Time-Reversal-Invariant Topological Superconductors and Superfluids in Two and Three Dimensions

Qi, Xiao-Liang; Hughes, Taylor L.; Raghu, S.; Zhang, Shou-Cheng

doi:10.1103/physrevlett.102.187001

Cited by 746 publications

(773 citation statements)

References 28 publications

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“…Since τ D has an extra factor of k F , retaining terms to first order in D gives us an additional term ∝ Dn 1/2 , resulting in a further contribution to the conductivity of the form ∝ Dn 3/2 , as is manifest in Eq. (35). Taking this fact into account, in order to keep the expressions simple, in Table I we have listed only the number density dependence explicitly, replacing the constants of proportionality by generic constants.…”

Section: A Density Dependencementioning

confidence: 99%

“…Given that superconductors are also gapped, topological superconductors have been predicted to exist. 1,14,34,35 Developments in different directions include the topological Anderson insulator, 36-38 the topological Mott insulator, 39 the topological magnetic insulator, 40 the fractional topological insulator, 41,42 the topological Kondo insulator, 43 as well as a host of topological phases arising from quadratic, rather than linear, band crossings. 44 Topological phases in transition-metal based strongly correlated systems have been the subject of Refs.…”

Section: Introductionmentioning

confidence: 99%

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Two-dimensional surface charge transport in topological insulators

et al. 2010

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We construct a theory of charge transport by the surface states of topological insulators in three dimensions. The focus is on the experimentally relevant case when the Fermi energy εF and transport scattering time τ satisfy εF τ / 1, but εF lies below the bottom of the conduction band. Our theory is based on the spin density matrix and takes the quantum Liouville equation as its starting point. The scattering term is determined to linear order in the impurity density ni and explicitly accounts for the absence of backscattering, while screening is included in the random phase approximation. The main contribution to the conductivity is ∝ n −1 i and has different carrier density dependencies for different forms of scattering, while an additional contribution is independent of ni. The dominant scattering angles can be inferred by studying the ratio of the transport time to the Bloch lifetime as a function of the Wigner-Seitz radius rs. The current generates a spin polarization that could provide a smoking-gun signature of surface state transport. We also discuss the effect on the surface states of adding metallic contacts.

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Section: A Density Dependencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two-dimensional surface charge transport in topological insulators

et al. 2010

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“…[27][28][29][30][31][32][33] Superconductors, described within a Bogoliubov de Gennes ͑BdG͒ framework can similarly be classified topologically. [34][35][36][37] The Bloch-BdG Hamiltonian H BdG ͑k͒ has a structure similar to an ordinary Bloch Hamiltonian, except that it has an exact particle-hole symmetry that reflects the particle-hole redundancy inherent to the BdG theory. Topological superconductors are also characterized by gapless boundary modes.…”

Section: Introductionmentioning

confidence: 99%

“…40 The spin degeneracy, however, leads to a doubling of the Majorana edge states. Though undoubled topological superconductors remain to be discovered experimentally, superfluid 3 He B is a related topological phase 34,35,37,41,42 and is predicted to exhibit 2D gapless Majorana modes on its surface. Related ideas have also been used to topologically classify Fermi surfaces.…”

Section: Introductionmentioning

confidence: 99%

Topological defects and gapless modes in insulators and superconductors

2010

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We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians.We consider Hamiltonians H(k,r) that vary slowly with adiabatic parameters r surrounding the defect and belong to any of the ten symmetry classes defined by time-reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three-dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions, and helical Majorana fermions, as well as zero-dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes. We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians H͑k , r͒ that vary slowly with adiabatic parameters r surrounding the defect and belong to any of the ten symmetry classes defined by time-reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three-dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions, and helical Majorana fermions, as well as zero-dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes. Disciplines Physical Sciences and Mathematics | Physics

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“…Such a state is called d + id or d − id. It has a rich phenomenology and is highly desirable for applications [129,130,131,132,133,134,135,136].…”

mentioning

confidence: 99%

Superconductivity from repulsive interaction

Maiti¹,

Chubukov²

2014

Novel Superfluids

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Abstract. The BCS theory of superconductivity named electron-phonon interaction as a glue that overcomes Coulomb repulsion and binds fermions into pairs which then condense and super-conduct. We review recent and not so recent works aiming to understand whether a nominally repulsive Coulomb interaction can by itself give rise to a superconductivity. We first discuss a generic scenario of the pairing by electron-electron interaction, put forward by Kohn and Luttinger back in 1965, and then turn to modern studies of the electronic mechanism of superconductivity in the lattice models for the cuprates, the Fe-pnictides, and the doped graphene. We show that the pairing in all three classes of materials can be viewed as lattice version of Kohn-Luttinger physics, despite that the pairing symmetries are different. We discuss under what conditions the pairing occurs and rationalize the need to do parquet renormalization-group analysis. We also discuss the interplay between superconductivity and density-wave instabilities.

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Time-Reversal-Invariant Topological Superconductors and Superfluids in Two and Three Dimensions

Cited by 746 publications

References 28 publications

Two-dimensional surface charge transport in topological insulators

Two-dimensional surface charge transport in topological insulators

Topological defects and gapless modes in insulators and superconductors

Superconductivity from repulsive interaction

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