TY  - JOUR
A1  - Lee, Ching Hua
A1  - Papić, Zlatko
A1  - Thomale, Ronny
T1  - Geometric construction of quantum Hall clustering Hamiltonians
JF  - Physical Review X
N2  - Many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain "pseudopotential" Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z\(_3\) states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicated many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU(n) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.
KW  - wave functions
KW  - Landau level
KW  - states
KW  - excitations
KW  - fluid
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-145233
VL  - 5
IS  - 4
ER  - 
TY  - JOUR
A1  - Elster, Lars
A1  - Platt, Christian
A1  - Thomale, Ronny
A1  - Hanke, Werner
A1  - Hankiewicz, Ewelina M.
T1  - Accessing topological superconductivity via a combined STM and renormalization group analysis
JF  - Nature Communications
N2  - The search for topological superconductors has recently become a key issue in condensed matter physics, because of their possible relevance to provide a platform for Majorana bound states, non-Abelian statistics, and quantum computing. Here we propose a new scheme which links as directly as possible the experimental search to a material-based microscopic theory for topological superconductivity. For this, the analysis of scanning tunnelling microscopy, which typically uses a phenomenological ansatz for the superconductor gap functions, is elevated to a theory, where a multi-orbital functional renormalization group analysis allows for an unbiased microscopic determination of the material-dependent pairing potentials. The combined approach is highlighted for paradigmatic hexagonal systems, such as doped graphene and water-intercalated sodium cobaltates, where lattice symmetry and electronic correlations yield a propensity for a chiral singlet topological superconductor. We demonstrate that our microscopic material-oriented procedure is necessary to uniquely resolve a topological superconductor state.
KW  - tunneling spectroscopy
KW  - Sr\(_2\)RuO\(_4\)
KW  - states
KW  - transition
KW  - insulators
KW  - surface
KW  - Majorana fermions
KW  - unconventional superconductivity
KW  - wave superconductors
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-148181
VL  - 6
IS  - 8232
ER  -