Weyl semimetal with broken time reversal and inversion symmetries

Abstract

Weyl semimetal is a new topological state of matter, characterized by the presence of nondegenerate band-touching nodes, separated in momentum space, in its bandstructure. Here we discuss a particular realization of a Weyl semimetal: a superlattice heterostructure, made of alternating layers of topological insulator (TI) and normal insulator (NI) material, introduced by one of us before. The Weyl node splitting is achieved most easily in this system by breaking time-reversal (TR) symmetry, for example by magnetic doping. If, however, spatial inversion (I) symmetry remains, the Weyl nodes will occur at the same energy, making it possible to align the Fermi energy simultaneously with both nodes. The goal of this work is to explore the consequences of breaking the I symmetry in this system. We demonstrate that, while this generally moves the Weyl nodes to different energies, thus eliminating nodal semimetal and producing a state with electron and hole Fermi surfaces, the topological properties of the Weyl semimetal state, i.e. the chiral edge states and the corresponding Hall conductivity, survive for moderate I symmetry breaking. Moreover, we demonstrate that a new topological phenomenon arises in this case, if an external magnetic field along the growth direction of the heterostructure is applied. Namely, this leads to an equilibrium dissipationless current, flowing along the direction of the field, whose magnitude is proportional to the energy difference between the Weyl nodes and to the magnetic field, with a universal coefficient, given by a combination of fundamental constants.Comment: 9 pages, 5 figures; minor corrections and extensions, published versio

Negative Refraction in Weyl Semimetals

“…[19,23,24] Here, we will give brief derivation of the electromagnetic response of WSM represented by electric displacement vector D. The more detailed derivation is given by Zyuzin and Burkov [25,26] or Hosur and Qi. [27] The action of electromagnetic field is given by,…”

Nernst and magnetothermal conductivity in a lattice model of Weyl fermions

“…Anomalous transport phenomena, however, have been already known to exist in a variety of systems which possess a non-trivial distribution of the Berry curvature flux 56,57 . In a WSM, more interestingly, each Weyl node is chiral, with the chirality quantum number protected by a quantized flux of the Berry curvature, also known as Chern flux, which results in another peculiar phenomenon known as chiral anomaly (or Adler-Bell-Jackiw anomaly) 10,16,58,59 . The chiral anomaly concerns with the nonconservation of chiral charge i.e.…”

“…Usually the robust topological protection is associated with a non-zero spectral gap in the bulk of the system, and the presence of protected zero energy surface states is regarded as the hallmark of a non-trivial topological phase of matter. However, recently it has been proposed that systems in three spatial dimensions, in the presence of broken time-reversal (TR) and/or spaceinversion (SI) symmetry, can also be topologically protected even without a bulk energy gap [10][11][12][13][14][15][16][17][18][19][20][21] . These are Weyl semimetals (WSM) -the nomenclature based on the Dirac/Weyl equation which is used to describe their low energy excitations 22 .…”

Anomaly induced chiral magnetic current in a Weyl semimetal: Chiral electronics

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“…In particular, they allow [5] to study, in a condensed matter system, the chiral magnetic effect expected [6][7][8][9][10], and possibly observed experimentally at Relativistic Heavy Ion Collider [11], in chirally imbalanced quark-gluon plasma in the presence of an external magnetic effect as a consequence of axial anomaly in QCD×QED. Closely related phenomena have been discussed in the physics of neutrinos [12], conductors with mirror isomer symmetry [13,14], primordial electroweak plasma [15] and quantum wires [16].…”