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arXiv:2606.31586

Topological zero-reflection points in multi-terminal quantum wire junctions

Abhiram Soori, Udit Khanna, Diptiman Sen

cond-mat.mes-hallquant-phSubmitted Jun 30, 2026• Announced Jul 1, 2026
v1 · Jun 30, 2026v2 · Jul 16, 2026v3 · Oct 14, 2026v4 · Oct 25, 2026v5 · Oct 27, 2026
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Abstract

We study scattering in noninteracting multi-terminal quantum wire junctions and show that junctions with dihedral symmetry can exhibit exact zero-reflection points for $N \ge 4$ terminals. By analyzing the scattering matrix, we identify these reflectionless points in the $(E,t')$ parameter space, where $E$ is the incident particle energy and $t'$ is the junction hopping amplitude. These points exhibit an even-odd dependence on $N$ and converge asymptotically to a common limiting value in the large-$N$ limit. We show that the reflectionless points are characterized by an integer winding number associated with the phase of the reflection amplitude, providing a topological description for their stability against weak on-site disorder. We also consider junctions with broken time-reversal symmetry and find that a magnetic flux can induce additional reflectionless points, including for the $N = 3$ case. For a four-terminal junction threaded by a $π$-flux, we identify a unique parameter regime in which the reflection amplitude vanishes over the entire energy band. Finally, we discuss experimental signatures through the behavior of Friedel oscillations and examine the stability of these reflectionless points in the presence of weak interactions.

Journal reference
Phys. Rev. B 114, 225423 (2026)
DOI
10.1103/5y2t-4cbg
Comments
15 pages, 1 table, 7 figures. Comments are welcome

