Surface States in Holographic Weyl Semimetals

Abstract

We study the surface states of a strongly coupled Weyl semimetal within holography. By explicit numerical computation of an inhomogeneous holographic Weyl semimetal, we observe the appearance of an electric current restricted to the surface in presence of an electric chemical potential. The integrated current is universal in the sense that it only depends on the topology of the phases showing that the bulk-boundary correspondence holds even at strong coupling. The implications of this result are subtle and may shed some light on anomalous transport at weak coupling. INTRODUCTIONWeyl semimetals (WSMs) are novel gapless topological states of matter with electronic low-energy excitations behaving as left-and right-handed Weyl fermions [1][2][3][4][5][6][7]. These quasiparticles are localized around Weyl nodes in the Brillouin zone, points where, in band theory, valence and conduction bands touch at the Fermi energy. The Nielsen-Ninomiya theorem [1] states that left-and right-handed Weyl nodes appear in pairs. The existence of these nodes requires either inversion or time reversal symmetry to be broken. In the latter case, Weyl nodes of opposite chirality are separated spatially in the Brillouin zone. Weyl nodes can be characterized as monopoles of Berry flux with charge ±1 which reflects the chirality of the excitations. As such, Weyl nodes represent topological objects in the Brillouin zone and are stable under most perturbations, including interactions. As in topological insulators, the existence of surface states is guaranteed by topology. Moreover, it has been shown [2] that the surface states of a WSM form so-called Fermi arcs connecting the projections of the Weyl nodes onto the surface Brillouin zone.The transport properties of WSMs are tightly bound to the axial anomaly of quantum field theories with Weyl fermions. This leads to anomaly-related phenomena in WSMs such as the anomalous Hall effect [8][9][10][11][12], the chiral magnetic effect [13,14] and related effects like the negative magnetoresistance [15,16]. Furthermore, it has been predicted that lattice deformations couple to the fermionic low-energy excitations with different signs, giving rise to effective axial gauge fields [17,18]. Such lattice deformations naturally arise at the surfaces of a WSM, inducing localised axial magnetic fields in their vicinity. Moreover, it was shown that the Fermi arcs can be understood from this perspective as zeroth Landau levels generated by these fields [19].It is important to remark that in the strong coupling regime the description in terms of bands, or even correlation functions, cannot be applied and therefore it is compelling to study to which extent the weak coupling intuitions can be extrapolated. In Refs. [20,21], the authors addressed the question whether the properties of a (homogeneous and infinite) WSM can be found in the strong coupling regime. To this end, they presented a holographic model which exhibits a topological phase transition from a trivial phase to a non-trivial WSM phase. In this letter...

Holographic topological semimetals

“…But the topologically protected edge currents should still exist 6 . This is exactly what [41] investigated. The authors numerically constructed solutions with spatial dependent boundary conditions of the form…”

“…This is the direct holographic counterpart of the Fermi-arcs associated to the surface of a Weyl semimetals. Figure with permission reproduced from[41], c 2017 by the American Physical Society.…”

Weyl semimetal/insulator transition from holography

“…In particular, holographic models for strongly interacting Weyl semimetals have been constructed in [9,10] in which the anomalous Hall conductivity is an order parameter to characterize the quantum topological phase transition. The effects of the surface state [11] and topological invariants [12] in this holographic model exhibit key features of topological Weyl semimetals. Therefore with strong interaction topological Weyl semimetal still exits and holography is a practical tool to explore its property.…”

Topological invariants for holographic semimetals

“…In [2,3] and [4], strongly coupled topological Weyl and nodal line semimetals were found in the framework of anti-de Sitter/conformal field theory (AdS/CFT) correspondence, which turns a strongly coupled field theoretical problem into a weakly coupled classical gravity problem [5,6,7]. The evidence that the holographic Weyl and nodal line semimetals are topological semimetals includes the anomalous Hall conductivity for Weyl semimetals [3], the induced effect of surface state [8], as well as the nodal loop from the dual fermion spectral functions [4]. Based on the holographic models of semimetals, many interesting observations have been made, including a prediction of nontrivial Hall viscosity in the quantum critical region due to the presence of the mixed gauge gravitational anomaly [9], the axial anomalous Hall effect [10], the behavior of AC conductivity [11], the disorder effect on the topological phase transition [12], and the properties of quantum chaos in the quantum critical region [13].…”