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词条 Topological insulator
释义

  1. Prediction and discovery

  2. Properties and applications

  3. See also

  4. References

  5. Further reading

{{Use American English|date=January 2019}}{{Short description|State of matter with insulating bulk but conductive boundary
}}{{technical|date=August 2016}}{{merge from|Topological insulator growth|date=July 2018}}

In the bulk of a non-interacting topological insulator, the electronic band structure resembles an ordinary band insulator, with the Fermi level falling between the conduction and valence bands. On the surface of a topological insulator there are special states that fall within the bulk energy gap and allow surface metallic conduction. Carriers in these surface states have their spin locked at a right-angle to their momentum (spin-momentum locking). At a given energy the only other available electronic states have different spin, so the "U"-turn scattering is strongly suppressed and conduction on the surface is highly metallic. Non-interacting topological insulators are characterized by an index (known as topological invariants) similar to the genus in topology.[1]

As long as time-reversal symmetry is preserved i.e. there is no magnetism, the index cannot change by small perturbations and the conducting states at the surface are symmetry protected. On the other hand in the presence of magnetic impurities, the surface states will generically become insulating. Nevertheless, if certain crystalline symmetries, like inversion, are present the index is still well defined. These materials are known as magnetic topological insulators and their insulating surfaces exhibit a half-quantized surface anomalous Hall conductivity.

Prediction and discovery

Time-reversal symmetry-protected two-dimensional edge states were predicted in 1987[6] to occur in quantum wells (very thin layers) of mercury telluride sandwiched between cadmium telluride and were observed in 2007.[7]

In 2006 it was predicted that similar topological insulators might be found in binary compounds involving bismuth,[8][9] and in particular "strong topological insulators" exist that cannot be reduced to multiple copies of the quantum spin Hall state.[10]

The first experimentally realized 3D topological insulator state (symmetry-protected surface states) was discovered in bismuth-antimony in 2008.[11] Shortly thereafter symmetry-protected surface states were also observed in pure antimony, bismuth selenide, bismuth telluride and antimony telluride using angle-resolved photoemission spectroscopy (ARPES).[12] Many semiconductors within the large family of Heusler materials are now believed to exhibit topological surface states.[13][14] In some of these materials the Fermi level actually falls in either the conduction or valence bands due to naturally occurring defects, and must be pushed into the bulk gap by doping or gating.[15][16] The surface states of a 3D topological insulator is a new type of two-dimensional electron gas (2DEG) where the electron's spin is locked to its linear momentum.[17]

Fully bulk insulating or intrinsic 3D topological insulator states exist in Bi-based materials.[18]

In 2014 it was shown that magnetic components, like the ones in spin-torque computer memory, can be manipulated by topological insulators.[19][20]

The effect is related to the metal-insulator transitions (Bose–Hubbard model).{{Citation needed|date=January 2018}}

Properties and applications

Spin-momentum locking[17] in the topological insulator allows symmetry-protected surface states to host Majorana particles if superconductivity is induced on the surface of 3D topological insulators via proximity effects.[21] (Note that Majorana zero-mode can also appear without topological insulators.[22])

The non-trivialness of topological insulators is encoded in the existence of a gas of helical Dirac fermions. Dirac particles which behave like massless relativistic fermions, have been observed in 3D topological insulators. Note that the gapless surface states of topological insulator differ from those in the quantum Hall effect: the gapless surface states of topological insulator are symmetry-protected (i.e. not topological), while the gapless surface states in quantum Hall effect are topological (i.e. robust against any local perturbations that can break all the symmetries). The topological invariants cannot be measured using traditional transport methods, such as spin Hall conductance, and the transport is not quantized by the invariants. An experimental method to measure topological invariants was demonstrated which provide a measure of the topological order.[23] (Note that the term topological order has also been used to describe the topological order with emergent gauge theory discovered in 1991.[24][25]) More generally (in what is known as the Ten-fold way) for each spatial dimensionality, each of the 10 Altland-Zirnbauer symmetry classes of random Hamiltonians labelled by the type of discrete symmetry (time-reversal symmetry, particle-hole symmetry, and chiral symmetry) has a corresponding group of topological invariants (either , or trivial) as described by the periodic table of topological invariants.[26]

The most promising applications of topological insulator are spintronic devices and dissipationless transistors for quantum computers based on the quantum spin Hall effect[7] and quantum anomalous Hall effect.[27] In addition, topological insulator materials have also found practical applications in advanced magnetoelectronic and optoelectronic devices.[28][29]

See also

  • Topological order
  • Topological quantum computer
  • Topological quantum field theory
  • Topological quantum number

References

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2. ^Zheng-Cheng Gu and Xiao-Gang Wen[https://arxiv.org/abs/0903.1069 Tensor-Entanglement-Filtering Renormalization Approach and Symmetry-Protected Topological Order]Phys. Rev. B80, 155131 (2009).
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Further reading

  • {{Cite journal| last = Hasan | first = M. Zahid |author2=Kane, Charles L. | year = 2010 | title = Topological Insulators | journal = Reviews of Modern Physics | volume = 82 | issue = 4| pages = 3045–3067 | doi = 10.1103/RevModPhys.82.3045 | url = http://rmp.aps.org/pdf/RMP/v82/i4/p3045_1 | accessdate = | pmid = | bibcode=2010RvMP...82.3045H|arxiv = 1002.3895 }}
  • {{Cite journal| last = Kane | first = Charles L. |author2=Moore, Joel E. | year = 2011 | title = Topological Insulators | journal = Physics World | volume = 24 | issue = | pages = 32 | doi = | url = http://physics.gmu.edu/~pnikolic/articles/Topological%20insulators%20(Physics%20World,%20February%202011).pdf | accessdate = | pmid = }}
  • {{Cite journal| last = Kane | first = Charles L. | year = 2008 | title = Topological Insulator: An Insulator with a Twist | journal = Nature | volume = 4 | issue = 5 | pages = 348–349 | doi = 10.1038/nphys955| url = http://www.nature.com/nphys/journal/v4/n5/pdf/nphys955.pdf | accessdate = | pmid = |bibcode = 2008NatPh...4..348K }}
  • {{Cite journal| last = Witze | first = A. | year = 2010 | title = Topological Insulators: Physics On the Edge | journal = Science News | volume = | issue = | pages = | doi = | url = http://www.sciencenews.org/view/feature/id/58909/title/Physics_on_the_edge | accessdate = }}
  • {{Cite journal| doi = 10.1038/466310a | volume = 466 | issue = 7304 | pages = 310–311 | last = Brumfiel | pmid = 20631773| first = G. | title = Topological insulators: Star material : Nature News | journal = Nature | accessdate = | year = 2010 | url = http://www.nature.com/news/2010/100714/full/466310a.html}}
  • {{Cite journal| last = Murakami | first = Shuichi | year = 2010 | title = Focus on Topological Insulators | journal = New Journal of Physics | volume = | issue = | pages = | doi = | url = http://iopscience.iop.org/1367-2630/focus/Focus%20on%20Topological%20Insulators | accessdate = }}
  • What’s a Topological Insulator?
  • "Topological Insulators," by Joel E. Moore, IEEE Spectrum, July 2011
  • {{Cite web|url=https://www.scientificamerican.com/article/the-strange-topology-that-is-reshaping-physics/|title=The Strange Topology That Is Reshaping Physics (Scientific American 2017) |last=|first=|date=|website=www.scientificamerican.com|archive-url=|archive-date=|dead-url=|accessdate=}}
{{DEFAULTSORT:Topological Insulator}}

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