## What's new? (updated on Nov. 15, 2013)

#### Nematicity: good or bad for superconductivity (Nov. 15, 2013)

Whether the breaking of rotational symmetry enhances or suppresses superconductivity is one important question in the study of high temperature superconductivity and another stroungly-correlated materials. Our recent work, pulished on__, offers an answer for the superconductivity in__

*Nature Communications**Sr*, which is believed to be a p+ip topological superconductor. We proved theortically that T

_{2}RuO_{4}_{C}shall be enhanced by breaking explicitly the rotational symmetry. This conclusion is supported directly by experimental observations.

[1] Y.A. Ying, N.E. Staley, Y. Xin, K. Sun, X. Cai, D. Fobes, T. Liu, Z.Q. Mao, and Y. Liu,

*Enhanced spin-triplet superconductivity near dislocations in Sr*, Nature Communications 4, 2596 (2013).

_{2}Ruo_{4}#### Topological crystalline Kondo insulators (Jun. 30, 2013)

In a recent work, we found that certain Kondo insulators are topological crystalline insulators. In particular, we proved that SmB_{6}is both a topological Kondo insulator and a topological crystalline insulators. The surface of this material has two different types of topological surface Dirac points, some of which are protected by the time-reversal symmetry and others are due to crystal symmetries.

[1] Mengxing Ye, J. W. Allen and Kai Sun,

*Topological crystalline Kondo insulators and universal topological surface states of SmB*, Arxiv preprint arXiv:1307.7191 (2013).

_{6}#### New experimental evidence of topological Kondo insulator (Jun. 21, 2013)

Quantum oscillations have been recently observed in SmB6 by my colleagues [1]. In addition, the data indicate that the surface state of SmB6 contains Dirac points [1], in good agreement with our theoretical prediction [2].[1] G. Li, Z. Xiang, F. Yu, T. Asaba, B. Lawson, P. Cai, C. Tinsman, A. Berkley, S. Wolgast, Y. S. Eo, Dae-Jeong Kim, C. Kurdak, J. W. Allen, Kai Sun, X. H. Chen, Y. Y. Wang, Z. Fisk, And Lu Li,

*Quantum oscillations in Kondo Insulator SmB6*, Arxiv preprint arXiv:1306.5221 (2013).

[2] Maxim Dzero, Kai Sun, Victor Galitski, and Piers Coleman,

*Topological Kondo Insulators*, Physical Review Letters

**104**, 106408 (2010).

#### Old model with a new twist (May. 1, 2013)

The Aubry-André-Harper model has been studied for many years. It has been known that in the gapped regime, this model can be mapped into a quantum HAll states and thus is topologically nontrivial. In our recent paper published on Physical Review Letters [1], we found that this famous old model supports another nontrivial topological in the gapless regime, by mapping the gapless off-diagonal Aubry-André-Harper model into two decoupled Majorana chains.[1] Sriram Ganeshan, Kai Sun and S. Das Sarma,

*Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models*, Physical Review Letters 110, 180403(2013).

#### Nature News Report (Dec. 11, 2012)

Two of my works on topological Kondo insulators are reported by a recent news on Nature:*Hopes surface for exotic insulator*.

#### Invited review appeared on NJP (Nov. 28, 2012)

Our invited review on the special issue of New journal of Physics, "Focus on Quantum Spin Liquids".[1] Christopher N. Varney, Kai Sun, Victor Galitski and Marcos Rigol, Quantum phases of hard-core bosons in a frustrated honeycomb lattice, New Journal of Physics 14, 115028 (2012)

#### Topological Kondo insulator: finally discovered (Nov. 27, 2012)

Back in 2010, my coworkers and I predicted that some of the strongly-correlated heavy-fermion compounds are topological insulators, which we called the topological Kondo insulators [1]. In particular, we predicated that SmB_{6}is a such strongly-correlated topological material [1].

Two years latter, this prediction is confirmed experimentally [2]. Recently, my coworkers and I proved that SmB

_{6}is indeed a surface conductor with a fully gapped insulating bulk (below T~4K). The robustness and high mobility of the surface states indicate that they shall have a topological nature.

In previous known 3D topological insulators, most of the materials have a large bulk conducivity, making it hard to access the topological surface states in transport measurements. This problem can be avoided in this heavy fermion topological insluator, which has an insulating bulk, making SmB

_{6}one idea material to characterzie and to investigate the tranposrt properties of the topological surface state.

[1] Maxim Dzero, Kai Sun, Victor Galitski, and Piers Coleman,

*Topological Kondo Insulators*, Physical Review Letters

**104**, 106408 (2010).

[2] Steven Wolgast, Cagliyan Kurdak, Kai Sun, J. W. Allen, Dae-Jeong Kim and Zachary Fisk, Discovery of the First Topological Kondo Insulator: Samarium Hexaboride. Arxiv preprint arXiv:1211.5104 (2012)

#### How to control a singlet–triplet spin qubit? (Aug. 14, 2012)

Our recent work is published on Nature Communications [1].In this work, simple electrical pulse sequences are discovered which carry out arbitrary spin rotations while cancelling the error to certain order.

