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Register a new userTime reversal symmetry protected chaotic fixed point in the quench dynamics of a topological $p$-wave superfluid
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We study the quench dynamics of a topological $p$-wave superfluid with two competing order parameters, $Delta_pm(t)$. When the system is prepared in the $p+ip$ ground state and the interaction strength is quenched, only $Delta_+(t)$ is nonzero. However, we show that fluctuations in the initial conditions result in the growth of $Delta_-(t)$ and chaotic oscillations of both order parameters. We term this behavior phase III. In addition, there are two other types of late time dynamics -- phase I where both order parameters decay to zero and phase II where $Delta_+(t)$ asymptotes to a nonzero constant while $Delta_-(t)$ oscillates near zero. Although the model is nonintegrable, we are able to map out the exact phase boundaries in parameter space. Interestingly, we find phase III is unstable with respect to breaking the time reversal symmetry of the interaction. When one of the order parameters is favored in the Hamiltonian, the other one rapidly vanishes and the previously chaotic phase III is replaced by the Floquet topological phase III that is seen in the integrable chiral $p$-wave model.
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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.
The single helical Fermi surface on the surface state of three-dimensional topological insulator Bi2Se3 is constrained by the time-reversal invariant bulk topology to possess a spin-singlet superconducting pairing symmetry. In fact, the Cu-doped, and pressure-tuned superconducting Bi2Se3 show no evidence of the time reversal symmetry breaking. We report on the detection of the time reversal symmetry (TRS) breaking in the topological superconductor Sr0.1Bi2Se3 , probed by zero-field (ZF) {mu}SR measurements. The TRS breaking provides strong evidence for the existence of spin-triplet pairing state. The temperature dependent super-fluid density deduced from transverse-field (TF) {mu}SR measurement yields nodeless superconductivity with low superconducting carrier density and penetration depth {lambda} = 1622(134) nm. From the microscopic theory of unconventional pairing, we find that such a fully gapped spin triplet pairing channel is promoted by the complex interplay between the structural hexagonal warping and higher order Dresselhaus spin-orbit coupling terms. Based on Ginzburg-Landau analysis, we delineate the mixing of singlet to triplet pairing symmetry as the chemical potential is tuned far above from the Dirac cone. Our observation of such spontaneous TRS breaking chiral superconductivity on a helical surface state, protected by the TRS invariant bulk topology, can open new avenues for interesting research and applications.
The second law of thermodynamics points to the existence of an `arrow of time, along which entropy only increases. This arises despite the time-reversal symmetry (TRS) of the microscopic laws of nature. Within quantum theory, TRS underpins many interesting phenomena, most notably topological insulators and the Haldane phase of quantum magnets. Here, we demonstrate that such TRS-protected effects are fundamentally unstable against coupling to an environment. Irrespective of the microscopic symmetries, interactions between a quantum system and its surroundings facilitate processes which would be forbidden by TRS in an isolated system. This leads not only to entanglement entropy production and the emergence of macroscopic irreversibility, but also to the demise of TRS-protected phenomena, including those associated with certain symmetry-protected topological phases. Our results highlight the enigmatic nature of TRS in quantum mechanics, and elucidate potential challenges in utilising topological systems for quantum technologies.
In general, magnetism and superconductivity are antagonistic to each other. However, there are several families of superconductors, in which superconductivity may coexist with magnetism, and only a few examples are known, when superconductivity itself induces spontaneous magnetism. The most known compounds are Sr$_2$RuO$_4$ and some noncentrosymmetric superconductors. Here, we report the finding of a narrow dome of a novel $s+is$ superconducting (SC) phase with broken time-reversal symmetry (BTRS) inside the broad $s$-wave SC region of the centrosymmetric multiband superconductor Ba$_{rm 1-x}$K$_{rm x}$Fe$_2$As$_2$ ($0.7 lesssim x lesssim 0.85$). We observe spontaneous magnetic fields inside this dome using the muon spin relaxation ($mu$SR) technique. Furthermore, our detailed specific heat study reveals that the BTRS dome appears very close to a change in the topology of the Fermi surface (Lifshitz transition). With this, we experimentally demonstrate the emergence of a novel quantum state due to topological changes of the electronic system.
We investigate an unconventional symmetry in time-periodically driven systems, the Floquet dynamical symmetry (FDS). Unlike the usual symmetries, the FDS gives symmetry sectors that are equidistant in the Floquet spectrum and protects quantum coherence between them from dissipation and dephasing, leading to two kinds of time crystals: the discrete time crystal and discrete time quasicrystal that have different periodicity in time. We show that these time crystals appear in the Bose- and Fermi-Hubbard models under ac fields and their periodicity can be tuned only by adjusting the strength of the field. These time crystals arise only from the FDS and thus appear in both dissipative and isolated systems and in the presence of disorder as long as the FDS is respected. We discuss their experimental realizations in cold atom experiments and generalization to the SU($N$)-symmetric Hubbard models.
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