TY - GEN AU - Friedlander, Tamar AU - Mayo, Avraham E. AU - Tlusty, Tsvi AU - Alon, Uri ID - 9773 TI - Evolutionary simulation code ER - TY - JOUR AB - The tunability of topological surface states and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In the newly discovered topological crystalline insulators (TCIs), theory predicts that the Dirac node is protected by a crystalline symmetry and that the surface state electrons can acquire a mass if this symmetry is broken. Recent studies have detected signatures of a spontaneously generated Dirac gap in TCIs; however, the mechanism of mass formation remains elusive. In this work, we present scanning tunnelling microscopy (STM) measurements of the TCI Pb 1â'x Sn x Se for a wide range of alloy compositions spanning the topological and non-topological regimes. The STM topographies reveal a symmetry-breaking distortion on the surface, which imparts mass to the otherwise massless Dirac electrons-a mechanism analogous to the long sought-after Higgs mechanism in particle physics. Interestingly, the measured Dirac gap decreases on approaching the trivial phase, whereas the magnitude of the distortion remains nearly constant. Our data and calculations reveal that the penetration depth of Dirac surface states controls the magnitude of the Dirac mass. At the limit of the critical composition, the penetration depth is predicted to go to infinity, resulting in zero mass, consistent with our measurements. Finally, we discover the existence of surface states in the non-topological regime, which have the characteristics of gapped, double-branched Dirac fermions and could be exploited in realizing superconductivity in these materials. AU - Zeljkovic, Ilija AU - Okada, Yoshinori AU - Maksym Serbyn AU - Sankar, Raman AU - Walkup, Daniel AU - Zhou, Wenwen AU - Liu, Junwei AU - Chang, Guoqing AU - Wang, Yungjui AU - Hasan, Md Z AU - Chou, Fangcheng AU - Lin, Hsin AU - Bansil, Arun AU - Fu, Liang AU - Madhavan, Vidya ID - 981 IS - 3 JF - Nature Materials TI - Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators VL - 14 ER - TY - JOUR AB - We propose a new approach to probing ergodicity and its breakdown in one-dimensional quantum manybody systems based on their response to a local perturbation. We study the distribution of matrix elements of a local operator between the system's eigenstates, finding a qualitatively different behavior in the manybody localized (MBL) and ergodic phases. To characterize how strongly a local perturbation modifies the eigenstates, we introduce the parameter g(L) = (In (Vnm/δ)) which represents the disorder-averaged ratio of a typical matrix element of a local operator V to energy level spacing δ this parameter is reminiscent of the Thouless conductance in the single-particle localization. We show that the parameter g(L) decreases with system size L in the MBL phase and grows in the ergodic phase. We surmise that the delocalization transition occurs when g(L) is independent of system size, g(L)=gc ~ 1. We illustrate our approach by studying the many-body localization transition and resolving the many-body mobility edge in a disordered one-dimensional XXZ spin-1=2 chain using exact diagonalization and time-evolving block-decimation methods. Our criterion for the MBL transition gives insights into microscopic details of transition. Its direct physical consequences, in particular, logarithmically slow transport at the transition and extensive entanglement entropy of the eigenstates, are consistent with recent renormalization-group predictions. AU - Maksym Serbyn AU - Papić, Zlatko AU - Abanin, Dmitry A ID - 982 IS - 4 JF - Physical Review X TI - Criterion for many-body localization-delocalization phase transition VL - 5 ER - TY - JOUR AB - Quasiparticle excitations can compromise the performance of superconducting devices, causing high-frequency dissipation, decoherence in Josephson qubits, and braiding errors in proposed Majorana-based topological quantum computers. Quasiparticle dynamics have been studied in detail in metallic superconductors but remain relatively unexplored in semiconductor-superconductor structures, which are now being intensely pursued in the context of topological superconductivity. To this end, we use a system comprising a gate-confined semiconductor nanowire with an epitaxially grown superconductor layer, yielding an isolated, proximitized nanowire segment. We identify bound states in the semiconductor by means of bias spectroscopy, determine the characteristic temperatures and magnetic fields for quasiparticle excitations, and extract a parity lifetime (poisoning time) of the bound state in the semiconductor exceeding 10 ms. AU - Higginbotham, Andrew P AU - Albrecht, S M AU - Kiršanskas, Gediminas AU - Chang, W AU - Kuemmeth, Ferdinand AU - Krogstrup, Peter AU - Jespersen, Thomas AU - Nygård, Jesper AU - Flensberg, Karsten AU - Marcus, Charles ID - 99 IS - 12 JF - Nature Physics TI - Parity lifetime of bound states in a proximitized semiconductor nanowire VL - 11 ER - TY - JOUR AB - In this note, we consider the dynamics associated to a perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and we prove the following result of ``micro-diffusion'': under generic assumptions on $ h$ and $ f$, there exists an orbit of the system for which the drift of its action variables is at least of order $ \sqrt {\varepsilon }$, after a time of order $ \sqrt {\varepsilon }^{-1}$. The assumptions, which are essentially minimal, are that there exists a resonant point for $ h$ and that the corresponding averaged perturbation is non-constant. The conclusions, although very weak when compared to usual instability phenomena, are also essentially optimal within this setting. AU - Bounemoura, Abed AU - Kaloshin, Vadim ID - 8495 IS - 4 JF - Proceedings of the American Mathematical Society SN - 0002-9939 TI - A note on micro-instability for Hamiltonian systems close to integrable VL - 144 ER -