Chiral chains with two valleys and disorder of finite correlation length

Abstract

In one-dimensional disordered systems with a chiral symmetry it is well-known that electrons at energy $E=0$ avoid localization and simultaneously exhibit a diverging density of states (DOS). For $N$ coupled chains with zero-correlation-length disorder, the diverging DOS remains for odd $N$, but a vanishing DOS is found for even $N$. We use a thin spinless graphene nanotube with disordered Semenoff mass and disordered Haldane coupling to construct $N=2$ chiral chain models which at low energy have two linear band crossings at different momenta $\pm K$ (two valleys) and disorder with an arbitrary correlation length $\xi$ in units of lattice constant $a$. We find that the finite momentum $\pm K$ forces the disorder in one valley to depend on the disorder in the other valley, thus departing from known analytical results which assume having $N$ independent disorders (whatever their spatial correlation lengths). Our main numerical results show that for this inter-dependent mass disorder the DOS is also suppressed in the limit of strongly coupled valleys (lattice-white noise limit, $\xi /a=0$) and exhibits a non-trivial crossover as the valleys decouple ($\xi /a\gtrsim 5$) into the DOS shapes of the $N=1$ continuum model with finite correlation length $\xi$. We also show that changing the intra-unit-cell geometry of the disordered Haldane coupling can tune the amount of inter-valley scattering yet at lowest energies it produces the decoupled-valley behavior ($N=1$) all the way down to lattice white noise.

References in corpus (12)

• Delocalization in coupled one-dimensional chains
• Anderson localization due to random magnetic field in two dimensions
• Density of states in coupled chains with off-diagonal disorder
• Anderson localization and the topology of classifying spaces
• Nonuniversality in quantum wires with off-diagonal disorder: a geometric point of view
• On Pseudogaps in One-Dimensional Models with Quasi-Long-Ranged-Order
• Feynman's Propagator Applied to Network Models of Localization
• Exact Numerical Calculation of the Density of States of the Fluctuating Gap Model
• Singularities and Pseudogaps in the Density of States of Peierls Chains
• Topological phase transitions in the 1D multichannel Dirac equation with random mass and a random matrix model
• Transport Properties and Density of States of Quantum Wires with Off-diagonal Disorder
• Exactly solvable toy model for the pseudogap state

Cited by in corpus (1)

• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes