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Register a new userProbing mirror anomaly and classes of Dirac semimetals with circular dichroism
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Added by
Abhirup Roy Karmakar
Publication date
2020
fields
Physics
and research's language is
English
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We theoretically investigate the optical activity of three dimensional Dirac semimetals (DSMs) using circular dichroism (CD). We show that DSMs in the presence of a magnetic field in any one of the mirror-symmetric planes of the materials exhibit a notable dichroic behavior. In particular, for different orientations of the light field with respect to the mirror-symmetric plane, the CD in type-II DSMs can detect the presence of mirror anomaly by showing sharply distinct patterns at the mirror-symmetric angle. Interestingly, CD can also distinguish type-II DSMs having only one Dirac point at a time-reversal invariant momentum from type-I DSMs with a pair of Dirac points on the rotation axis of the crystals.
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In addition to the well known chiral anomaly, Dirac semimetals have been argued to exhibit mirror anomaly, close analogue to the parity anomaly of ($2+1$)-dimensional massive Dirac fermions. The observable response of such anomaly is manifested in a singular step-like anomalous Hall response across the mirror-symmetric plane in the presence of a magnetic field. Although this result seems to be valid in type-II Dirac semimetals (strictly speaking, in the linearized theory), we find that type-I Dirac semimetals do not possess such an anomaly in anomalous Hall response even at the level of the linearized theory. In particular, we show that the anomalous Hall response continuously approaches zero as one approaches the mirror symmetric angle in a type-I Dirac semimetal as opposed to the singular Hall response in a type-II Dirac semimetal. Moreover, we show that, under certain condition, the anomalous Hall response may vanish in a linearized type-I Dirac semimetal, even in the presence of time reversal symmetry breaking.
We have studied theoretically the Weyl semimetals the point symmetry group of which has reflection planes and which contain equivalent valleys with opposite chiralities. These include the most frequently studied compounds, namely the transition metals monopnictides TaAs, NbAs, TaP, NbP, and also Bi$_{1-x}$Sb$_x$ alloys. The circular photogalvanic current, which inverts its direction under reversal of the light circular polarization, has been calculated for the light absorption under direct optical transitions near the Weyl points. In the studied materials, the total contribution of all the valleys to the photocurrent is nonzero only beyond the simple Weyl model, namely, if the effective electron Hamiltonian is extended to contain either an anisotropic spin-dependent linear contribution together with a spin-independent tilt or a spin-dependent contribution cubic in the electron wave vector $bf{k}$. With allowance for the tilt of the energy dispersion cone in a Weyl semimetal of the $C_{4v}$ symmetry, the photogalvanic current is expressed in terms of the components of the second-rank symmetric tensor that determines the energy spectrum of the carriers near the Weyl node; at low temperature, this contribution to the photocurrent is generated within a certain limited frequency range $Delta $. The photocurrent due to the cubic corrections, in the optical absorption region, is proportional to the light frequency squared and generated both inside and outside the $Delta$ window.
Light interaction with rotating nanostructures gives rise to phenemona as varied as optical torques and quantum friction. Here we reveal that circular dichroism of rotating optically-isotropic particles has an unexpectedly strong dependence on their internal geometry. In particular, nanorings and nanocrosses exhibit a splitting of $2Omega$ in the particle optical resonances, while compact particles display weak circular dichroism at low rotation frequency $Omega$, but a strong circular dichroism at high $Omega$. We base our findings on a quantum-mechanical description of the polarizability of rotating particles, which has not been rigorously addressed so far. Specifically, we use the random-phase approximation and populate the particle electronic states according to the principle that they are thermally equilibrated in the rotating frame. We further provide insight into the rotational superradience effect and the ensuing optical gain, originating in population inversion as regarded from the lab frame, in which the particle is out of equilibrium. Surprisingly, we find the optical frequency cutoff for superradiance to deviate from the rotation frequency $Omega$. Our results unveil a rich, unexplored phenomenology of light interaction with rotating objects.
Twisted bilayer graphene is a chiral system which has been recently shown to present circular dichroism. In this work we show that the origin of this optical activity is the rotation of the Dirac fermions helicities in the top and bottom layer. Starting from the Kubo formula, we obtain a compact expression for the Hall conductivity that takes into account the dephasing of the electromagnetic field between the top and bottom layers and gathers all the symmetries of the system. Our results are based in both a continuum and a tight-binding model, and they can be generalized to any two-dimensional Dirac material with a chiral stacking between layers.
Recently Weyl fermions have attracted increasing interest in condensed matter physics due to their rich phenomenology originated from their nontrivial monopole charges. Here we present a theory of real Dirac points that can be understood as real monopoles in momentum space, serving as a real generalization of Weyl fermions with the reality being endowed by the $PT$ symmetry. The real counterparts of topological features of Weyl semimetals, such as Nielsen-Ninomiya no-go theorem, $2$D sub topological insulators and Fermi arcs, are studied in the $PT$ symmetric Dirac semimetals, and the underlying reality-dependent topological structures are discussed. In particular, we construct a minimal model of the real Dirac semimetals based on recently proposed cold atom experiments and quantum materials about $PT$ symmetric Dirac nodal line semimetals.
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