Disorder and Interactions in Dirac Materials
Abstract
Dirac semimetals constitute a new class of electronic materials that are attracting enormous interest for both fundamental reasons (these materials have exotic `topological properties), and for practical reasons (they may serve as platforms for a new generation of quantum technologies). While interest in Dirac semimetals began with two dimensional systems such as graphene, in recent years the focus has shifted to three dimensional systems such as Weyl semimetals. Still newer classes of Dirac materials are emerging, such as the Weyl loop semimetals, which may support qualitatively new phenomena. However, most theoretical investigations have assumed that the material of interest is ideally clean, whereas real materials always have disorder (heterogeneity), such as impurities, vacancies and dislocations. The PI proposes to study the effects of disorder and its interplay with interactions (particularly in the context of superconductivity) in these materials. The work proposed will be primarily theoretical, employing field theory techniques that the PI is expert in, but will be supported by numerical simulations, and will be compared with emerging experiments in this field. The research consists of two major thrusts. The first focuses on Weyl semimetals, starting with the effects of chemical potential disorder. This problem is dominated by non-perturbative effects that are missed by conventional calculations, as the PI has recently pointed out. In the first year of the grant, the PI will construct a theoretical framework capable of incorporating these non-perturbative effects, and will use it to extract quantities such as spectral functions and transport coefficients that will be directly compared with experiment. In the second year, the theoretical framework will be expanded to incorporate more general types of disorder which are inevitably present in real materials, and will clarify which forms of disorder most strongly affect the physics and which types are irrelevant. The PI will also explore the interplay of disorder with Coulomb interactions in these materials, taking into account the non-perturbative effects. In the third year the PI will explore the effect of disorder on superconductivity (both intrinsic and proximity induced) in these materials, and on the non-Abelian anyon excitations that may be thereby realized. This work is not only fundamentally important, but is immediately relevant for experiments, and for the incorporation of Dirac materials into future technologies ranging from magnetic field sensors to quantum computers. The second thrust is devoted to emerging Dirac materials, such as Weyl loop semimetals, type II Weyl semimetals, quadratic band crossings (which are parent phases for double Weyl semimetals), and correlated phases that realize a Dirac dispersion for their quasiparticles. The PI will explore issues such as the possible exotic (fully gapped and chiral) superconducting phases that may arise in Weyl loop semimetals, the novel metallic phases that may arise in disordered interacting quadratic band crossing materials, and the interplay of disorder and superconductivity in all the above. This research will not only deepen our understanding of quantum states of matter in disordered Dirac materials, but will inform emerging experiments, and may uncover new technological possibilities. The timeline for this thrust is flexible, but the PI anticipates focusing on quadratic band crossings in year one, type II Weyl materials in year two, and correlated Dirac materials in year three, with the work on Weyl loop materials continuing throughout the period of the grant. This thrust will also be adapted as necessary to seize emerging opportunities. The PIs long term objective is to establish a world leading theory effort exploring the interplay of disorder and interactions in new materials. This grant will enable the development of a powerful research effort exploring this timely and important problem.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Oct 15, 2018
- Source ID
- W911NF1710482
Entities
People
- Rahul Nandkishore
Organizations
- Army Contracting Command
- United States Army
- University of Colorado Boulder