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arXiv:1302.0088 · Physical Review Letters

Universal Impurity-Induced Bound State in Topological Superfluids

Hui Hu, Lei Jiang, Han Pu, Yan Chen, Xia-Ji Liu

Published Jan 10, 2013• 55 citations
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Abstract

We predict a universal midgap bound state in topological superfluids, induced by either nonmagnetic or magnetic impurities in the strong scattering limit. This universal state is similar to the lowest-energy Caroli-de Gennes-Martricon bound state in a vortex core, but is bound to localized impurities. We argue that the observation of such a universal bound state can be a clear signature for identifying topological superfluids. We theoretically examine our argument for a spin-orbit coupled ultracold atomic Fermi gas trapped in a two-dimensional harmonic potential by performing extensive self-consistent calculations within the mean-field Bogoliubov-de Gennes theory. A realistic scenario for observing a universal bound state in ultracold 40K atoms is proposed.

DOI
10.1103/physrevlett.110.020401

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We predict a universal midgap bound state in topological superfluids, induced by either nonmagnetic or magnetic impurities in the strong scattering limit. This universal state is similar to the lowest-energy Caroli-de Gennes-Martricon bound state in a vortex core, but is bound to localized impurities. We argue that the observation of such a universal bound state can be a clear signature for identifying topological superfluids. We theoretically examine our argument for a spin-orbit coupled ultracold atomic Fermi gas trapped in a two-dimensional harmonic potential by performing extensive self-consistent calculations within the mean-field Bogoliubov-de Gennes theory. A realistic scenario for observing a universal bound state in ultracold 40K atoms is proposed.
We investigate theoretically nonmagnetic impurity scattering in a one-dimensional atomic topological superfluid in harmonic traps by solving self-consistently the microscopic Bogoliubov-de Gennes equation. In sharp contrast to topologically trivial Bardeen-Cooper-Schrieffer sss-wave superfluid, topological superfluid can host a midgap state that is bound to localized nonmagnetic impurity. For strong impurity scattering, the bound state becomes universal, with nearly zero energy and a wave function that closely follows the symmetry of that of Majorana fermions. We propose that the observation of such a universal bound state could be useful evidence for characterizing the topological nature of topological superfluids. Our prediction is applicable to an ultracold, resonantly interacting Fermi gas of 40{}^{40}40K atoms with spin-orbit coupling confined in a two-dimensional optical lattice.
The role of impurities as experimental probes in the detection of quantum material properties is well appreciated. Here we study the effect of a single classical magnetic impurity in trapped ultracold Fermi superfluids. Depending on its shape and strength, a magnetic impurity can induce single or multiple midgap bound states in a superfluid Fermi gas. The multiple midgap states could coincide with the development of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase within the superfluid. As an analog of the scanning tunneling microsope, we propose a modified rf spectroscopic method to measure the local density of states which can be employed to detect these states and other quantum phases of cold atoms. A key result of our self-consistent Bogoliubov-de Gennes calculations is that a magnetic impurity can controllably induce an FFLO state at currently accessible experimental parameters.
A spin-imbalanced superfluid Fermi gas harmonically trapped in a two-dimensional optical lattice with a single classical magnetic impurity is investigated by Bogoliubov-de Gennes equations. In both the spin-balanced and weak spin-imbalanced cases, we show that a strong magnetic impurity can change the sign of the pairing order parameter. The amplitude of the sign-changed order parameter caused by impurity is affected by the strength of the impurity potential, temperature, and particle density. Compared to the spin-balanced case, we find that an additional in-gap bound state can be induced by a strong magnetic impurity in the weak spin-imbalanced case. In the strong spin-imbalanced case where the Fulde-Ferrell-Larkin-Ovchinnikov state is established as the ground state, the impurity induces wide spatial oscillations of pairing order parameters and can enhance the order parameters by suppressing the local spin imbalance.
In cold atom experiments, we have tools to create spin dependent optical potential, which gives us the possibility to achieve classical magnetic impurity in cold atom systems. Here we study the physics of magnetic impurity. A localized magnetic impurity can induce a mid-gap bound state, the Yu-Shiba state, in superfluid Fermi gas. We propose a modified RF spectroscopy to measure the local density of states, as a cold-atom analog of STM, which may be used to detect Yu-Shiba state. In addition, magnetic impurity can locally induce population imbalance in the system, potentially providing a method to realize FFLO-like state in a controlled way. We demonstrate such a possibility by solving the self-consist Bogoliubov-de Gennes equations.
A spin-imbalanced superfluid Fermi gas harmonically trapped in a two-dimensional optical lattice with a single classical magnetic impurity is investigated by Bogoliubov-de Gennes equations. In both the spin-balanced and weak spin-imbalanced cases, we show that a strong magnetic impurity can change the sign of the pairing order parameter. The amplitude of the sign-changed order parameter caused by impurity is affected by the strength of the impurity potential, temperature, and particle density. Compared to the spin-balanced case, we find that an additional in-gap bound state can be induced by a strong magnetic impurity in the weak spin-imbalanced case. In the strong spin-imbalanced case where the Fulde-Ferrell-Larkin-Ovchinnikov state is established as the ground state, the impurity induces wide spatial oscillations of pairing order parameters and can enhance the order parameters by suppressing the local spin imbalance.
We theoretically predict an exotic topological superfluid state with a spatially modulated pairing gap in one-dimensional spin-orbit-coupled Fermi gases. This inhomogeneous topological superfluidity is induced by applying simultaneously a perpendicular Zeeman magnetic field and an equally weighted Rashba and Dresselhaus spin-orbit coupling in one-dimensional optical lattices. Based on the self-consistent Bogoliubov-de Gennes theory, we confirm that this novel topological phase is a unique condensation of Cooper pairs, which manifests the interplay between the inhomogeneity of a superfluid and its nontrivial topological structure. The properties of the emergent Majorana bound states are investigated in detail by examining the associated Z2 topological number, the eigenenergy and density of states spectra, as well as the wave functions of the localized Majorana end modes. The experimental feasibility of observing this new topological state of matter is also discussed.