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Due to strong spin-orbit coupling, charge carriers in three-dimensional quadratic band touching Luttinger semimetals have non-trivial wavefunctions characterized by a pseudospin of 3/2. We compute the dielectric permittivity of such…
Crystalline semimetals with certain space group symmetries may possess unusual electronic structure topology, distinct from the conventional Weyl and Dirac semimetals. Characteristic property of these materials is the existence of…
We review recent theoretical progress in the understanding and prediction of novel topological semimetals. Topological semimetals define a class of gapless electronic phases exhibiting topologically stable crossings of energy bands.…
Semimetals, in which conduction and valence bands touch but do not form Fermi surfaces, have attracted considerable interest for their anomalous properties starting with the discovery of Dirac matter in graphene and other two-dimensional…
Weyl semimetal (WSM) is a newly discovered quantum phase of matter that exhibits topologically protected states characterized by two separated Weyl points with linear dispersion in all directions. Here, via combining theoretical analysis…
Quantum critical points (QCPs), zero-temperature phase transitions, are windows to fundamental quantum-mechanical phenomena associated with universal behaviour and can provide parallels to the physics of black holes. Magnetic QCPs have been…
We perform a complete classification of two-band $\bk\cdot\mathbf{p}$ theories at band crossing points in 3D semimetals with $n$-fold rotation symmetry and broken time-reversal symmetry. Using this classification, we show the existence of…
Features below the first conductance plateau in ballistic quantum point contacts (QPCs) are often ascribed to electron interaction and spin effects within the single mode limit. In QPCs with a highly asymmetric geometry, we observe sharp…
Intuitively, the dispersion characteristics of Weyl nodes with opposite charges in single-pair charge-2 Weyl semimetals are the same, quadratic or linear. We theoretically predicted that single-pair hybrid charge-2 Weyl semimetals (the…
In the search for stable topological semimetals with clean band profiles, we have screened all the 3$d$ metal-intercalated transition-metal dichalcogenides (3dI-TMDCs) by performing hybrid-functional-based ab initio calculations. Two…
Topologically protected fermionic quasiparticles occur in metals with band degeneracy as a consequence of band structure topology. Here we unveil topological semimetal and metal phases in a variety of non-symmorphic collinear…
Unconventional superconducting states of matter are realized in the presence of strong spin orbit coupling. In particular, non degenerate bands can support odd parity superconductivity with rich topological content. Here we study whether…
Weyl semimetals (WSMs) constitute a 3D phase with linearly-dispersing Weyl excitations at low energy, which lead to unusual electrodynamic responses and open Fermi arcs on boundaries. We derive a simple criterion to identify and…
Strong spin-orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin-orbit and strong electron-electron interactions is just beginning to be understood. Central…
We analyze the validity of a quasiparticle description of a superconducting state at a metallic quantum-critical point (QCP). A normal state at a QCP is a non-Fermi liquid with no coherent quasiparticles. A superconducting order gaps out…
Topological Weyl semimetal (TWS) is a metal, where low energy excitations behave like Weyl fermions of high-energy physics. It was recently shown that due to the lower symmetry of condensed matter systems, they can realize two distinct…
Luttinger semimetals include materials like gray tin ($\alpha$-Sn) and mercury telluride, which are three-dimensional gapless semiconductors having a quadratic band crossing point (QBCP). Due to a growing interest in QBCPs and new…
Topological band theory has revolutionized our understanding of electronic structure of materials, in particular, a novel state - Weyl semimetal - has been predicted for systems with strong spin-orbit coupling (SOC). Here, a new class of…
Topological semimetals in three dimensions display band-touchings at points (Weyl or Dirac semimetals) or nodal lines in the Brillouin zone. Weyl semimetals can occur with internal symmetries only (time-reversal ${\cal T}$, charge…
Electron correlations amplify quantum fluctuations and, as such, they have been recognized as the origin of a rich landscape of quantum phases. Whether and how they lead to gapless topological states is an outstanding question, and a…