TY  - JOUR
A1  - Lee, Ching Hua
A1  - Sutrisno, Amanda
A1  - Hofmann, Tobias
A1  - Helbig, Tobias
A1  - Liu, Yuhan
A1  - Ang, Yee Sin
A1  - Ang, Lay Kee
A1  - Zhang, Xiao
A1  - Greiter, Martin
A1  - Thomale, Ronny
T1  - Imaging nodal knots in momentum space through topolectrical circuits
JF  - Nature Communications
N2  - Knots are intricate structures that cannot be unambiguously distinguished with any single topological invariant. Momentum space knots, in particular, have been elusive due to their requisite finely tuned long-ranged hoppings. Even if constructed, probing their intricate linkages and topological "drumhead" surface states will be challenging due to the high precision needed. In this work, we overcome these practical and technical challenges with RLC circuits, transcending existing theoretical constructions which necessarily break reciprocity, by pairing nodal knots with their mirror image partners in a fully reciprocal setting. Our nodal knot circuits can be characterized with impedance measurements that resolve their drumhead states and image their 3D nodal structure. Doing so allows for reconstruction of the Seifert surface and hence knot topological invariants like the Alexander polynomial. We illustrate our approach with large-scale simulations of various nodal knots and an experiment which maps out the topological drumhead region of a Hopf-link. Topological phases with knotted configurations in momentum space have been challenging to realize. Here, Lee et al. provide a systematic design and measurement of a three-dimensional knotted nodal structure, and resolve its momentum space drumhead states via a topolectrical RLC-type circuit.
KW  - nodal knots
KW  - topolectrical circuits
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-230407
VL  - 11
ER  - 
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  -