Quantitative microscopic theory of the 0.7-anomaly and its zero-bias peak in quantum point contacts at finite temperature and finite bias

The conductance of a quantum point contact shows a universal shoulder near $0.7\,G_0$ (with $G_0=2e^2/h$), usually accompanied by a zero-bias peak in the nonlinear conductance. Bauer and coworkers (Nature 501, 73 (2013)) proposed a common microscopic origin — a smeared van Hove singularity in the local density of states at the bottom of the lowest one-dimensional subband, which enhances the Hartree barrier, the spin susceptibility, and the inelastic scattering rate — but their functional renormalization group treatment was restricted to zero temperature and zero bias with truncations exact only to second order in the interaction, and agreement with experiment was qualitative. The following problem remains open: a controlled, nonperturbative microscopic calculation of the conductance at finite temperature and finite source–drain bias, including the zero-bias peak and its temperature dependence, for realistic barrier electrostatics and material platforms with significant spin–orbit coupling, together with quantitative theory–experiment benchmarking that confirms or refutes the proposed common origin.

Background

A quantum point contact (QPC) is a short, narrow constriction, typically gate-defined in a two-dimensional electron gas, in which electrons occupy one-dimensional subbands. Its linear conductance is quantized in units of $G_0=2e^2/h$ as the constriction is opened (van Wees et al., Phys. Rev. Lett. 60, 848 (1988)). Shortly after this discovery, experiments found an additional shoulder near $0.7\,G_0$ whose strength grows with temperature (Thomas et al., Phys. Rev. Lett. 77, 135 (1996)). Proposed explanations invoked spontaneous spin polarization, ferromagnetic spin coupling, quasi-bound states acting like Kondo impurities, Wigner crystallization (electrons freezing into a spatially ordered array at low density), and inelastic scattering. The Kondo effect itself is the canonical many-body phenomenon in which a localized spin is screened by conduction electrons, producing a low-energy scale and a zero-bias resonance; Meir, Hirose, and Wingreen (Phys. Rev. Lett. 89, 196802 (2002)) argued that a weakly localized state near the top of the QPC barrier could drive an analogous '0.7' resonance. The zero-bias peak (ZBP) is an enhancement of the differential conductance at vanishing source–drain voltage that typically accompanies the 0.7-anomaly. In Bauer et al. (Nature 501, 73 (2013)), the authors combined experiments with a functional renormalization group (fRG) treatment — a controlled-in-principle scheme that flows the many-body vertex from weak to strong coupling, here truncated at orders exact to second order in the interaction strength $U$ — and qualitative Keldysh second-order perturbation theory (SOPT) for inelastic effects at finite temperature $T$ and source–drain voltage $V_{\rm sd}$. Their mechanism: the local density of states at the QPC center has a smeared van Hove ridge (a remnant of the one-dimensional band-edge singularity) at the bottom of the lowest subband; when this ridge lies near the chemical potential, it enhances the Hartree (mean-field electrostatic) barrier, the local spin susceptibility, and the inelastic scattering rate, jointly producing the 0.7-anomaly and the ZBP, with Kondo-like Fermi-liquid behavior at low energy. The authors themselves flagged what remained unfinished: the quantitative treatment was restricted to zero $T$ and zero $V_{\rm sd}$ (finite-energy properties were captured only qualitatively by SOPT, which underestimates some features, such as the zero-field shoulder amplitude); spin–orbit and orbital magnetic effects were neglected; only smooth, roughly parabolic barriers were analyzed, without establishing when spontaneous spin polarization or truly localized moments arise for other barrier shapes or in the presence of disorder; the detailed temperature dependence of the ZBP and a nonperturbative treatment of inelastic scattering at finite bias were deferred; and comparison with experiment remained qualitative. Later work addressed pieces of this list — spin–orbit effects at zero temperature (Goulko et al., Phys. Rev. Lett. 113, 266402 (2014)), the geometric crossover between Kondo quantum dots and QPCs (Heyder et al., Phys. Rev. B 92, 195401 (2015)), finite-temperature spin-fluctuation dynamics within an extended coupled-ladder fRG (Schimmel et al., Phys. Rev. Lett. 119, 196401 (2017)), and the spin–orbit-induced '0.7 analog' at high magnetic fields (Weidinger et al., Phys. Rev. B 98, 115112 (2018)) — but no published work delivers a controlled, quantitative, finite-$T$/finite-bias account of the anomaly and its ZBP.

