### Jeffrey Teo

*Ph.D., 2011, Pennsylvania*

*Associate Professor*

*Theoretical Condensed Matter Physics*

#### Research Interests

A central theme of condensed matter physics is the study of systems with *emergent* collective degrees of freedom that can behave very differently from the microscopic individual constituents from which they arise. Quantum mechanics provides a further *topological* twist to the conventional theory. Due to strong correlation effects, the quantum ground state of a condensed matter system can be spatially entangled to an extent where its emergent quasiparticles behave so exotically that they are impossible to be realized by conventional fundamental particles. For example, an excitation in a fractional quantum Hall state can carry a fraction of an electric charge and obey fractional statistics, but at a fundamental level these excitations are the collective behavior of integer charged, fermionic electrons. These quantum entangled *topological phases of matter* are typically gapped and cannot be unentangled by any adiabatic process without closing the excitation energy gap or violating a symmetry. As a result, the unusual characteristics of their emergent quasiparticles are robust against perturbations. Interestingly these phases also can have tremendous implications for applications including dissipationless electric transport and topological quantum computation.

My research is centered around topological phases of matter, the realization of exotic quasiparticles as topological defects, and the search of topological materials.

**Recent research areas**

__Fractional Ising-like twist defects in topological phases__

Ising anyon (zero energy Majorana) quasiparticles have the ability to store quantum information non-locally in space to act as robust quantum bits. Recently, there have been theoretical proposals for realizing the even more exotic *fractional* Majorana quasiparticles in fractional topological insulator heterostructures, and in dislocations of a bilayer quantum Hall fluid. We recently demonstrated the statistical distinction between semiclassical topological defects and quantum deconfined excitations at a fundamental level. For example, the spin statistics theorem is modified for defects, and exchange-braiding relations satisfy a new set of algebraic structures. In fact, our framework is applicable to the general scenario, and will be valuable to all investigations of exotic defects.

__Zero energy Majorana bound states at lattice defects in topological crystalline superconductors__

*topological crystalline superconductors*(TCS). The existence of non-Abelian bound states at crystalline defects is a bit unexpected and contradicts the conventional wisdom that the low energy effective description of the electronic system should decoupled from the underlying lattice. We showed this effect results from the intertwined spatial symmetry and topology in the TCS states. Even when bulk crystalline defects are absent, our result extends to corners on the boundary of the bulk crystal. The results of this work are widely applicable to the large class of fourfold symmetric layered perovskite superconductors and threefold symmetric doped graphene or transition metal dichalcogenides.

__Search and classification of topological crystalline materials__

#### Graduate Students

#### Selected Publications

*Topologically Induced Fermion Parity Flips in Superconductor Vortices*, arXiv:1502.01029 (2015).

*Effective response theory for zero energy Majorana bound states in three spatial dimensions*, arXiv:1501.04109 (2015).

*Interaction Enabled Topological Crystalline Phases*, arXiv:1409.1234 (2014).

*Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the ADE Classification*, Phys. Rev. B

**90**, 235149 (2014); arXiv:1403.6478 (2014).

*Conflicting Symmetries in Topologically Ordered Surface States of Three-dimensional Bosonic Symmetry Protected Topological Phases*, Phys. Rev. B

**89**, 235103 (2014); arXiv:1403.2018 (2014).

*Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations*, Phys. Rev. B

**89**, 224503 (2014); arXiv:1311.0496 (2013).

*Braiding Statistics and Congruent Invariance of Twist Defects in Bosonic Bilayer Fractional Quantum Hall States*, Phys. Rev. B

**90**, 155111 (2014); arXiv:1308.5984 (2013).

*Topological phase states of the SU(3) QCD*, J. Phys.: Conf. Ser.

**482**, 012035 (2014); arXiv:1306.2648 (2013).

*Unconventional Fusion and Braiding of Topological Defects in a Lattice Model*, Phys. Rev. B

**90**, 115118 (2014); arXiv:1306.1538 (2013).

*Disclination Classes, Fractional Excitations, and the Melting of Quantum Liquid Crystals*, Phys. Rev. Lett.

**111**, 025304 (2013); arXiv:1302.3617.

*Existence of Majorana-Fermion Bound States on Disclinations and the Classification of Topological Crystalline Superconductors in Two Dimensions*, Phys. Rev. Lett.

**111**, 047006 (2013); arXiv:1208.6303.

*Spin texture on the Fermi surface of tensile-strained HgTe*, Phys. Rev. B

**87**, 045202 (2013); arXiv:1206.0684.

*Dirac Semimetal in Three Dimensions*, Phys. Rev. Lett.

**108**, 140405 (2012); arXiv:1111.6483.

*From Luttinger liquid to non-Abelian quantum Hall states*, Phys. Rev. B 89, 085101 (2014); arXiv:1111.2617 (2011).

*Topological Insulators and Superconductors*, Publicly accessible Penn Dissertations, Paper 384 (2011).

*Topological Defects and Gapless Modes in Insulators and Superconductors*, Phys. Rev. B

**82**, 115120 (2010) [Editors' suggestion]; arXiv:1006.0690.

*Majorana Fermions and Non-Abelian Statistics in Three Dimensions*, Phys. Rev. Lett.

**104**, 046401 (2010) [Selected as a Viewpoint in

*Physics*]; arXiv:0909.4741.

*Critical Behavior of a Point Contact in a Quantum Spin Hall Insulator*, Phys. Rev. B

**79**, 235321 (2009) [Editors' suggestion]; arXiv:0904.3109.

*Surface States of the Topological Insulator Bi_{1-x}Sb_x*, Phys. Rev. B

**78**, 045426 (2008) [Selected as a Viewpoint in

*Physics*, Editors' suggestion]; arXiv:0804.2664.

*Geometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operator*, Phys. Rev. Lett.

**95**, 050406 (2005); arXiv:quant-ph/0502168.