Paper Citation Record · LEDGER

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory

As of 7 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2505.24150.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2505.24150 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:43:02.181017Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:21:08.810875Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-07T05:21:08.905962Z

Reference resolution

37 of 37 outbound references displayed

verified exact1
verified fuzzy32
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7f1abf92-5fa2-423b-acdc-2803fea8d44e · outbound

This paper cites an unresolved cited work.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:43:08.782769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2accd2ab-126a-47df-b0a5-a6951825bf47 · outbound

This paper cites Semiclassical solution for the running escaping wave at x >∆/F , i.e.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Semiclassical solution for the running escaping wave at x >∆/F , i.e

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:08.567626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6fca06f8-5c7c-495a-b852-e970a48ee3e9 · outbound

This paper cites (3.12) The sign ± in the phase correlates with the sign ∓ in b(x).

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory (3.12) The sign ± in the phase correlates with the sign ∓ in b(x)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:08.315828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e62e50f5-6d87-4450-b064-98303f89af19 · outbound

This paper cites an unresolved cited work.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:43:08.047950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 72c42b88-ffa7-4e66-81d2-0d716aec6727 · outbound

This paper cites As discussed in Ref.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory As discussed in Ref

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:07.882287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 99d361a3-7bac-4a70-8c70-86adc9e3f8b2 · outbound

This paper cites (4.1) In this case the standing wave far away on the left from the tunnelling region is best approximated as the solu- tion of an effective linear Dirac equation.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory (4.1) In this case the standing wave far away on the left from the tunnelling region is best approximated as the solu- tion of an effective linear Dirac equation

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:07.612881Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 271e1e2b-662d-4a1a-894e-a0d01a7f349a · outbound

This paper cites Therefore the x- density of states is ρx = dpx π = dε πv = F dx πv.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Therefore the x- density of states is ρx = dpx π = dε πv = F dx πv

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:07.312772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8d49e3fb-6185-4ee7-bf13-d66acfecd48e · outbound

This paper cites (4.9) According to Eq.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory (4.9) According to Eq

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:07.099103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6d236b8a-4492-405b-8763-1d1380775ce8 · outbound

This paper cites Direct observation of a widely tunable bandgap in bi- layer graphene,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Direct observation of a widely tunable bandgap in bi- layer graphene,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:06.932638Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 76ae9ee9-6026-48ab-af1d-f9e8bc676892 · outbound

This paper cites Electronic transport in dual-gated bilayer graphene at large dis- placement fields,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Electronic transport in dual-gated bilayer graphene at large dis- placement fields,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:06.813422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f808439f-1c53-437e-85f0-978080815e33 · outbound

This paper cites Screening of the band gap in electrically biased bilayer graphene: From Hartree to Hartree-Fock.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Screening of the band gap in electrically biased bilayer graphene: From Hartree to Hartree-Fock

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T12:43:00.207883Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 52215878-e9eb-436e-822e-89e865bd00c2 · outbound

This paper cites Persistent current states in bilayer graphene,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Persistent current states in bilayer graphene,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:06.644860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6ade06d1-2c2e-4bb4-ab13-152b2f01411f · outbound

This paper cites Spontaneous momentum polarization and diodicity in Bernal bilayer graphene.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Spontaneous momentum polarization and diodicity in Bernal bilayer graphene

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-07T12:43:02.405255Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 78bf5aa9-ca82-475e-ba0d-a744c3dd4a45 · outbound

This paper cites Isospin- and momentum-polarized orders in bi- layer graphene,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Isospin- and momentum-polarized orders in bi- layer graphene,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:06.517023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e3ee2ed6-6be6-4c5e-863e-79d7841a2997 · outbound

This paper cites Exciton conden- sation in biased bilayer graphene,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Exciton conden- sation in biased bilayer graphene,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:06.310893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e1e7024d-d401-4971-87db-b515a57ebf4d · outbound

This paper cites Cascade of isospin phase transitions in bernal-stacked bilayer graphene at zero magnetic field,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Cascade of isospin phase transitions in bernal-stacked bilayer graphene at zero magnetic field,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:06.204803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7c0e52f3-f336-439e-aa1e-191ef697df98 · outbound

This paper cites Isospin magnetism and spin-polarized superconductivity in bernal bilayer graphene,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Isospin magnetism and spin-polarized superconductivity in bernal bilayer graphene,

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:06.107441Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8e8ae369-985e-44b5-b9ac-55c195bd9716 · outbound

This paper cites A theory of the electri- cal breakdown of solid dielectrics,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory A theory of the electri- cal breakdown of solid dielectrics,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:06.036955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4c5410be-980e-44b2-aad9-cbc21ca9a6e3 · outbound

This paper cites ¨Uber das verhalten eines elektrons im homo- genen elektrischen feld nach der relativistischen theorie diracs,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory ¨Uber das verhalten eines elektrons im homo- genen elektrischen feld nach der relativistischen theorie diracs,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:05.889646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5b9cb170-23a0-497a-859e-f3defdf8c2fe · outbound

This paper cites Consequences of dirac’s theory of positrons,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Consequences of dirac’s theory of positrons,

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:05.790016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 613dbbe4-1a04-4778-a7e2-8b1d5feafd58 · outbound

