Extended Supersymmetric Structures in Gapped and Superconducting Graphene

Abstract

In view of the many quantum field theoretical descriptions of graphene in 2 + 1 dimensions, we present another field theoretical feature of graphene, in the presence of defects. Particularly, we shall be interested in gapped graphene in the presence of a domain wall and also for superconducting graphene in the presence of a vortex. As we explicitly demonstrate, the gapped graphene electrons that are localized on the domain wall are associated with four N = 2 one-dimensional supersymmetries, with each pair combining to form an extended N = 4 supersymmetry with non-trivial topological charges. The case of superconducting graphene is more involved, with the electrons localized on the vortex being associated with n one-dimensional supersymmetries, which in turn combine to form an N = 2n extended supersymmetry with non-trivial topological charges. As we shall prove, all supersymmetries are unbroken, a feature closely related to the number of the localized fermions and also to the exact form of the associated operators. In addition, the corresponding Witten index is invariant under compact and odd perturbations.

Supersymmetric SYK model and random matrix theory

“…It is remarkable that the above computation is very similar to our work from Section 3.2.1 to 3.2.2. Applications of this property can be found in [62,63]. They describe a supersymmetric Quantum Mechanics system where fermions scatter off domain walls.…”

“…Some evidence of this point also could be found in some other models or setups. For instance, Witten parity is the Klein operator which separates the bosonic and fermionic sectors in the N = 2 supersymmetric systems [62,63]. [64] provides a more nontrivial example, where the odd parity operators are used to move states along a chain of different fermion sectors.…”

Higgs Phase in a Gauge U(1) Non-Linear CP1-Model. Two Species of BPS Vortices and Their Zero Modes

“…In [20,21], the topological defects and structures of this last model have been thoroughly described. Moreover, this framework has been proven to play a role as an effective theory in describing graphene physics at Dirac points in [22]. Besides the topological vortices of the standard nonlinear gauged model, we also discovered in [5] similar self-dual vortices existing in the Chern-Simons version of our model.…”

N=2 Supersymmetry with Central Charge: A Twofold Implementation

“…In the context of supersymmetric mechanics with central charge, some investigations of field-theoretical models may correspond to (quantum) mechanical systems, namely, in the study of superconducting cosmic strings, localized fermions on domain walls, gapped and superconducting graphene [26]. Moreover, in some well-known mechanical situations, such as Coulomb, Aharonov-Bohm-Coulomb and Aharonov-Casher systems, it is possible to accommodate extended supersymmetries with central charge [27], which explain the degeneracy of the energy spectra.…”