[1] X. Wang, L.S. Bishop, JP Kestner, E. Barnes, K. Sun, and S.D. Sarma,

*Composite Pulses for Robust Universal Control of Singlet-Triplet Qubits*, Nature Communications

**3**, 997 (2012).

#### Zero-energy edge modes in classical mechanics (Jul. 31, 2012)

Our recent work is published on PNAS [1]. See also the accompanying Commentary from Vincenzo Vitelli [2].The existence of zero-energy edge modes is one of the key phenomena in topological insulators, which is a quantum topological state of matter. In our recent paper published on PNAS [1], we found that similar phenomenon can also be observed in classical systems without quantum physics, due to an emergent conformal symmetry in one type of isostatic systems. This system also shows holographic property, where the edge fully determines the bulk.

[1] Kai Sun, Anton Souslov, Xiaoming Mao and T. C. Lubensky,

*Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices*, Proceedings of the National Academy of Sciences of the United States of America,

**109**, 12369 (2012).

[2] Accompanying Commentary:

*Topological soft matter: Kagome lattices with a twist*by Vincenzo Vitelli, PNAS

**109**, 12266 (2012).

#### Fractional Chern insulators and fractional quantum Hall effects (Jul. 18, 2012)

In previous numerical studies, it has been found that a fractional Chern insulator shares the same topological properties with the corresponding fractional quantum Hall state, which indicates that these two states may be topologically equivalent. Our recent study confirms that this is indeed the case by showing that they are adiabatically connected (i.e. they are two different regimes of the same phase)[1] Ying-Hai Wu, J. K. Jain and Kai Sun,

*Adiabatic Continuity Between Hofstadter and Chern Insulators*, Physical Review B 86, 165129 (2012).

#### The Chern number becomes large (May 25, 2012)

In a recently posted draft on arXiv, we present a systematic way to construct topological flatband models with arbitrary Chern numbers, by enhancing the translational symmetry in topological-flatband multi-layers.[1] Shuo Yang, Zheng-Cheng Gu, Kai Sun and S. Das Sarma,

*Topological flat band models with arbitrary Chern numbers*, Arxiv preprint arXiv:1205.5792 (2012)

#### Double-well potential, high angular momentum orbitals and topological insulators in ultracold atomic gases (Nov. 20, 2011)

Our recent work is published on Nature PhysicsIn a recent publication on Nature Physics [1], my coworkers and I proposed a new laser setup, which leads to the formation of a double-well potential. We predicted theoretically that this optical lattice will results in an interaction induced topological insulator, when fermionic particles with repulsive interactions are loaded onto this lattice. See also the news release on this work [2].

[1] Kai Sun, W. Vincent Liu, Andreas Hemmerich, and S. Das Sarma,

*Topological Semimetal in a Fermionic Optical Lattice*, Nature Physics

**8**, 67 (2012).

[2] News Release:

*Topological matter in optical lattices*.

#### Frustrated magnetism (Aug. 8, 2011)

Our recent work is published on Physical Review Letters, and highlighted in Physics ViewPoint.[1] Christopher N. Varney, Kai Sun, Victor Galitski, and Marcos Rigol,

*Kaleidoscope of Exotic Quantum Phases in a Frustrated XY Model*, Physical Review Letters

**107**, 077201 (2011).

[2] Accompanying viewpoint:

*Quantum liquids move to a higher dimension*by Tameem Albash and Stephan Haas, Physics 4, 62 (2011).

#### Topological flatbands and fractional topological insulators (Jul. 12, 2011)

Our recent works are published on Nature Communications and Physical Review Letters, and highlighted in Physics ViewPoint.It was discovered recently that the topological flatband models we proposed do support fractional topological states, once repulsive interactions are introduced. See our recent papers on Physical Review Letters and Nature Communications for details [1-2], as well as the accompanying viewpoint article by Rahul Roy and Shivaji L. Sondhi[3].

[1] Kai Sun, Zhengcheng Gu, Hosho Katsura, and S. Das Sarma,

*Nearly Flatbands with Nontrivial Topology*, Physical Review Letters

**106**, 236803 (2011).

[2] D. N. Sheng, Zheng-Cheng Gu, Kai Sun, and L. Sheng,

*Fractional Quantum Hall Effect in the Absence of Landau Levels*, Nature Communications

**2**, 389 (2011)

[3] Accompanying viewpoint:

*Fractional quantum Hall effect without Landau levels,*by Rahul Roy and Shivaji L. Sondhi, Physics

**4**, 46 (2011).