Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 468

The DOI matches its Crossref record; 58 of the 58 references it cites were found in a registry or an index.

Electrical linear-response theory in an arbitrary magnetic field: A new Fermi-surface formation

Baranger, Harold U., Stone, A. Douglas·1989·Physical Review B
DOI 10.1103/physrevb.40.8169
Open this paper in CoChat — free account

Abstract

We develop a novel formulation of dc electrical linear-response theory for a phase-coherent conductor with multiple leads valid in arbitrarily strong magnetic field and for a given impurity configuration and measuring geometry. This formulation is convenient for discussion of the quantum Hall effect and mesoscopic transport phenomena. We express the total current response ${I}_{m}$ through lead $m$ completely in terms of the voltages ${V}_{n}$ applied at the leads, independent of the electric field in the material, i.e., ${I}_{m}=\ensuremath{\Sigma}{n}^{}{g}_{\mathrm{mn}}{V}_{n}$. We show that while the current-density response is not in general expressible as a Fermi-surface quantity, the total transport current determined by these conductance coefficients ${g}_{\mathrm{mn}}$ does depend only on the wave functions (or Green functions) at the Fermi surface as $T\ensuremath{\rightarrow}0$. This yields new and useful Green-function expressions for the ${g}_{\mathrm{mn}}$ and the longitudinal and Hall resistances. When transformed by appropriate applications of scattering theory, these expressions are shown to be equivalent to the relation ${g}_{\mathrm{mn}}={T}_{\mathrm{mn}}$, where ${T}_{\mathrm{mn}}$ is the sum of all the transmission coefficients between leads $m$ and $n$, as first obtained by B\"uttiker on the basis of phenomenological arguments. A brief discussion of the relation between this formula and other proposed Landauer formulas is given. It is noted that the occurrence of the quantum Hall effect is very natural in this formulation and simple conditions on the scattering matrix of the conductor which imply the quantum Hall effect are derived.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physrevb.40.8169

Cites

58 of 58 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Cited by

See all 468

Metadata

Authors
Baranger, H. U., & Stone, A. D.
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
1989-10-15
Volume
40
Issue
12
Pages
8169-8193
ISSN
0163-1829 (ISSN-L)
DOI
10.1103/physrevb.40.8169
OpenAlex
W2061302254
Cited by
468
References
58
FWCI
15.95
Type
journal article
Language
en
Open access
closed

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.