Exotic Lifshitz transitions in topological materials

Beenakker noticed that the peculiar band structure of Dirac fermions in 2D solids allows for the specular Andreev reflection in these systems which has no analogue in other 2D electron systems. An interesting deformation of the Dirac equation in the solid state is to tilt it which has now materials realization. In this work we report another peculiar feature of the Andreev reflection in tilted 2D Dirac cone systems. The tilt deformation of the Dirac equation is characterized by two parameters ζ = ζ(cos θ, sin θ). We show that when the tilt parameter is tuned to its "horizon value" ζ = 1, irrespective of the incidence angle of electrons, the Andreev reflected hole is always reflected perpendicular to the interface. Furthermore at the horizon value, if the tilt direction is perpendicular to the interface, the conductance will be energy independent for the entire sub gap energies. For generic tilt ζ, the tilt dependence of the conductance line shape can be used to extract information about the direction and magnitude of the tilt.

Section: Discussionsupporting

confidence: 94%

Perpendicular Andreev reflection: Solid-state signature of black-hole horizon

Faraei¹,

Jafari²

2019

“…Following Volovik [26,27], the dispersion of a tilted Dirac cone can be viewed as a null-surface in a Painelevé-Gullstrand spacetime,…”

Section: The T-lorentz Transformationsmentioning

confidence: 99%

Electric field assisted amplification of magnetic fields in tilted Dirac cone systems

Jafari

2019

We show that the continuum limit of the tilted Dirac cone in materials such as 8P mmn-borophene and layered organic conductor α-(BEDT-TTF)2I3 deformation of the Minkowski spacetime of Dirac materials. From its Killing vectors we construct an emergent tilted-Lorentz (t-Lorentz) symmetry group for such systems. With t-Lorentz transformations we are able to obtain the exact solution of the Landau bands for a crossed configuration of electric and magnetic fields. For any given tilt parameter 0 ≤ ζ < 1 if the ratio χ = vF Bz/cEy of the crossed magnetic and electric fields that satisfies χ ≥ 1 + ζ one can always find appropriate t-boosts in both valleys labeled by ± in such a way the electric field can be t-boosted away, whereby the resulting pure effective magnetic field B ± z governs the Landau level spectrum around each valley. The effective magnetic field in one of the valleys is always larger than the applied perpendicular magnetic field. This amplification comes at the expense of of diminishing the effective field in the opposite valley and can be detected in various quantum oscillation phenomena in tilted Dirac cone systems. Tuning the ratio of electric and magnetic fields to χmin = 1 + ζ leads to valley selective collapse of Landau levels. Our geometric description of the tilt in Dirac systems reveals an important connection between the tilt and an incipient "rotating source" when the tilt parameter can be made to depend on spacetime in certain way.

“…Volovik et al recently studied the emergent metric in the inhomogeneous WSM [19][20][21]. They found a general correspondence between the emergent vielbein e i µ and the effective Hamiltonian near a Weyl node K = (K x , K y , K z ), i.e.,…”

Section: Introductionsmentioning

confidence: 99%

Quantum chaos associated with an emergent ergosurface in the transition layer between type-I and type-II Weyl semimetals

Chen

Luo

et al. 2020

We present emergent ergosurfaces (ES) in a transition layer between type-I and type-II Weyl semimetals (WSMs). The Hawking temperature defined by the surface gravity at the acoustic event horizon which coincides with the ES when the tangent velocity v is small is in a measurable interval. On the type-II WSM side, i.e., inside the ES when v is large, the motion of the quasiparticles may be chaotic after a critical surface as they are governed by an effective inverted oscillator potential induced by the mismatch between the type-I and type-II Weyl nodes. In a relevant lattice model, we calculate out of time ordered correlators (OTOCs). We find that the OTOCs are fast scrambling with a quantum Lyapunov exponent in high temperature and the scrambling is saturated after the Ehrenfest time. This confirms the quantum chaotic behavior. I. INTRODUCTIONS