Density of states, screening and the width of the quantum Hall plateaus

K. Tsemekhman; V. Tsemekhman; C. Wexler

Home/Archive/arXiv

arXiv · cond-mat/9810076

Density of states, screening and the width of the quantum Hall plateaus

K. Tsemekhman·V. Tsemekhman·C. Wexler

View original source ↗Read source document ↗Export metadata ↓

Abstract

We present a consistent treatment of the quantum Hall effect within the electrostatic approximation. We derive the form of the density of states (DOS) which differs from the usual gaussian shape valid for non-interacting electrons. Below a crossover temperature, this DOS gradually transforms into the non-interacting DOS near the Fermi energy. We obtain an estimate of this crossover temperature, which determines the range of validity of this framework, and allows a reconciliation of the width and temperature dependence of the quantum Hall plateaus with experiments. The DOS dramatically enhances the electron-lattice relaxation rate, thus reducing the possibility of electron overheating.

Explore related subjects

cond-mat.mes-hall cond-mat.stat-mech cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

K. Tsemekhman, V. Tsemekhman, C. Wexler. 1998-10-07. Density of states, screening and the width of the quantum Hall plateaus. https://arxiv.org/abs/cond-mat/9810076

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Second-order dc conductivity in the velocity-gauge Keldysh formalism: gauge-invariant decomposition into nonlinear Drude, Berry-curvature-dipole, and quantum-metric responses

We derive a gauge-invariant clean-limit decomposition of the second-order dc nonlinear conductivity in multiband tight-binding systems within the velocity-gauge Keldysh Green's function formalism. In the constant-relaxation-time approximation, the dc response separates into four contributions with distinct lifetime $τ$ scalings and physical origins: the nonlinear Drude term $σ^{\mathrm{ND}}_{ijk}\proptoτ^{2}$, the Berry-curvature-dipole term $σ^{\mathrm{BCD}}_{ijk}\proptoτ$, the intraband quantum-metric-dipole term $σ^{\mathrm{intra\text{-}QMD}}_{ijk}\proptoτ^{0}$, and the interband quantum-metric-dipole term $σ^{\mathrm{inter\text{-}QMD}}_{ijk}\proptoτ^{0}$. The intraband term is a Fermi-surface dipole of the ordinary band quantum metric, while the interband term is written, in the present representation, as a Fermi-sea-type response involving a band-normalized quantum metric. Working entirely within the velocity-gauge Keldysh--Kubo framework, we show that all connection-dependent commutator terms generated in the band-basis expansion cancel exactly between the covariant-quantum-connection sector $σ^{\mathcal{C}}_{ijk}$ and the three-Berry-connection sector $σ^{\mathcal{T}}_{ijk}$, making the role of the Peierls contact velocity vertices $V_{ij}$ and $V_{ijk}$ explicit; a complementary projector-based derivation appears in Ulrich et al., Phys. Rev. B 113, L201107 (2026), and our Fermi-surface dc-limit expression agrees with that reference after accounting for index and convention differences. As a diagnostic illustration, we introduce a real two-band model in which the Berry curvature and hence the BCD response vanish identically while the intraband quantum-metric dipole remains finite, establishing a practical route to quantum-metric dc responses not reducible to the Berry-curvature-dipole mechanism.

cond-mat.mes-hall↗

arXiv2026

Narrow-Sense Type-III Dirac Cones and Additional Flat Lines on a Honeycomb Lattice with Anisotropic Next-Nearest-Neighbor Hoppings

Critically tilted Dirac cones have attracted considerable attention because of their unconventional electronic properties in two-dimensional massless Dirac-fermion systems. Among them, the narrow-sense type-III Dirac cone is characterized by a flat dispersion along the direction connecting the two Dirac points. Using a tight-binding model on a single-orbital honeycomb lattice, we demonstrate that narrow-sense type-III Dirac cones can be realized by tuning anisotropic next-nearest-neighbor hoppings. Type-I and type-II Dirac cones emerge on either side of the critical point, enabling a systematic investigation of the electronic properties across the type-I, narrow-sense type-III, and type-II regimes. We further find that the present model exhibits additional flat lines in momentum space whose energy coincides with the Dirac-point energy at the narrow-sense type-III critical point. These flat lines lead to a pronounced enhancement of the density of states above the Fermi energy and, consequently, the electronic specific heat is substantially enhanced compared with that expected for an ideal narrow-sense type-III Dirac cone. Our results show that the honeycomb lattice with anisotropic next-nearest-neighbor hoppings provides a simple platform for exploring unconventional thermodynamic properties arising from the energy coincidence of narrow-sense type-III Dirac cones and additional flat lines at the Fermi energy.

cond-mat.mes-hall↗

arXiv2026

Time evolution in the multi-component dynamical Keldysh models

We construct a time evolution operator for a dynamical quantum models with a multi-component random Gaussian field characterized by a long correlation time. We analyze three paradigmatic cases: non-Abelian $SU(2)$ symmetry class for the three-component Gaussian noise and Abelian symmetry classes $U(1)$ and $Z_2$ for the two- and one-component noises correspondingly. Starting with a limiting case of the infinite correlation time (Keldysh model) we shown that statistics of the two-component random field with a non-zero mean is described by the Rice distribution. We derived and solved the system of coupled linear differential equations for the exact diagonal and off-diagonal single-particle Green's functions. We showed how the finite time correlation in Keldysh models are accounted by a continuous fractions method.

cond-mat.mes-hall↗