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Register a new userDIII Topological Superconductivity with Emergent Time-Reversal Symmetry
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We find a new class of topological superconductors which possess an emergent time-reversal symmetry that is present only after projecting to an effective low-dimensional model. We show that a topological phase in symmetry class DIII can be realized in a noninteracting system coupled to an $s$-wave superconductor only if the physical time-reversal symmetry of the system is broken, and we provide three general criteria that must be satisfied in order to have such a phase. We also provide an explicit model which realizes the class DIII topological superconductor in 1D. We show that, just as in time-reversal invariant topological superconductors, the topological phase is characterized by a Kramers pair of Majorana fermions that are protected by the emergent time-reversal symmetry.
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Fascinating phenomena have been known to arise from the Dirac theory of relativistic quantum mechanics, which describes high energy particles having linear dispersion relations. Electrons in solids usually have non-relativistic dispersion relations but their quantum excitations can mimic relativistic effects. In topological insulators, electrons have both a linear dispersion relation, the Dirac behavior, on the surface and a non-relativistic energy dispersion in the bulk. Topological phases of matter have attracted much interest, particularly broken-symmetry phases in topological insulator materials. Here, we report by Nb doping that the topological insulator Bi2Se3 can be turned into a bulk type-II superconductor while the Dirac surface dispersion in the normal state is preserved. A macroscopic magnetic ordering appears below the superconducting critical temperature of 3.2 K indicating a spontaneous spin rotation symmetry breaking of the Nb magnetic moments. Even though such a magnetic order may appear at the edge of the superconductor, it is mediated by superconductivity and presents a novel phase of matter which gives rise to a zero-field Hall effect.
Magnetotransport measurements are a popular way of characterizing the electronic structure of topological materials and often the resulting datasets cannot be described by the well-known Drude model due to large, non-parabolic contributions. In this work, we focus on the effects of magnetic fields on topological materials through a Zeeman term included in the model Hamiltonian. To this end, we re-evaluate the simplifications made in the derivations of the Drude model and pinpoint the scattering time and Fermi velocity as Zeeman-term dependent factors in the conductivity tensor. The driving mechanisms here are the aligment of spins along the magnetic field direction, which allows for backscattering, and a significant change to the Fermi velocity by the opening of a hybridization gap. After considering 2D and 3D Dirac states, as well as 2D Rashba surface states and the quasi-2D bulk states of 3D topological insulators, we find that the 2D Dirac states on the surfaces of 3D topological insulators produce magnetoresistance, that is significant enough to be noticable in experiments. As this magnetoresistance effect is strongly dependent on the spin-orbit energy, it can be used as a telltale sign of a Fermi energy located close to the Dirac point.
We consider a natural generalization of the lattice model for a periodic array of two layers, A and B, of spinless electrons proposed by Fu [Phys. Rev. Lett. 106, 106802 (2011)] as a prototype for a crystalline insulator. This model has time-reversal symmetry and broken inversion symmetry. We show that when the intralayer next-nearest-neighbor hoppings ta2, a = A, B vanish, this model supports a Weyl semimetal phase for a wide range of the remaining model parameters. When the effect of ta2 is considered, topological crystalline insulating phases take place within the Weyl semimetal one. By mapping to an effective Weyl Hamiltonian we derive some analytical results for the phase diagram as well as for the structure of the nodes in the spectrum of the Weyl semimetal.
Recent topological band theory distinguishes electronic band insulators with respect to various symmetries and topological invariants, most commonly, the time reversal symmetry and the $rm Z_2$ invariant. The interface of two topologically distinct insulators hosts a unique class of electronic states -- the helical states, which shortcut the gapped bulk and exhibit spin-momentum locking. The magic and so far elusive property of the helical electrons, known as topological protection, prevents them from coherent backscattering as long as the underlying symmetry is preserved. Here we present an experiment which brings to light the strength of topological protection in one-dimensional helical edge states of a $rm Z_2$ quantum spin-Hall insulator in HgTe. At low temperatures, we observe the dramatic impact of a tiny magnetic field, which results in an exponential increase of the resistance accompanied by giant mesoscopic fluctuations and a gap opening. This textbook Anderson localization scenario emerges only upon the time-reversal symmetry breaking, bringing the first direct evidence of the topological protection strength in helical edge states.
We introduce $mathbb Z_2$-valued bulk invariants for symmetry-protected topological phases in $2+1$ dimensional driven quantum systems. These invariants adapt the $W_3$-invariant, expressed as a sum over degeneracy points of the propagator, to the respective symmetry class of the Floquet-Bloch Hamiltonian. The bulk-boundary correspondence that holds for each invariant relates a non-zero value of the bulk invariant to the existence of symmetry-protected topological boundary states. To demonstrate this correspondence we apply our invariants to a chiral Harper, time-reversal Kane-Mele, and particle-hole symmetric graphene model with periodic driving, where they successfully predict the appearance of boundary states that exist despite the trivial topological character of the Floquet bands. Especially for particle-hole symmetry, combination of the $W_3$ and the $mathbb Z_2$-invariants allows us to distinguish between weak and strong topological phases.
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