[Paper Review] Inhomogeneous Weyl and Dirac semimetals: Transport in axial magnetic fields and Fermi arc surface states from pseudo Landau levels

Adolfo G. Grushin, Venderbos, Jorn W. F.+2 more|DSpace@MIT (Massachusetts Institute of Technology)|Jul 14, 2016

Graphene research and applications4 citations

TL;DR

This paper proposes that spatially inhomogeneous Weyl node separation in Weyl and Dirac semimetals generates an emergent axial magnetic field $\mathbf{B}_5$, which induces pseudo-Landau levels and enhances conductivity as $\sigma \sim \mathbf{B}_5^2$ due to a chiral pseudo-magnetic effect. Key results show that Fermi arcs are reinterpreted as $n=0$ pseudo-Landau levels, and bulk $\mathbf{B}_5$ creates interpolating pseudo-Landau levels between surfaces, with equilibrium bound currents analogous to those in magnetic materials.

ABSTRACT

Topological Dirac and Weyl semimetals have an energy spectrum that hosts Weyl nodes appearing in pairs of opposite chirality. Topological stability is ensured when the nodes are separated in momentum space and unique spectral and transport properties follow. In this work we study the effect of a space dependent Weyl node separation, which we interpret as an emergent background axial vector potential, on the electromagnetic response and the energy spectrum of Weyl and Dirac semimetals. This situation can arise in the solid state either from inhomogeneous strain or non-uniform magnetization and can also be engineered in cold-atomic systems. Using a semiclassical approach we show that the resulting axial magnetic field $\mathbf{B}_{5}$ is observable through an enhancement of the conductivity as $σ\sim \mathbf{B}_{5} ^{2}$ due to an underlying chiral pseudo magnetic effect. We then use two lattice models to analyze the effect of $\mathbf{B}_5$ on the spectral properties of topological semimetals. We describe the emergent pseudo-Landau level structure for different spatial profiles of $\mathbf{B}_5$, revealing that (i) the celebrated surface states of Weyl semimetals, the Fermi arcs, can be reinterpreted as $n=0$ pseudo-Landau levels resulting from a $\mathbf{B}_5$ confined to the surface (ii) as a consequence of position-momentum locking a bulk $\mathbf{B}_5$ creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces and (iii) there are equilibrium bound currents proportional to $\mathbf{B}_{5}$ that average to zero over the sample, which are the analogs of bound currents in magnetic materials. We conclude by discussing how our findings can be probed experimentally.

Motivation & Objective

• To investigate the electromagnetic and spectral response of Weyl and Dirac semimetals under spatially varying Weyl node separation, interpreted as an emergent axial vector potential.
• To explore the emergence of an axial magnetic field $\mathbf{B}_5 = \nabla \times \mathbf{b}$ from inhomogeneous strain or magnetization in topological semimetals.
• To demonstrate that Fermi arc surface states can be reinterpreted as zeroth Landau level states arising from surface-confined $\mathbf{B}_5$.
• To analyze the formation of pseudo-Landau levels in bulk due to spatially varying $\mathbf{B}_5$, including their real-space interpolation between opposite surfaces.
• To identify measurable transport and spectral signatures, such as conductivity enhancement and bound currents, for experimental detection.

Proposed method

• A semiclassical approach is used to model the response of Weyl and Dirac fermions to an emergent axial gauge field arising from spatially varying Weyl node separation $\mathbf{b}$.
• The axial magnetic field $\mathbf{B}_5 = \nabla \times \mathbf{b}$ is derived from the spatial gradient of the momentum-space node separation vector.
• Two lattice models are employed to compute the energy spectrum under $\mathbf{B}_5$, revealing the formation of pseudo-Landau levels for different spatial profiles of $\mathbf{B}_5$.
• The conductivity is calculated under $\mathbf{B}_5$, showing a quadratic enhancement $\sigma \sim \mathbf{B}_5^2$ due to chiral pseudo-magnetic effects.
• The model includes position-momentum locking effects, which lead to bound currents proportional to $\mathbf{B}_5$ that average to zero over the sample.
• Cold-atomic systems are proposed as a tunable platform to engineer $\mathbf{B}_5$ via space-dependent onsite potentials, enabling experimental realization of the predicted phenomena.

Experimental results

Research questions

• RQ1 How does an inhomogeneous Weyl node separation lead to the emergence of an axial magnetic field $\mathbf{B}_5$ in Weyl and Dirac semimetals?
• RQ2 Can the Fermi arc surface states in Weyl semimetals be understood as the $n=0$ pseudo-Landau level of a surface-confined axial magnetic field?
• RQ3 What is the nature of the pseudo-Landau level spectrum formed in the bulk when $\mathbf{B}_5$ varies spatially, and how does it interpolate between opposite surfaces?
• RQ4 How does $\mathbf{B}_5$ affect the transport properties, particularly the conductivity, and can this be experimentally probed via a chiral pseudo-magnetic effect?
• RQ5 What are the equilibrium bound currents induced by $\mathbf{B}_5$, and how do they compare to those in conventional magnetic materials?

Key findings

• The axial magnetic field $\mathbf{B}_5$ generated by inhomogeneous strain or magnetization leads to a quadratic enhancement of conductivity as $\sigma \sim \mathbf{B}_5^2$, observable via transport measurements.
• Fermi arc surface states in Weyl semimetals are identified as the $n=0$ pseudo-Landau level of a surface-confined axial magnetic field, providing a new interpretation of their topological origin.
• Bulk $\mathbf{B}_5$ with spatial variation produces pseudo-Landau levels that interpolate in real space between Fermi arcs on opposite surfaces, forming a chiral, momentum-locked band structure.
• Equilibrium bound currents proportional to $\mathbf{B}_5$ emerge in the system, which average to zero over the sample and are analogous to bound currents in magnetic materials.
• A conservative estimate yields $|\mathbf{B}_5| \sim 4$ T in a Cd3As2 thin film under 1% strain gradient, which is above the detection threshold of SQUIDs and magnetic loops.
• Cold-atomic systems offer a viable platform to engineer $\mathbf{B}_5$ via space-dependent onsite potentials, enabling direct measurement of the center-of-mass velocity and conductivity enhancement.