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Topological Insulators & Berry's Phase

New Topological States of Matter: Platform for emergent Dirac, Majorana & Weyl fermions (CalTech)
Bose seminar (Public lecture), S.N. Bose Center for Advanced Study (DU)
Frontiers of Cond.Matter.Physics Lecture Series Columbia-Rice-Tokyo Univ. (2015)
New Topological States of Matter (Inst. for Adv. Study Distinguished Lecture at HKUST)
Physics Colloquium at Harvard University
Physics Colloquium at California Institute of Technology
Physics Colloquium at Columbia University
Physics Colloquium at UC-Berkeley
Pedagogical Lecture Series
Physics World interview (100 Second Science Series)
PNAS Front Matter homepage (September, 2016): Topological Insulators

KITP Talk Proc. (2007)(Topo.Insulators in 2007)
"Search&Discovery" Physics Today
Nature 452, 970 (2008) [Submitted in 2007]
KITP Talk Proc. (2008)
Science 323, 919 (2009)
Nature Physics 5, 398 (2009)
Nature 460, 1101 (2009)
Nature 460, 1106 (2009)
Phys. Rev. Lett. 103, 146401 (2009)
Phys. Rev. Lett. 105, 036404 (2010)
Nature Mater. 9, 546 (2010)
Nature Physics 6, 855 (2010)
Nature Physics 7, 32 (2011)
Science 332, 560 (2011)
Nature Physics 8, 616 (2012)
Science 341, 1496 (2013)
Nature Commun. 4:2991 (2013)
Nature Physics 10, 943 (2014)
Nature Physics 10, 956 (2014)
Nature Commun. 5: 3841 (2014)
Phys. Rev. Lett. 114, 016403 (2015)
Nature Commun. 6: 6870 (2015)
Science 347, 294 (2015)
Phys. Rev. Lett. 115, 116801 (2015)
ACS Nano DOI: 10.1021/acsnano.6b00987 (2016)
Reviews on Topological Insulators:
Rev. Mod. Phys 82, 3045 (2010)
Ann. Rev. Cond. Mat. Phys 2, 55 (2011)
Book Chapter on Topo. Insulators, Elesevier (2013)
Book Chapter on Topo. Insulators, Wiley&Sons (2015)
Physics World interview on Topo. Insulators (100 Second Science Series) 2016

 
  NbSe2  
  Demonstration of a Fully Bulk Insulating (Intrinsic) Topological Insulator
Nature Physics 10, 956 (2014)

A very recent achievement of condensed matter physics was the discovery that crystalline solids can be characterized by numbers called topological invariants. A topological invariant is a global property of a crystal and, as a result, it is robust against imperfections of the sample or local perturbations. In addition, a non-trivial topological invariant gives rise to electron states near the surface of the sample, with important consequences for applications. For instance, a topological insulator behaves as an ordinary insulator in the bulk of the sample, but because of the non-trivial topological invariant, it has electron surface states which allow it to conduct electricity on the sample surface. Because the topological invariant is a global property of the system, these surface states are robust against disorder. Despite advances in understanding the physics of topological insulators, progress of making actual devices has been limited by the materials currently available. While many topological insulators have been discovered, few of the materials currently known have a sufficiently low bulk conductivity and other key properties, hindering the proposed applications. More precisely, for the advancement of the field, it is crucial to find materials with a large bulk band gap, a chemical potential in the bulk band gap and furthermore at the energy of the surface Dirac point, and surface states with high mobility. This will allow us to develop technologies that take advantage of the unique quantum phenomena associated with the topological surface states.

Very recently, we have discovered a fully insulating (intrinsic) topological insulator, BiSbSe2Te, which has sufficiently low residual bulk conductivity and sufficiently high surface mobility. This allows us to observe quantized Hall current arising from topological surface states for the first time. Our discovery of a true topological insulator that features surface state quantum Hall effects provides an excellent platform which can facilitate the transition of topological insulators from the realm of pure physics to the realm of device engineering.

