Transport scaling and critical tilt effects in disordered two-dimensional Dirac fermions

Abstract

Two-dimensional (2D) Dirac fermions occur ubiquitously in condensed matter systems from topological phases to quantum critical points. Since the advent of topological semimetals, where the dispersion is often tilted around the band crossing where the Dirac fermion can appear, tilt has emerged as a key handle that controls physical properties. We study how tilt affects the transport and spectral properties of tilted 2D Dirac fermions under scalar disorder. Although our spectral analyses always show conformity to appropriate Gaussian ensembles, suggestive of delocalization, the conductivity scaling $g(L)$ shows a surprising richness. For a single Dirac node, relevant for quantum Hall transitions and topological insulator surface states, we find $g(L)\sim a_1\log (L)$ with a tilt-dependent coefficient $a_1>0$. Interestingly, when the tilt and transport directions are aligned, $a_1$ and hence $g(L)$ shows a spike at the critical point between the type-I and type-II regimes of the Dirac node. For systems with two Dirac nodes with unbroken time-reversal symmetry, pertinent to quasi-2D Dirac materials, we find $g(L)\sim L^{a_1}(\log L{)}^{a_2}$. However, we find a surprising tension between tilt along and perpendicular to the transport directions. For the former, $a_1$ changes sign as a function of tilt, hinting at a tilt-driven localization-delocalization transition, while $a_1<0$ for all tilts in the latter case, implying localization. These localized behaviors also reveal tension with the delocalization seen in spectral properties and suggest differing localization tendencies in real and Hilbert spaces. Overall, our work identifies tilt as an essential control parameter that uncovers rich and unconventional transport physics in 2D Dirac materials.

18 pages, 13 figures

References in corpus (58)

• Topological Insulators
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Type-II Weyl Semimetals
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Anderson Transitions
• Localization of interacting fermions at high temperature
• Topological Materials: Weyl Semimetals
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• All-graphene integrated circuits via strain engineering
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• Strongly enhanced charge-density-wave order in monolayer NbSe${}_2$
• Quantum Hall Ferromagnetism in Graphene
• Scaling Theory of the Integer Quantum Hall Effect
• Quantum transport of massless Dirac fermions in graphene
• Localization of ultrasound in a three-dimensional elastic network
• Riemannian symmetric superspaces and their origin in random matrix theory
• Theory of the topological Anderson insulator
• Three-dimensional localization of ultracold atoms in an optical disordered potential
• Anomalous Hall Effect in Weyl Metals
• Pressure-Induced Zero-Gap Semiconducting State in Organic Conductor $\alpha$-(BEDT-TTF)${}_2$I${}_3$ Salt
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• Linear magnetoresistance caused by mobility fluctuations in the n-doped Cd3As2
• Periodically driven ergodic and many-body localized quantum systems
• Demonstration of one-parameter scaling at the Dirac point in graphene
• Arc-tunable Weyl Fermion metallic state in Mo${}_x$W${}_{1-x}$Te${}_2$
• Disorder-induced Floquet Topological Insulators
• Topological delocalization of two-dimensional massless Dirac fermions
• Multifractality and critical fluctuations at the Anderson transition
• Fermi arcs and their topological character in the candidate type-II Weyl semimetal MoTe2
• Matterwave localization in disordered cold atom lattices
• Electronic properties of 8-Pmmn borophene
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Higgs mode and its decay in a two dimensional antiferromagnet
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• Strain-induced pseudomagnetic field in Dirac semimetal borophene
• Quantum transport in Dirac materials: signatures of tilted and anisotropic Dirac and Weyl cones
• Nodal Arc in Disordered Dirac Fermions: Connection to Non-Hermitian Band Theory
• Effect of electron-hole asymmetry on optical conductivity in 8-Pmmn borophene
• Anomalous Nernst and Thermal Hall Effects in Tilted Weyl Semimetals
• Observation of two-dimensional Anderson localisation of ultracold atoms
• Large Disparity Between Optical and Fundamental Band Gaps in Layered In2Se3
• Signature of tilted Dirac cones in Weiss oscillations of $8-Pmmn$ borophene
• Origin of the quasi-quantized Hall effect in ZrTe5
• The random magnetic flux problem in a quantum wire
• Correlations of Eigenfunctions in Disordered Systems
• Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping
• Tilted-Cone Induced Cusps and Nonmonotonic Structures in Dynamical Polarization Function of Massless Dirac Fermions
• Anderson localization transition in disordered hyperbolic lattices
• Effects of the Dirac cone tilt in two-dimensional Dirac semimetal
• Disordered Weyl semimetals and their topological family
• Two mechanisms of disorder-induced localization in photonic-crystal waveguides
• Anderson localization versus hopping asymmetry in a disordered lattice
• Landau Quantization for an electric quadrupole moment of Position-Dependent Mass Quantum Particles interacting with Electromagnetic fields
• Localization of light in a three-dimensional disordered crystal of atoms
• Photonic Topological Transitions and Epsilon-Near-Zero Surface Plasmons in Type-II Dirac Semimetal NiTe${}_2$
• Interplay between tilt, disorder, and Coulomb interaction in type-I Dirac fermions
• What can we learn from diffusion about Anderson localization of a degenerate Fermi gas?