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arxiv: 1906.08508 · v1 · pith:K5WRZPMWnew · submitted 2019-06-20 · ❄️ cond-mat.supr-con

AC anomalous Hall effect in topological insulator Josephson junctions

A.G. Mal'shukov This is my paper

Pith reviewed 2026-05-25 19:33 UTC · model grok-4.3

classification ❄️ cond-mat.supr-con
keywords anomalous Hall effecttopological insulatorJosephson junctionvoltage biasHall current oscillationsballistic transportZeeman fields-wave superconductors
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The pith

Voltage bias drives an oscillating anomalous Hall current in a topological insulator Josephson junction, with amplitude falling linearly as bias increases and phase shifted by π/2 from the Josephson current.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper calculates the nonstationary anomalous Hall current that appears when a voltage is applied across a Josephson junction made from two s-wave superconducting contacts on the surface of a three-dimensional topological insulator that carries a homogeneous Zeeman field. In the ballistic weak-tunneling regime the Hall current oscillates in time, its phase lags the Josephson current by π/2, and its amplitude decreases linearly with the contact voltage difference; a fixed phase difference between the superconductors produces no Hall current at all. A reader would care because the result ties the time-dependent Hall response directly to the voltage-driven dynamics of the superconducting phase on the topological surface states.

Core claim

In a voltage-biased Josephson junction on a topological insulator surface the anomalous Hall current oscillates temporally; the oscillations are shifted by π/2 relative to the Josephson current, their amplitude decreases linearly with the electric potential difference between the contacts, and no Hall current is generated by a stationary phase difference between the contact order parameters.

What carries the argument

The time-dependent anomalous Hall current generated by the combination of the Zeeman field and the voltage-driven phase evolution of the superconducting contacts acting on the ballistic surface states of the topological insulator.

If this is right

  • The Hall current is strictly AC under voltage bias and vanishes for static phase differences.
  • Its amplitude scales linearly downward with increasing contact voltage difference.
  • The π/2 phase lag between Hall and Josephson currents is fixed by the underlying dynamics.
  • The effect exists only in the ballistic weak-tunneling limit where 4π-periodic features are absent.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The linear voltage dependence of the amplitude offers a concrete scaling relation that could be checked by varying bias in a single device.
  • The same surface-state response might appear under a time-varying phase drive even without net voltage bias.
  • Comparison of the effect in topological versus trivial surface states could serve as a transport signature of topology in hybrid junctions.

Load-bearing premise

Tunneling between the superconducting contacts and the topological insulator surface is weak enough that the 4π-periodic topological Josephson effect is absent.

What would settle it

A measurement showing either a time-independent Hall current under fixed superconducting phase difference or the absence of π/2-shifted oscillations under finite voltage bias would falsify the central claim.

Figures

Figures reproduced from arXiv: 1906.08508 by A.G. Mal'shukov.

Figure 1
Figure 1. Figure 1: Fig.1. It will be assumed that the superconducting con [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1: (Color online) Two superconducting contacts are [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The anomalous Hall current as a function of the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

A nonstationary anomalous Hall current is calculated for a voltage biased Josephson junction, which is composed of two s-wave superconducting contacts deposited on the top of a three dimensional topological insulator (TI). A homogeneous Zeeman field was assumed at the surface of TI. The problem has been considered within the ballistic approximation and on the assumption that tunneling of electrons between contacts and the surface of TI is weak. In this regime the Josephson current has no features of the $4\pi$-periodic topological effect which is associated with Andreev bound states. It is shown that the Hall current oscillates in time. The phase of these oscillations is shifted by $\pi/2$ with respect to the Josephson current and their amplitude linearly decreases with the electric potential difference between contacts. It is also shown that the Hall current cannot be induced by a stationary phase difference of contact's order parameters.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript calculates a nonstationary anomalous Hall current in a voltage-biased Josephson junction consisting of two s-wave superconducting contacts on the surface of a 3D topological insulator with an applied homogeneous Zeeman field. Working in the ballistic limit under weak tunneling (explicitly excluding 4π-periodic Andreev bound states), the authors show that the Hall current oscillates in time with a π/2 phase shift relative to the Josephson current, that its amplitude decreases linearly with the contact voltage difference, and that no Hall current is generated by a stationary phase difference between the superconducting order parameters.

Significance. If the central calculational result holds, the work supplies an explicit, falsifiable prediction for an AC anomalous Hall response in a topologically nontrivial Josephson junction under bias. The result is obtained directly from the stated approximations without additional free parameters or ad-hoc fitting, and the secondary claim (absence of Hall current for static phase) follows immediately from the same framework. This could serve as a benchmark for future experiments probing time-dependent Hall transport in TI-superconductor hybrids.

minor comments (3)
  1. [Abstract] The abstract states the main results but supplies no equations or derivation outline; the reader must reach the body of the paper to locate the explicit expressions for the time-dependent Hall current and the linear voltage dependence.
  2. [§2] Notation for the Zeeman field strength, tunneling amplitude, and voltage bias should be introduced once in §2 and used consistently; several symbols appear to be redefined in later sections without cross-reference.
  3. [Figure 3] Figure captions for the time-dependent current plots should explicitly state the parameter values (e.g., Zeeman field magnitude, bias voltage) used to generate the curves.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our work and for recommending minor revision. The referee's summary accurately reflects the scope and main findings of the manuscript. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper derives its central results (time-dependent Hall current with π/2 phase shift relative to Josephson current, linear voltage dependence of amplitude, and absence of Hall current for stationary phase difference) via direct calculation under explicitly stated approximations: ballistic transport and weak tunneling (explicitly excluding 4π-periodic Andreev states). No equations or steps reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations; the claims are calculational outputs from the stated model rather than renamings or imported uniqueness theorems. The derivation is self-contained against the paper's own framework.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Review performed on abstract only; no equations or sections available to identify free parameters, axioms, or invented entities.

axioms (2)
  • domain assumption Ballistic approximation for electron motion
    Stated as the regime in which the calculation is performed.
  • domain assumption Weak tunneling between superconducting contacts and TI surface
    Explicitly assumed to suppress the 4π-periodic topological Josephson effect.

pith-pipeline@v0.9.0 · 5674 in / 1343 out tokens · 26051 ms · 2026-05-25T19:33:35.773159+00:00 · methodology

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Reference graph

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