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Register a new userSeeing topological edge and bulk currents in time-of-flight images
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Added by
Alvaro Rubio-Garc\\'ia
Publication date
2019
fields
Physics
and research's language is
English
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Here we provide a general methodology to directly measure the topological currents emerging in the optical lattice implementation of the Haldane model. Alongside the edge currents supported by gapless edge states, transverse currents can emerge in the bulk of the system whenever the local potential is varied in space, even if it does not cause a phase transition. In optical lattice implementations the overall harmonic potential that traps the atoms provides the boundaries of the topological phase that supports the edge currents, as well as providing the potential gradient across the topological phase that gives rise to the bulk current. Both the edge and bulk currents are resilient to several experimental parameters such as trapping potential, temperature and disorder. We propose to investigate the properties of these currents directly from time-of-flight images with both short-time and long-time expansions.
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We provide evidence that, alongside topologically protected edge states, two-dimensional Chern insulators also support localised bulk states deep in their valance and conduction bands. These states manifest when local potential gradients are applied to the bulk, while all parts of the system remain adiabatically connected to the same phase. In turn, the bulk states produce bulk current transverse to the strain. This occurs even when the potential is always below the energy gap, where one expects only edge currents to appear. Bulk currents are topologically protected and behave like edge currents under external influence, such as temperature or local disorder. Detecting topologically resilient bulk currents offers a direct means to probe the localised bulk states.
In this work we provide a general methodology to directly measure topological order in cold atom systems. As an application we propose the realisation of a characteristic topological model, introduced by Haldane, using optical lattices loaded with fermionic atoms in two internal states. We demonstrate that time-of-flight measurements directly reveal the topological order of the system in the form of momentum space skyrmions.
The bulk-edge correspondence (BEC) refers to a one-to-one relation between the bulk and edge properties ubiquitous in topologically nontrivial systems. Depending on the setup, BEC manifests in different forms and govern the spectral and transport properties of topological insulators and semimetals. Although the topological pump is theoretically old, BEC in the pump has been established just recently [1] motivated by the state-of-the-art experiments using cold atoms [2,3]. The center of mass (CM) of a system with boundaries shows a sequence of quantized jumps in the adiabatic limit associated with the edge states. Although the bulk is adiabatic, the edge is inevitably non-adiabatic in the experimental setup or in any numerical simulations. Still the pumped charge is quantized and carried by the bulk. Its quantization is guaranteed by a compensation between the bulk and edges. We show that in the presence of disorder the pumped charge continues to be quantized despite the appearance of non-quantized jumps.
The boundaries of quantum materials can host a variety of exotic effects such as topologically robust edge states or anyonic quasiparticles. Here, we show that fermionic systems such as graphene that admit a low energy Dirac description can exhibit counterintuitive relativistic effects at their boundaries. As an example, we consider carbon nanotubes and demonstrate that relativistic bulk spinor states can have non zero charge density on the boundaries, in contrast to the sinusoidal distribution of non-relativistic wave functions that are necessarily zero at the boundaries. This unusual property of relativistic spinors is complementary to the linear energy dispersion relation exhibited by Dirac materials and can influence their coupling to leads, transport properties or their response to external fields.
A time periodic driving on a topologically trivial system induces edge modes and topological properties. In this work we consider triplet and singlet superconductors subject to periodic variations of the chemical potential, spin-orbit coupling and magnetization, in both topologically trivial and nontrivial phases, and study their influence on the charge and spin currents that propagate along the edges of the two-dimensional system, for moderate to large driving frequencies. Currents associated with the edge modes are induced in the trivial phases and enhanced in the topological phases. In some cases there is a sign reversal of the currents as a consequence of the periodic driving. The edge states associated with the finite quasi-energy states at the edge of the Floquet zone are in general robust, while the stability of the zero quasi-energy states depends on the parameters. Also, the spin polarization of the Floquet spectrum quasi-energies is strong as for the unperturbed topological phases. It is found that in some cases the unperturbed edge states are immersed in a continuum of states due to the perturbation, particularly if the driving frequency is not large enough. However, their contribution to the edge currents and spin polarization is still significant.
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