title: All Majorana Models with Translation Symmetry are Supersymmetric.
abstract: We establish results similar to Kramers and Lieb-Schultz-Mattis theorems but involving only translation symmetry and for Majorana modes. In particular, we show that all states are at least doubly degenerate in any one- and two-dimensional array of Majorana modes with translation symmetry, periodic boundary conditions, and an odd number of modes per unit cell. Moreover, we show that all such systems have an underlying N=2 supersymmetry and explicitly construct the generator of the supersymmetry. Furthermore, we establish that there cannot be a unique gapped ground state in such one-dimensional systems with antiperiodic boundary conditions. These general results are fundamentally a consequence of the fact that translations for Majorana modes are represented projectively, which in turn stems from the anomalous nature of a single Majorana mode. An experimental signature of the degeneracy arising from supersymmetry is a zero-bias peak in tunneling conductance.
authors: Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.
authors: Timothy H
authors: TH
authors: Hsieh
authors: Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.
authors: Gábor B
authors: GB
authors: Halász
authors: Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.|Department of Physics, University of California at San Diego, La Jolla, California 92093, USA.
authors: Tarun
authors: T
authors: Grover