Problem Statement

Construct a controlled, quantitative microscopic theory of the 0.7-anomaly in quantum point contacts (QPCs) — the conductance shoulder near $0.7\,G_0$, where $G_0=2e^2/h$ is the conductance quantum, that appears as a short one-dimensional constriction is opened, and which is typically accompanied by a zero-bias peak (ZBP), an enhancement of the differential conductance at vanishing source–drain voltage — going beyond the restrictions of Bauer et al. (Nature 501, 73 (2013)): second-order-in-$U$ functional renormalization group at $T=0$ and $V_{\rm sd}=0$, plus qualitative second-order Keldysh perturbation theory for inelastic effects. A complete answer should (1) treat inelastic scattering nonperturbatively or with a systematically improvable, controlled scheme, yielding quantitative predictions for the conductance $G(V_{\rm g}, B, T, V_{\rm sd})$ — as a function of gate voltage $V_{\rm g}$, magnetic field $B$, temperature $T$, and source–drain voltage $V_{\rm sd}$ — including the zero-bias peak and its temperature dependence, for realistic QPC models; (2) establish how, and whether, spin–orbit and orbital magnetic effects, non-parabolic barrier shapes, and disorder (at least one representative of each) modify or destroy the proposed common origin — the smeared van Hove ridge (a remnant of the one-dimensional band-edge singularity in the local density of states at the bottom of the lowest subband) whose proximity to the chemical potential enhances the Hartree barrier, the spin susceptibility, and the inelastic scattering rate — including whether spontaneous spin polarization or truly localized moments can arise in these regimes; and (3) benchmark the predictions quantitatively (not merely qualitatively) against experimental data across the parameter space of interaction strength, barrier shape, and material platform, to the extent that published experimental data permit. The single overarching objective is a validated microscopic account of the anomaly's linear and nonlinear transport phenomenology; the components above are the jointly required ingredients of that account, and the theory either confirms the common origin claimed in the source or identifies where it fails.