This paper cites Common-path in- terference and oscillatory zener tunneling in bilayer graphene p-n junctions,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Common-path in- terference and oscillatory zener tunneling in bilayer graphene p-n junctions,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:05.622870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 33b207b0-fe12-4b40-a7f3-f5bfed1b1bdb · outbound

This paper cites Ground-state decay rate for the zener breakdown in band and mott insulators,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Ground-state decay rate for the zener breakdown in band and mott insulators,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:05.509652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e93ce622-1961-49ad-9b25-ce9a08f6811e · outbound

This paper cites Quantum elec- trodynamics with anisotropic scaling: Heisenberg–euler action and schwinger pair production in the bilayer graphene,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Quantum elec- trodynamics with anisotropic scaling: Heisenberg–euler action and schwinger pair production in the bilayer graphene,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:05.371249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 052d8ca5-b9bc-4e74-af38-90eabc5d610d · outbound

This paper cites Steep-slope switching using bilayer graphene tunnel field effect transistors,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Steep-slope switching using bilayer graphene tunnel field effect transistors,

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:05.217199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8eae396a-e611-45b8-965c-c3132a75c7df · outbound

This paper cites Steep slope field effect transis- tors based on 2d materials,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Steep slope field effect transis- tors based on 2d materials,

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:05.065531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f2c86b70-650c-434e-947e-ed04bcb810e0 · outbound

This paper cites On the calculation of the transmission co- efficient by means of the phase-integral method,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory On the calculation of the transmission co- efficient by means of the phase-integral method,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:04.934750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a7823891-bdbc-49e4-8a5f-fb508caec472 · outbound

This paper cites an unresolved cited work.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:43:04.724849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e7bca95c-8f09-4fdc-9769-1e0e3fd6894e · outbound

This paper cites The electronic properties of bilayer graphene,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory The electronic properties of bilayer graphene,

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:04.475795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1da9173b-e149-42b6-a9be-af1d6d479104 · outbound

This paper cites Common path interference in zener tunneling is a uni- versal phenomenon,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Common path interference in zener tunneling is a uni- versal phenomenon,

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:04.309029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2874ed9e-b2c5-4311-a8cc-7b271e336687 · outbound

This paper cites The return of the quartic oscillator: The complex wkb method,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory The return of the quartic oscillator: The complex wkb method,

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:04.034377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation fe52498e-0823-499c-b62d-e57caf1ad65a · outbound

This paper cites Edge states and topological in- variants of non-hermitian systems,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Edge states and topological in- variants of non-hermitian systems,

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:03.862918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation da16dad0-a322-4953-8b49-8cacb0b939fe · outbound

This paper cites Ex- ceptional topology of non-hermitian systems,.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Ex- ceptional topology of non-hermitian systems,

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:03.608045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f9dc10e2-1b4e-426b-97d2-d784f9406f26 · outbound

This paper cites (A1) The full wavefunction Ψ R = φReiS+ is given by ΨR = r J 2v s F pA(x) (x − x−) 1 2 (x − x+) 1 2 ! eiS+.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory (A1) The full wavefunction Ψ R = φReiS+ is given by ΨR = r J 2v s F pA(x) (x − x−) 1 2 (x − x+) 1 2 ! eiS+

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:03.395989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ebbe62b2-2b9d-42cf-9db3-b4e3a832d4a8 · outbound

This paper cites Under this, acl : ( x − x+) 1 2 → i(x+ − x) 1 2 , (A3) cl : ( x − x+) 1 2 → −i(x+ − x) 1 2 (A4) and acl : iS+ → −S+, (A5) cl : iS+ → S+.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Under this, acl : ( x − x+) 1 2 → i(x+ − x) 1 2 , (A3) cl : ( x − x+) 1 2 → −i(x+ − x) 1 2 (A4) and acl : iS+ → −S+, (A5) cl : iS+ → S+

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:03.207876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 54fb2534-e05f-4a52-ac3c-74a050dc6cb8 · outbound

This paper cites Since we desire a standing wave for x < x−, we will need to keep both paths in the complex plain.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Since we desire a standing wave for x < x−, we will need to keep both paths in the complex plain

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:03.024115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6c899df4-5c05-4531-b941-72dbdc8e88b5 · outbound

This paper cites (A18) One can verify the current (A18) by direct numerical methods.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory (A18) One can verify the current (A18) by direct numerical methods

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:02.833668Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 58a353b0-6ee8-482e-8bca-39db2b51a8f0 · outbound

This paper cites Therefore the x-density of states is ρx = dpx π = dϵ πv = F dx πv (A21) Note that we divide byπ instead of 2π because this is the standing wave.

Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory Therefore the x-density of states is ρx = dpx π = dϵ πv = F dx πv (A21) Note that we divide byπ instead of 2π because this is the standing wave

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:43:02.642721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

Observation 74609096-9e02-4b20-b0d0-810467257bd7 · inbound

Exciton condensation from level repulsion: application to bilayer graphene cites this paper.

Exciton condensation from level repulsion: application to bilayer graphene Zener tunnelling in biased bilayer graphene via analytic continuation of semiclassical theory

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:21:08.912656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.