire Devices', Physical Review Letters 123, 107703 (2019). DOI: 10.1103/PhysRevLett.123.107703, https://doi.org/10.1103/PhysRevLett.123.107703
10. Mouyang Cheng, Ryotaro Okabe, Abhijatmedhi Chotrattanapituk, Mingda Li, 'Machine learning detection of Majorana zero modes from zero-bias peak measurements', Matter 7, 2507–2520 (2024). DOI: 10.1016/j.matt.2024.05.028, https://doi.org/10.1016/j.matt.2024.05.028
11. Donghao Liu, Dmitri Gutman, 'Conductance anomaly in a partially open adiabatic quantum point contact', Physical Review B 113, 235412 (2026). DOI: 10.1103/vh89-rpxl, https://doi.org/10.1103/vh89-rpxl (preprint arXiv:2510.20678, https://arxiv.org/abs/2510.20678)
12. A. Srinivasan, I. Farrer, D. A. Ritchie, A. R. Hamilton, 'Improving reproducibility of quantum devices with completely undoped architectures', Applied Physics Letters 117, 183101 (2020). DOI: 10.1063/5.0024923, https://doi.org/10.1063/5.0024923
13. Sebastian Krinner, Martin Lebrat, Dominik Husmann, Charles Grenier, Jean-Philippe Brantut, Tilman Esslinger, 'Mapping out spin and particle conductances in a quantum point contact', Proceedings of the National Academy of Sciences 113, 8144–8149 (2016). DOI: 10.1073/pnas.1601812113, https://doi.org/10.1073/pnas.1601812113
14. Mukunda P. Das, Frederick Green, 'Conductance anomalies in quantum point contacts and 1D wires', Advances in Natural Sciences: Nanoscience and Nanotechnology 8, 023001 (2017). DOI: 10.1088/2043-6254/aa5e17, https://doi.org/10.1088/2043-6254/aa5e17