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We study scattering in noninteracting multi-terminal quantum wire junctions and show that junctions with dihedral symmetry can exhibit exact zero-reflection points for N≥4N \ge 4N≥4 terminals. By analyzing the scattering matrix, we identify these reflectionless points in the (E,t′)(E,t')(E,t′) parameter space, where EEE is the incident particle energy and t′t't′ is the junction hopping amplitude. These points exhibit an even-odd dependence on NNN and converge asymptotically to a common limiting value in the large-NNN limit. We show that the reflectionless points are characterized by an integer winding number associated with the phase of the reflection amplitude, providing a topological description for their stability against weak on-site disorder. We also consider junctions with broken time-reversal symmetry and find that a magnetic flux can induce additional reflectionless points, including for the N=3N = 3N=3 case. For a four-terminal junction threaded by a πππ-flux, we identify a unique parameter regime in which the reflection amplitude vanishes over the entire energy band. Finally, we discuss experimental signatures through the behavior of Friedel oscillations and examine the stability of these reflectionless points in the presence of weak interactions.
We study the conductance of three or more semi-infinite wires which meet at a junction. The electrons in the wires are taken to interact weakly with each other through a short-range density-density interaction, and they encounter a general scattering matrix at the junction. We derive the renormalization-group equations satisfied by the S-matrix, and we identify its fixed points and their stabilities. The conductance between any pair of wires is then studied as a function of physical parameters such as temperature. We discuss the possibility of observing the effects of junctions in present day experiments, such as the four-terminal conductance of a quantum wire and crossed quantum wires.
We investigate the transport of correlated fermions through a junction of three one-dimensional quantum wires pierced by a magnetic flux. We determine the flow of the conductance as a function of a low-energy cutoff in the entire parameter space. For attractive interactions and generic flux the fixed point with maximal asymmetry of the conductance is the stable one, as conjectured recently. For repulsive interactions and arbitrary flux we find a line of stable fixed points with vanishing conductance as well as stable fixed points with symmetric conductance (4/9)(e(2)/h).
Generating non-locally entangled electron pairs via Cooper-pair splitting is vital for solid-state quantum information processing. However, isolating the underlying crossed Andreev reflection (CAR) is challenging due to competing transport processes like electron tunneling (ET) and local Andreev reflection (AR). Here, we propose a flux-tunable four-terminal normal metal-superconductor junction that achieves deterministic, 100\% efficient CAR. We demonstrate that at exactly half a magnetic flux quantum (φ=πφ=πφ=π), exact destructive Aharonov-Bohm and Peierls interferences structurally forbid ET and AR respectively. By tuning the central junction hopping, electron reflection is also suppressed to zero. Using the Cauchy argument principle, we prove that this suppression manifests as a quantized topological winding number, guaranteeing a topologically protected unit CAR probability. We establish that this regime is characterized by a strictly positive cross-correlation shot noise, providing an unambiguous experimental signature of Cooper-pair splitting. Furthermore, this perfect CAR is nearly broadband within the superconducting gap and remarkably robust against structural disorder, offering a highly resilient architecture for deterministic nonlocal entanglement generation.
We construct a scattering matrix formulation for the topological classification of one-dimensional superconductors with effective time-reversal symmetry in the presence of interactions. For an isolated system, Fidkowski and Kitaev have shown that such systems have a Z_{8} topological classification. We here show that these systems have a unitary scattering matrix at zero temperature when weakly coupled to a normal-metal lead, with a topological index given by the trace of the Andreev-reflection matrix, trr_{he}. With interactions, trr_{he} generically takes on the finite set of values 0, ±1, ±2, ±3, and ±4. We show that the two topologically equivalent phases with trr_{he}=±4 support emergent many-body end states, which we identify to be a topologically protected Kondo-like resonance. The path in phase space that connects these equivalent phases crosses a non-Fermi-liquid fixed point where a multiple-channel Kondo effect develops. Our results connect the topological index to transport properties, thereby highlighting the experimental signatures of interacting topological phases in one dimension.
We consider a honeycomb network built of quantum wires, with each node of the network having a Y junction of three wires with a ring through which flux can be inserted. The junctions are the basic circuit elements for the network, and they are characterized by $3\ifmmode\times\else\texttimes\fi{}3$ conductance tensors. The low energy stable fixed point tensor conductances result from quantum effects, and are determined by the strength of the interactions in each wire and the magnetic flux through the ring. We consider the limit where there is decoherence in the wires between any two nodes, and study the array as a network of classical three-lead circuit elements whose characteristic conductance tensors are determined by the quantum fixed point. We show that this network has some remarkable transport properties in a range of interaction parameters: It has a Hall resistance quantized at Rxy=h/e2{R}_{xy}=h/{e}^{2}Rxy​=h/e2, although the longitudinal resistivity is nonvanishing. We show that these results are robust against disorder, in this case nonhomogeneous interaction parameters ggg for the different wires in the network.
In this paper, we discuss strong coupling limits of topological quantum critical points (TQCPs) where quantum phase transitions between two topological distinct superconducting states take place. We illustrate that while superconducting phases on both sides of TQCPs spontaneously break the same symmetries, universality classes of critical states can be identified only when global symmetries in topological states are further specified. In dimensions d=2and3d=2\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}3d=2and3, we find that continuous (d+1)th(d+1)\mathrm{th}(d+1)th-order transitions at weakly interacting TQCPs that were pointed out previously in the presence of the emergent Lorentz symmetry can be terminated by strongly interacting fixed points of Majorana fields. For 2d2d2d time reversal symmetry breaking TQCPs, termination points are supersymmetric with N=4Nf=1\mathcal{N}=4{N}_{f}=1N=4Nf​=1 (where Nf{N}_{f}Nf​ is the number of four-component Dirac fermions and N\mathcal{N}N is the number of two-component real fermions) beyond which transitions are discontinuous first-order ones. For 2d2d2d time reversal symmetric TQCPs without other global symmetries, termination points of (d+1)th(d+1)\mathrm{th}(d+1)th-order continuous transition lines are generically conformal invariant without supersymmetry. Beyond these strong coupling fixed points, there are first-order discontinuous transitions as far as the protecting symmetry is not spontaneously broken but no direct transitions if the protecting symmetry is spontaneously broken in the presence of strong interactions. In this case, termination points can become supersymmetric with N=4Nf=2\mathcal{N}=4{N}_{f}=2N=4Nf​=2 only when interacting Majorana fermions further display an emergent global U(1)\text{U}(1)U(1) symmetry. In 3d3d3d, strong coupling termination points can be further effectively represented by new emergent gapless real bosons weakly coupled with free gapless Majorana fermions. However, in 1d1d1d, time reversal symmetric (d+1)th(d+1)\mathrm{th}(d+1)th continuous transition lines of TQCPs are terminated by simple free Majorana fermion fixed points.