References

1. Florian Bauer, Jan Heyder, Enrico Schubert, David Borowsky, Daniela Taubert, Benedikt Bruognolo, Dieter Schuh, Werner Wegscheider, Jan von Delft, Stefan Ludwig, 'Microscopic origin of the 0.7-anomaly in quantum point contacts', Nature 501, 73–78 (2013). DOI: 10.1038/nature12421, https://doi.org/10.1038/nature12421
2. B. J. van Wees, H. van Houten, C. W. J. Beenakker, J. G. Williamson, L. P. Kouwenhoven, D. van der Marel, C. T. Foxon, 'Quantized conductance of point contacts in a two-dimensional electron gas', Phys. Rev. Lett. 60, 848–850 (1988). DOI: 10.1103/PhysRevLett.60.848, https://doi.org/10.1103/PhysRevLett.60.848
3. K. J. Thomas, J. T. Nicholls, M. Y. Simmons, M. Pepper, D. R. Mace, D. A. Ritchie, 'Possible spin polarization in a one-dimensional electron gas', Phys. Rev. Lett. 77, 135–138 (1996). DOI: 10.1103/PhysRevLett.77.135, https://doi.org/10.1103/PhysRevLett.77.135
4. Yigal Meir, Kenji Hirose, Ned S. Wingreen, 'Kondo model for the "0.7 anomaly" in transport through a quantum point contact', Phys. Rev. Lett. 89, 196802 (2002). DOI: 10.1103/PhysRevLett.89.196802, https://doi.org/10.1103/PhysRevLett.89.196802
5. Olga Goulko, Florian Bauer, Jan Heyder, Jan von Delft, 'Effect of spin-orbit interactions on the 0.7 anomaly in quantum point contacts', Phys. Rev. Lett. 113, 266402 (2014). DOI: 10.1103/PhysRevLett.113.266402, https://doi.org/10.1103/PhysRevLett.113.266402 (arXiv:1408.0746, https://arxiv.org/abs/1408.0746)
6. 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', Phys. Rev. B 92, 195401 (2015). DOI: 10.1103/PhysRevB.92.195401, https://doi.org/10.1103/PhysRevB.92.195401 (arXiv:1409.3415, https://arxiv.org/abs/1409.3415)
7. Dennis H. Schimmel, Benedikt Bruognolo, Jan von Delft, 'Spin fluctuations in the 0.7 anomaly in quantum point contacts', Phys. Rev. Lett. 119, 196401 (2017). DOI: 10.1103/PhysRevLett.119.196401, https://doi.org/10.1103/PhysRevLett.119.196401 (arXiv:1703.02734, https://arxiv.org/abs/1703.02734)
8. Lukas Weidinger, Christian Schmauder, Dennis H. Schimmel, Jan von Delft, 'Functional renormalization group treatment of the 0.7 analog in quantum point contacts', Phys. Rev. B 98, 115112 (2018). DOI: 10.1103/PhysRevB.98.115112, https://doi.org/10.1103/PhysRevB.98.115112 (arXiv:1805.06311, https://arxiv.org/abs/1805.06311)
9. Max Geier, Jaan Freudenfeld, Jorge T. Silva, Vladimir Umansky, Dirk Reuter, Andreas D. Wieck, Piet W. Brouwer, Stefan Ludwig, 'Electrostatic potential shape of gate-defined quantum point contacts', Phys. Rev. B 101, 165429 (2020). DOI: 10.1103/PhysRevB.101.165429, https://doi.org/10.1103/PhysRevB.101.165429 (arXiv:2002.12303, https://arxiv.org/abs/2002.12303)
10. Marek M. Rams, Michael Zwolak, 'Breaking the entanglement barrier: Tensor network simulation of quantum transport', Phys. Rev. Lett. 124, 137701 (2020). DOI: 10.1103/PhysRevLett.124.137701, https://doi.org/10.1103/PhysRevLett.124.137701 (arXiv:1904.12793, https://arxiv.org/abs/1904.12793)
11. K. L. Hudson, A. Srinivasan, O. Goulko, J. Adam, Q. Wang, L. A. Yeoh, O. Klochan, I. Farrer, D. A. Ritchie, A. Ludwig, A. D. Wieck, J. von Delft, A. R. Hamilton, 'New signatures of the spin gap in quantum point contacts', Nature Communications 12, 5 (2021). DOI: 10.1038/s41467-020-19895-3, https://doi.org/10.1038/s41467-020-19895-3
12. 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 (arXiv:2404.06784, https://arxiv.org/abs/2404.06784)
13. Jonas D. Gerber, Efe Ersoy, Michele Masseroni, Markus Niese, Artem O. Denisov, Christoph Adam, Lara Ostertag, Jessica Richter, Takashi Taniguchi, Kenji Watanabe, Yigal Meir, Thomas Ihn, Klaus Ensslin, 'Spin-valley 0.7 anomaly in bilayer graphene/WSe$_2$ quantum point contacts', Phys. Rev. B 114, L111401 (2026). DOI: 10.1103/zss4-lmlm, https://doi.org/10.1103/zss4-lmlm (arXiv:2511.06384, https://arxiv.org/abs/2511.06384)
14. Donghao Liu, Dmitri Gutman, 'Conductance anomaly in a partially open adiabatic quantum point contact', Phys. Rev. B 113, 235412 (2026). DOI: 10.1103/vh89-rpxl, https://doi.org/10.1103/vh89-rpxl (arXiv:2510.20678, https://arxiv.org/abs/2510.20678)
15. Nair Aucar Boidi, Mikhail Kiselev, 'A density matrix renormalization group approach to quantum point contacts', arXiv:2607.02183 (2026), https://arxiv.org/abs/2607.02183