Topological semimetals have energy bands near the Fermi energy sticking together at isolated points/lines/planes in the momentum space, which are often accompanied by stable surface states and intriguing bulk topological responses. Although it has been known that certain crystalline symmetries play an important role in protecting band degeneracy, a general recipe for stabilizing the degeneracy, especially in the presence of spin-orbit coupling, is still lacking. Here we show that a class of novel topological semimetals with point/line nodes can emerge in the presence of an off-centered rotation/mirror symmetry whose symmetry line/plane is displaced from the center of other symmorphic symmetries in nonsymmorphic crystals. Due to the partial translation perpendicular to the rotation axis/mirror plane, an off-centered rotation/mirror symmetry always forces two energy bands to stick together and form a doublet pair in the relevant invariant line/plane in momentum space. Such a doublet pair provides a basic building block for emerging topological semimetals with point/line nodes in systems with strong spin-orbit coupling. 1 arXiv:1604.00843v3 [cond-mat.mtrl-sci]

We discuss the phase diagram and phase transitions in U (1)×Z2 three-band superconductors with broken time reversal symmetry. We find that beyond mean field approximation and for sufficiently strong frustration of interband interactions there appears an unusual metallic state precursory to a superconducting phase transition. In that state, the system is not superconducting. Nonetheless, it features a spontaneously broken Z2 time reversal symmetry. By contrast, for weak frustration of interband coupling the energy of a domain wall between different Z2 states is low and thus fluctuations restore broken time reversal symmetry in the superconducting state at low temperatures.In recent years, the discovery of superconductors such as the Iron Pnictides 1 , has generated much interest for multiband superconducting systems. From a theoretical viewpoint, one of the main reasons for the strong interest is that in contrast to previously known two-band materials, iron-based superconductors may exhibit dramatically different physics due to the possibility of frustrated inter-band Josephson couplings originating with more than two bands crossing the Fermi-surface 2-5 . In two-band superconductors the Josephson coupling locks the phase differences between the bands to 0 or π. By contrast, if one has three bands and the frustration of interband coupling is sufficiently strong, the ground state interband phase difference can be different from 0 or π. This leads to a superconducting state which breaks time reversal symmetry (BTRS) 2,3 . From a symmetry viewpoint such a ground state breaks U(1) × Z 2 4 . Recently, such a scenario has received solid theoretical support 5 in connection with hole-doped Ba 1 − x K x Fe 2 As 2 . The possibility of this new physics arising also in other classes of materials is currently under investigation 6 . For other scenarios of time reversal symmetry breakdown in ironbased superconductors discussed in the literature, see 7,8 .Three band superconductors with frustrated interband Josephson couplings feature several properties that are radically different from their two-band counterparts. These include (I) the appearance of a massless so-called Leggett mode at the Z 2 phase transition 9 ; (II) the existence of new mixed phase-density collective modes in the state with broken time-reversal symmetry (BTRS) 4,5,10 in contrast to the "phase-only" Leggett collective mode in two-band materials 11 ; and (III) the existence of (meta-)stable excitations characterized by CP 2 topological invariants 12,13 . So far the phase diagram of frustrated three-band superconductors has been investigated only at the meanfield level 3,5 . However, the iron-based materials feature relatively high T c , as well as being far from the type-I regime. Hence, one may expect fluctuations to be of importance.In this paper, we study the phase diagram of a threeband superconductor in two spatial dimensions in the London limit, beyond mean-field approximation. The results should apply to relatively thin films of ironbased superconducto...

Using Monte Carlo simulations, we explore the phase diagram and the phase transitions in U(1) × Z2 n-band superconductors with spontaneously broken time-reversal symmetry (also termed s + is superconductors), focusing on the three-band case. In the limit of infinite penetration length, the system under consideration can, for a certain parameter regime, have a single first order phase transition from a U(1) × Z2 broken state to a normal state due to a nontrivial interplay between U(1) vortices and Z2 domain walls. This regime may also apply to multicomponent superfluids. For other parameters, when the free energy of the domain walls is low, the system undergoes a restoration of broken Z2 time reversal symmetry at temperatures lower than the temperature of the superconducting phase transition.We show that inclusion of fluctuations can strongly suppress the temperature of the Z2-transition when frustration is weak. The main result of our paper is that for relatively short magnetic field penetration lengths, the system has a superconducting phase transition at a temperature lower than the temperature of the restoration of the broken Z2 symmetry.Thus, there appears a new phase which is U(1)-symmetric, but breaks Z2 time reversal symmetry, an anomalous dissipative (metallic) state.

We investigate the magnetization processes of a standard Ginzburg-Landau model for chiral pwave superconducting states in an applied magnetic field. We find that the phase diagram is dominated by triangular lattices of doubly quantized vortices. Only in close vicinity to the upper critical field, the lattice starts to dissociate into a structure of single-quanta vortices. The degeneracy between states with opposite chirality is broken in a nonzero field. If the magnetization starts with an energetically unfavorable chirality, the process of chirality-inversion induced by the external magnetic field results in the formation of a sequence of metastable states with characteristic magnetic signatures that can be probed by standard experimental techniques.

We study the three dimensional SU(2)-symmetric noncompact CP 1 model, with two charged matter fields coupled minimally to a noncompact Abelian gauge-field. The phase diagram and the nature of the phase transitions in this model have attracted much interest after it was proposed to describe an unusual continuous transition associated with deconfinement of spinons. Previously, it has been demonstrated for various two-component gauge theories that weakly first-order transitions may appear as continuous ones of a new universality class in simulations of relatively large, but finite systems. We have performed Monte-Carlo calculations on substantially larger systems sizes than those in previous works. We find that in some area of the phase diagram where at finite sizes one gets signatures consistent with a single first-order transition, in fact there is a sequence of two phase transitions with an O(3) paired phase sandwiched in between. We report (i) a new estimate for the location of a bicritical point and (ii) the first resolution of bimodal distributions in energy histograms at relatively low coupling strengths. We perform a flowgram analysis of the direct transition line with rescaling of the linear system size in order to obtain a data collapse. The data collapses up to coupling constants where we find bimodal distributions in energy histograms.