 
 
Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator

Y. Xu, I. Miotkowski, C. Liu, J. Tian, H. Nam, N. Alidoust, J. Hu, C.-K. Shih, M. Z. Hasan and Y. P. Chen
Nature Physics 10, 956 (2014)

 
  DS
Nature 460, 1101 (2009)


 
  TI1  
 

(a), In the quantum Hall effect, the circular motion of electrons in a magnetic field, B, is interrupted by the sample boundary. At the edge, electrons execute "skipping orbits" as shown, intimately leading to perfect conduction in one direction along the edge. (b), The edge of the "quantum spin Hall effect state" or 2D topological insulator contains left-moving and right-moving modes that have opposite spin and are related by time-reversal symmetry. This edge can also be viewed as half of a quantum wire, which would have spin-up and spin-down electrons propagating in both directions. (c), The surface of a 3D topological insulators supports electronic motion in any direction along the surface, but the direction of electron's motion uniquely determines its spin direction and vice versa. The 2D energy-momentum relation has a "spin-Dirac cone" structure but with helical or momentum space chiral spin texture with Berry's phase(spins go around in a closed loop in momentum space).


 
  TI1  
 
The first 3D topological insulator: Bi1-xSbx

D. Hsieh, D. Qian, Y. Xia, et al., Nature 452, 970 (2008)
D. Hsieh, Y. Xia, L. A. Wray, et al., Science 323, 919 (2009)


 
  TI3  
 
First detection of Z2 (symmetry protected) Topological-Order: spin-momentum locking of spin-helical Dirac electrons in Bi2Se3 and Bi2Te3

Y. Xia, D. Qian, L. A. Wray, et al., Nature Physics 5, 398 (2009)
D. Hsieh, Y. Xia, D. Qian, et al., Nature 460, 1101 (2009)

 
 

The discoveries of new forms of matter have been so definitive that they are used to name periods in the history of mankind, such as Stone Age, Bronze Age, and Iron Age. Although all matter is composed of component particles, particles can organize in various ways leading to different phases of matter. Finding all possible distinct phases that matter can form and understanding the physics behind each of them are fundamentally important goals in physics research and often lead to new technologies, benefiting our society. A topological phase is an unusual type of crystalline solid, characterized by a nontrivial topological number. This number is a global quantity, which depends on the crystal's bulk electronic wavefunctions.

From 2007 to 2009, our group pioneered the experimental discovery of the 3D Z2 topological insulator (TI) phase in bismuth-based materials. This is the first realization of a topological phase in bulk crystals. A 3D TI features spin-polarized Dirac electronic states on its surface, which enjoys a robust protection against disorder. An unusual property of these electron surface states is that the spin of the electron is locked to its momentum. This property, which our group experimentally demonstrated via the spin-ARPES method, not only provides an experimental measurement of the topological invariant in a 3D topological insulator, but also has important consequences to spintronic applications. One proposed application is to induce ferromagnetism in these surface states and to prepare the topological insulator sample in a 2D thin film geometry. Under these conditions, the boundary of the film can exhibit quantized Hall currents even without external magnetic fields. Such a quantum anomalous Hall state can allow for the development of low-power electronics. Another proposal is to induce superconductivity on the surface of a topological insulator. This would give rise to an exotic emergent excitation called a Majorana fermion, which does not exist as a fundamental particle in nature and may allow the development of a fault-tolerant quantum computer. Inspired by these fascinating properties, the experimental discovery of the 3D topological insulator has truly attracted research interest world-wide, and the field of "Topological Insulator" has become widely known across other areas of physics.


 
  DS
 
 
Berry's phase and quantization in topological insulators.
M. Zahid Hasan
Physics 3, 62 (2010)

 
  NbSe2  
  NbSe2  
  Demonstration of a Fully Bulk Insulating (Intrinsic) Topological Insulator
 
 
Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator.
Published in Y. Xu, I. Miotkowski, C. Liu, J. Tian, H. Nam, N. Alidoust, J. Hu, C.-K. Shih, M. Z. Hasan and Y. P. Chen,
Nature Physics 10, 956 (2014).