Timothy H. Hsieh

Spin-filtered edge states with an electrically tunable gap in a two-dimensional topological crystalline insulator

Three-dimensional topological crystalline insulators were recently predicted and observed in the SnTe class of IV-VI semiconductors, which host metallic surface states protected by crystal symmetries. In this work, we study thin films of these materials and expose their potential for device applications. We demonstrate that thin films of SnTe and Pb(1-x)Sn(x)Se(Te) grown along the (001) direction are topologically non-trivial in a wide range of film thickness and carry conducting spin-filtered edge states that are protected by the (001) mirror symmetry through a topological invariant. Application of an electric field perpendicular to the film will break the mirror symmetry and generate a bandgap in these edge states. This functionality motivates us to propose a topological transistor device in which charge and spin transport are maximally entangled and simultaneously controlled by an electric field. The high on/off operation speed and coupling of spin and charge in such a device may lead to electronic and spintronic applications for topological crystalline insulators.

Majorana Fermions and Exotic Surface Andreev Bound States in Topological Superconductors: Application to CuₓBi₂Se₃

The recently discovered superconductor Cu(x)Bi2Se3 is a candidate for three-dimensional time-reversal-invariant topological superconductors, which are predicted to have robust surface Andreev bound states hosting massless Majorana fermions. In this work, we analytically and numerically find the linearly dispersing Majorana fermions at k=0, which smoothly evolve into a new branch of gapless surface Andreev bound states near the Fermi momentum. The latter is a new type of Andreev bound states resulting from both the nontrivial band structure and the odd-parity pairing symmetry. The tunneling spectra of these surface Andreev bound states agree well with a recent point-contact spectroscopy experiment [S. Sasaki et al., Phys. Rev. Lett. 107, 217001 (2011)] and yield additional predictions for low temperature tunneling and photoemission experiments.

Fracton Topological Phases from Strongly Coupled Spin Chains

We provide a new perspective on fracton topological phases, a class of three-dimensional topologically ordered phases with unconventional fractionalized excitations that are either completely immobile or only mobile along particular lines or planes. We demonstrate that a wide range of these fracton phases can be constructed by strongly coupling mutually intersecting spin chains and explain via a concrete example how such a coupled-spin-chain construction illuminates the generic properties of a fracton phase. In particular, we describe a systematic translation from each coupled-spin-chain construction into a parton construction where the partons correspond to the excitations that are mobile along lines. Remarkably, our construction of fracton phases is inherently based on spin models involving only two-spin interactions and thus brings us closer to their experimental realization.

All Majorana Models with Translation Symmetry are Supersymmetric

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.

Orthogonal magnetization and symmetry breaking in pyrochlore iridate Eu2Ir2O7

A torque magnetometry study of the pyrochlore iridate Eu2Ir2O7 reveals an unusual symmetry-breaking effect that persists above the Neel temperature of this antiferromagnet.

Topological bootstrap: Fractionalization from Kondo coupling

We show how entanglement can be used to realize fractionalized topological phases of matter from more conventional phases. Topologically ordered phases of matter can host fractionalized excitations known as “anyons,” which obey neither Bose nor Fermi statistics. Despite forming the basis for topological quantum computation, experimental access to these exotic phases has been very limited. We present a new route toward realizing fractionalized topological phases by literally building on unfractionalized phases, which are much more easily realized experimentally. Our approach involves a Kondo lattice model in which a gapped electronic system of noninteracting fermions is coupled to local moments via the exchange interaction. Using general entanglement-based arguments and explicit lattice models, we show that gapped spin liquids can be induced in the spin system, and we demonstrate the power of this “topological bootstrap” by realizing chiral and Z2 spin liquids. This technique enables the realization of many long sought-after fractionalized phases of matter.