Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1007.3907

Dirac point metamorphosis from third-neighbor couplings in graphene

Cristina Bena·Laurent Simon
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the band structure and the density of states of graphene in the presence of a next-to-nearest-neighbor coupling (N2) and a third-nearest-neighbor coupling (N3). We show that for values of N3 larger or equal to 1/3 of the value of the nearest-neighbor hopping (NN), extra Dirac points appear in the spectrum. If N3 is exactly equal to 1/3 NN, the new Dirac points are localized at the M points of the Brillouin zone and are hybrid: the electrons have a linear dispersion along the GammaM direction and a quadratic dispersion along the perpendicular direction MK. For larger values of N3 the new points have a linear dispersion, and are situated along the MK line. For a value of N3 equal to 1/2 NN, these points merge with the Dirac cones at the K points, yielding a gapless quadratic dispersion around K, while for larger values each quadratic point at K splits again into four Dirac points. The effects of changing the N2 coupling are not so dramatic. We calculate the density of states and we show that increasing the N3 coupling lowers the energy of the Van Hove singularities, and when N3 is larger than 1/3 NN the Van Hove singularities split in two, giving rise to extra singularities at low energies.

Explore related subjects

cond-mat.mes-hall

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Cristina Bena, Laurent Simon. 2010-07-22. Dirac point metamorphosis from third-neighbor couplings in graphene. https://doi.org/10.1103/physrevb.83.115404

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

KEEP EXPLORING

Related papers

arXiv2026

Inverse Purcell Suppression of Decoherence in Majorana Qubits via Environmental Engineering

We show that the electromagnetic or phononic environment of a topological quantum device can be engineered to actively suppress decoherence. For a Majorana qubit in a superconducting wire, the exponentially small splitting $ε\sim e^{-L/ξ}$ that provides topological protection also makes the qubit vulnerable to low-frequency noise. From a microscopic local interaction, we derive the effective low-energy coupling between the Majorana parity operator and a bosonic field; the coupling strength itself is proportional to $ε$, reflecting the qubit's non-local nature. The resulting pure-dephasing rate scales as $Γ_ϕ\propto ε^2 S(ε)$, with $S(ε)$ the environmental noise power at frequency $ε$. In the experimentally relevant high-temperature regime ($k_B T \gtrsim \hbarε$), this gives $Γ_ϕ\propto ερ(ε) T$, where $ρ(ε)$ is the environmental density of states. By engineering an environment with a suppressed low-frequency density of states, $ρ_{\text{eng}}(ω) = ρ_0 (ω/ω_c)^α$ for $ω< ω_c$ ($α> 0$), the dephasing rate drops to $Γ_ϕ^{\text{eng}} \propto ε^{α+1} \propto e^{-(α+1)L/ξ}$. Thus, longer wires yield exponentially better coherence---a direct synergy with topological protection. This "inverse Purcell" effect, which suppresses the density of states at the qubit frequency, provides a quantitative design principle for environmental engineering. Our work establishes spectral density shaping as a practical method for enhancing coherence in topological quantum devices.

cond-mat.mes-hall↗
arXiv2026

Axionic tunneling from a topological Kondo insulator

Discoveries over the past two decades have revealed the remarkable ability of quantum materials to emulate relativistic properties of the vacuum, from Dirac cones in graphene to Dirac surface states of topological insulators. Yet one of the most elusive consequences of topology in quantum matter -- the axionic ${\bf E}\cdot{\bf B}$ contribution to the electromagnetic response, predicted to produce strong magnetoelectric effects -- remains experimentally challenging to detect. Here we report evidence for an axion-like magnetoelectric response obtained through scanning tunneling microscopy (STM) using a SmB$_6$ nanowire tip on an antiferromagnetic Fe$_{1+x}$Te sample. Our measurements reveal a striking voltage-induced magnetization: millivolt biases generate measurable tip magnetizations that reverse with the voltage. The magnitude, tunability, and reversibility of this signal are consistent with an axion-like ${\bf E} \cdot {\bf B}$ coupling, which naturally accounts for the voltage-odd magnetic component of the tip spectral function while strongly constraining a conventional static-magnetism interpretation. Moreover, millivolt-scale control of spin polarization in a tunnel junction provides a new route for probing axionic electrodynamics and opens avenues for future STM and spintronic applications.

cond-mat.mes-hall↗
arXiv2026

Exciton-mediated optical control of liquid-solid friction

Interfacial friction in nanofluidic systems can arise from fluctuation-induced coupling between liquid charge fluctuations and the internal excitations of the confining solid. Here, we develop a microscopic theory of exciton-mediated solid-liquid friction based on the coupling between optically generated excitons and charge fluctuations in water. We distinguish between static excitons, localized by disorder or functionalization, and dynamic excitons, which interact with water through polarization fluctuations. In both cases, we derive analytical formulas for the excitonic friction, which is experimentally tunable and can significantly reduce the slip length and thereby the hydraulic permeability of nanochannels. Applying our framework to carbon nanotubes, we quantitatively reproduce the recent measurements of Kistwal et al., showing a reduction of nanotube diffusion under optical excitation, without fitting parameters. More broadly, our results establish excitons as a mechanism to optically control nanofluidic transport and suggest that excitonic photoluminescence could provide an optical probe of flow velocity inside nanochannels.

cond-mat.mes-hall↗