Effective theory of two-dimensional chiral superfluids: Gauge duality and Newton-Cartan formulation

Moroz, Sergej; Hoyos, Carlos

doi:10.1103/physrevb.91.064508

Cited by 31 publications

(44 citation statements)

References 72 publications

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“…3.3, the discussion on L tot was extended to the BCS-to-BEC topological phase transition regime, where the system possesses the constant L tot ¼ Nħ=2 in both the BCS and BEC phases. 194) Further studies on the edge or bulk mass current have been performed by numerous researchers 59,126,191,192,[231][232][233]401,[411][412][413][414][415][416][417][418][419][420] in connection with the intrinsic angular momentum paradox. In the next section, we review the edge mass current in 3 He-A, following Ref.…”

Section: Intrinsic Angular Momentum Paradoxmentioning

confidence: 99%

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

et al. 2016

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In this article, we give a comprehensive review of recent progress in research on symmetry-protected topological superfluids and topological crystalline superconductors, and their physical consequences such as helical and chiral Majorana fermions. We start this review article with the minimal model that captures the essence of such topological materials. The central part of this article is devoted to the superfluid 3 He, which serves as a rich repository of novel topological quantum phenomena originating from the intertwining of symmetries and topologies. In particular, it is emphasized that the quantum fluid confined to nanofabricated geometries possesses multiple superfluid phases composed of the symmetry-protected topological superfluid B-phase, the A-phase as a Weyl superfluid, the nodal planar and polar phases, and the crystalline ordered stripe phase. All these phases generate noteworthy topological phenomena, including topological phase transitions concomitant with spontaneous symmetry breaking, Majorana fermions, Weyl superfluidity, emergent supersymmetry, spontaneous edge mass and spin currents, topological Fermi arcs, and exotic quasiparticles bound to topological defects. In relation to the mass current carried by gapless edge states, we also briefly review a longstanding issue on the intrinsic angular momentum paradox in 3 He-A. Moreover, we share the current status of our knowledge on the topological aspects of unconventional superconductors, such as the heavy-fermion superconductor UPt 3 and superconducting doped topological insulators, in connection with the superfluid 3 He.In Sect. 3, we will share the topological aspect of a spinpolarized chiral p-wave superconducting state as a specific model having nontrivial w 2d ¼ Ch 1 . Topology subject to discrete symmetriesNaively, any one-dimensional closed loop S 1 cannot cover the target space S 2 . Thus, a generic 2 Â 2 Hamiltonian in one dimension cannot provide a stable topological structure. However, discrete symmetries of H in Eq. (3) impose strong constraints on the spinorm, and thus nontrivial topological numbers can be introduced even in one dimension, as illustrated below.Particle-hole symmetry C 2 ¼ þ1 (class D)-Let us first suppose that the minimal Hamiltonian (13) holds the PHS C ¼ x K (C 2 ¼ þ1). The operation of PHS changes the spinor mðkÞ to ½Àm x ðÀkÞ; Àm y ðÀkÞ;m z ðÀkÞ. For the momentum space characterized by S 2 , there are two particle-hole invariant momenta, k ¼ 0 and jkj ¼ 1, where the infinite points are identical to a single point. At the particle-hole invariant momenta, the spinorm must point to the north or south pole on S 2 . Therefore, we have two different situations: One is that the spinorsm at k ¼ 0 and jkj ¼ 1 point in the same direction,m z ð0Þ ¼m z ð1Þ; ð26Þ Fig. 3. (Color online) Target spaces M subject to discrete symmetries T and C. Possible trajectories ofm on M with C 2 ¼ þ1 are also depicted.Fig. 24. (Color online) Low-lying quasiparticle spectra for the axisymmetric w-vortex (a) and v-vortex (b) with k z ¼ 0 and ...

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Section: Intrinsic Angular Momentum Paradoxmentioning

confidence: 99%

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

et al. 2016

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“…In fact, many condensed matter systems are described by non-relativistic field theories and coupling these systems to non-relativistic backgrounds provides appropriate external sources conjugated to their conserved currents. In the context of NC geometry, the appropriate way of performing this coupling has been studied from the theoretical point of view [29][30][31][32][33][34] and typical condensed matter applications include, e.g., the description of the quantum Hall effect [35][36][37][38] and even aging in materials [39][40][41][42][43][44][45][46].…”

Section: Jhep04(2016)145mentioning

confidence: 99%

“…where 38) JHEP04 (2016)145 with h µ ν the spatial projector h µ ν = h µρ h νρ . Note that the expression (5.38) is the only part of the Christoffel connection that is appearing due to the overall contraction with e µ a e ν b in (5.35).…”

Section: Identification With Hořava-lifshitz Gravitymentioning

confidence: 99%

A Schrödinger approach to Newton-Cartan and Hořava-Lifshitz gravities

Afshar

Bergshoeff

Mehra

et al. 2016

J. High Energ. Phys.

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Abstract:We define a 'non-relativistic conformal method', based on a Schrödinger algebra with critical exponent z = 2, as the non-relativistic version of the relativistic conformal method. An important ingredient of this method is the occurrence of a complex compensating scalar field that transforms under both scale and central charge transformations. We apply this non-relativistic method to derive the curved space Newton-Cartan gravity equations of motion with twistless torsion. Moreover, we reproduce z = 2 Hořava-Lifshitz gravity by classifying all possible Schrödinger invariant scalar field theories of a complex scalar up to second order in time derivatives.

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“…we give the transformation rules for the gauge fields as [21] δτ µ = ∂ µ ξ , 6) and the corresponding curvatures are given by…”

Section: Bargmann Algebramentioning

confidence: 99%

“…As the scale invariant potential terms are already Schrödinger invariant, we start our investigation with the kinetic terms. For an arbitrary scaling dimension of the complex scalar Ψ, the b 0 ≡ τ µ b µ terms in the terms relevant to S (6) , S (7) and S (8) are given by…”

Section: Schrödinger Gravitymentioning

confidence: 99%

Scale invariance in Newton–Cartan and Hořava–Lifshitz gravity

Devecioğlu

Ozdemir

Ozkan

et al. 2018

Class. Quantum Grav.

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We present a detailed analysis of the construction of z = 2 and z = 2 scale invariant Hořava-Lifshitz gravity. The construction procedure is based on the realization of Hořava-Lifshitz gravity as the dynamical Newton-Cartan geometry as well as a non-relativistic tensor calculus in the presence of the scale symmetry. An important consequence of this method is that it provides us the necessary mechanism to distinguish the local scale invariance from the local Schrödinger invariance. Based on this result we discuss the z = 2 scale invariant Hořava-Lifshitz gravity and the symmetry enhancement to the full Schrödinger group.

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Effective theory of two-dimensional chiral superfluids: Gauge duality and Newton-Cartan formulation

Cited by 31 publications

References 72 publications

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

A Schrödinger approach to Newton-Cartan and Hořava-Lifshitz gravities

Scale invariance in Newton–Cartan and Hořava–Lifshitz gravity

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Effective theory of two-dimensional chiral superfluids: Gauge duality and Newton-Cartan formulation

Cited by 31 publications

References 72 publications

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to3He—

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to3He—

A Schrödinger approach to Newton-Cartan and Hořava-Lifshitz gravities

Scale invariance in Newton–Cartan and Hořava–Lifshitz gravity

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Product

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Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—

Symmetry-Protected Topological Superfluids and Superconductors —From the Basics to³He—