Chirality-Dependent Hall Effect in Weyl Semimetals

Abstract

We generalize a semiclassical theory and use the argument of angular momentum conservation to examine the ballistic transport in lightly-doped Weyl semimetals, taking into account various phase-space Berry curvatures. We predict universal transverse shifts of the wave-packet center in transmission and reflection, perpendicular to the direction in which the Fermi energy or velocities change adiabatically. The anomalous shifts are opposite for electrons with different chirality, and can be made imbalanced by breaking inversion symmetry. We discuss how to utilize local gates, strain effects, and circularly polarized lights to generate and probe such a chirality Hall effect.When a strong topological insulator [1, 2] undergoes a phase transition to a trivial band insulator in three dimensions, a gapless Dirac point [3][4][5][6] emerges at the critical point, if both time-reversal (T ) and inversion (P) symmetries are present. Remarkably, when one of the two symmetries is broken, the critical point expands in the phase diagram and the Dirac point splits into pairs of Weyl points related by the unbroken symmetry. This emergent phase [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], dubbed as Weyl semimetal (WSM), is an appealing topological state of matter, with the Fermi surface being those Weyl points.In the simplest case when T symmetry is broken, a WSM at long wavelength only has one pair of Weyl points, which may be described by the HamiltonianHere v's are the Fermi velocities, σ's are Pauli matrices, and τ = ± denote the left-and right-handed Weyl fermions, which are required to come in pairs by the Nielsen-Ninomiya theorem [22]. τ bẑ are the positions of the pair of Weyl points in the Brillouin zone (BZ), and 2b 0 is their energy splitting, which vanishes when P symmetry is not broken. Since all three σ's are used up locally at each Weyl point, small perturbations may renormalize the parameters but cannot open a gap. Indeed, each Weyl point is protected by the Chern number (±1) of the valence band on a constant-energy surface enclosing it. Weyl points can only be annihilated in pairs of opposite chirality, when they are brought together (b, b 0 = 0) or when the translational symmetry is broken by strong interactions or by short-range scatterers.The topological properties of WSM can be best seen by considering a slice of the BZ normal toẑ. The Chern number of the slice changes from 0 to 1 and back to 0 as it crosses the two Weyl points successively. As a consequence, each nontrivial slice contributes an e 2 /h to the Hall conductivity [9-11] producing σ xy = be 2 /πh in the bulk, and also contributes one edge state to the surface forming a surface Fermi arc connecting the two projected Weyl points. Recently, the Weyl points and surface arcs appear to be observed in optical experiments [23][24][25].This progress may herald a flurry of exciting experiments on the appealing transport effects [26][27][28] predicted in WSM, e.g., the chiral magnetic effect [29][30][31][32][33][34][35][36] when b 0 becomes non...

Imbert-Fedorov shift in Weyl semimetals: Dependence on monopole charge and intervalley scattering

“…This approach is used to calculate the IF shift in WSMs in Ref. 13 , in the case where the band structure and the Berry curvature are slowly varying. Now we show that the IF shift between two WSMs with the same monopole charge N can be calculated in this way, which further confirms the results obtained above.…”

“…The IF shift in both optical systems and WSMs has been interpreted semiclassically 6,13 . The semiclassical equations of motion (EOM) govern the trajectory of wave packets, and dictate that the IF shift of a wave packet is due to its anomalous velocity 31 , and hence is an integral of the Berry curvature.…”

“…Different from the quantum mechanical treatment, the trajectory of a wave packet is fixed, which ignores the possibility that the wave packet may split. Another interpretation of the IF shift is from the conservation of total angular momentum (TAM) 6,13 , which only works if the two media have the same monopole charge, and the composite system has a rotational symmetry. Therefore, there is a limit in these two methods.…”

“…However, if the Berry curvature has an abrupt change at an interface, difficulties arise. Moreover, near the Weyl point where the gap closes, non-Abelian treatment is needed 13 . As such, processes like Klein tunneling are not straightforward to account for.…”

Electronic properties in a quantum well structure of Weyl semimetal

“…Therefore, the Weyl nodes occur always in pairs with opposite chirality and consequently the Fermi arc states emerge on the surface [9][10][11][12]. Due to these unique characteristics, WSMs can show various exotic phenomena, such as transport anomaly [13][14][15], high Chern number quantum anomalous Hall effect states [16,17] and electrical optical physics [18,19]. WSMs have been theoretically proposed in a number of candidate systems, including Rn 2 Ir 2 O 7 pyrochlore [20], zinc-blende lattice [21], ABi 1−x Sb x Te 3 (A=La or Lu) [22], HgCr 2 Se 4 [11], TaAs [23,24], TaP [25].…”