The Higgs mode associated with amplitude fluctuations of the superconducting gap in uniform superconductors usually is heavy, which makes its excitation and detection difficult. We report on the existence of a gapless Higgs mode in the Fulde-Ferrell-
Larkin-Ovchinnikov states. This feature is originated from the Goldstone mode associated with the translation symmetry breaking. The existence of the gapless Higgs mode is demonstrated by using both a phenomenological model and microscopic Bardeen-Cooper-Schrieffer (BCS) theory. The gapless Higgs mode can avoid the decay into other low energy excitations, which renders it stable and detectable.
Motivated by the experiments on the organic compound $(Per)_{2}[Pt(mnt)_{2}]$, we study the ground state of the one-dimensional Kondo lattice model at quarter filling with the density matrix renormalization group method. We show a coupled dimer and b
ond-order-wave (BOW) state in the weak coupling regime for the localized spins and itinerant electrons, respectively. The quantum phase transitions for the dimer and the BOW orders occur at the same critical coupling parameter $J_{c}$, with the opening of a charge gap. The emergence of the combination of dimer and BOW order agrees with the experimental findings of the simultaneous Peierls and spin-Peierls transitions at low temperatures, which provides a theoretical understanding of such phase transition. We also show that the localized spins in this insulating state have quasi-long ranged spin correlations with collinear configurations, which resemble the classical dimer order in the absence of a magnetic order.
The electronic structure and possible electronic orders in monolayer NbF$_4$ are investigated by density functional theory and functional renormalization group. Because of the niobium-centered octahedra, the energy band near the Fermi level is found
to derive from the $4d_{xy}$ orbital, well separated from the other bands. Local Coulomb interaction drives the undoped system into an antiferromagnetic insulator. Upon suitable electron/hole doping, the system is found to develop $d_{x^2-y^2}$-wave superconductivity with sizable transition temperature. Therefore, the monolayer NbF$_4$ may be an exciting $4d^1$ analogue of cuprates, providing a new two-dimensional platform for high-$T_c$ superconductivity.
We report the existence of the charge density wave (CDW) in the ground state of 1D Kondo lattice model at the filling of n=0.75 in the weak coupling region. The CDW is driven by the effective Coulomb repulsion mediated by the localized spins. Based o
n our numerical results using the density matrix renormalization group method, we show that the CDW phase appears in the paramagnetic region previously known as the Tomonaga-Luttinger liquid. The emergence of this phase serves as an example of CDW phase induced without bare repulsive interactions, and enriches the phase diagram of the 1D Kondo lattice model.
Recent experiments show the spontaneous breaking of rotational symmetry in the superconducting topological insulators M$_{x}$Bi$_{2}$Se$_{3}$ (M represents Cu, Sr, or Nd), suggesting that the pairing belongs to a two-dimensional representation of the
$D_{3d}$ symmetry group of the crystal. Motivated by these progresses, we construct an exhaustive list of possible two-component pairings of the M$_{x}$Bi$_{2}$Se$_{3}$ superconductors, both for the odd-parity $E_{u}$ representation and for the even-parity $E_{g}$ representation. Starting from a tight-binding model for the normal phase of Bi$_{2}$Se$_{3}$ and M$_{x}$Bi$_{2}$Se$_{3}$, we firstly construct the pairing channels in the spin-orbital basis, up to second-nearest-neighbor pairing correlations in the basal plane. We then infer the properties of these pairings by transforming them to the band (pseudospin) basis for the conduction band. A comparison with the key experimental consensuses on M$_{x}$Bi$_{2}$Se$_{3}$ superconductors shows that the true pairings should also be multichannel. Besides a nematic and time-reversal symmetric pairing combination, the other pairings that we have identified are chiral and nematic at the same time, which may be nonunitary and have a spontaneous magnetization. A complementary set of experiments are proposed to identify the true pairing symmetries of these superconductors and their evolution with the doping concentration $x$.
With a generic lattice model for electrons occupying a semi-infinite crystal with a hard surface, we study the eigenstates of the system with a bulk band gap (or the gap with nodal points). The exact solution to the wave functions of scattering state
s is obtained. From the scattering states, we derive the criterion for the existence of surface states. The wave functions and the energy of the surface states are then determined. We obtain a connection between the wave functions of the bulk states and the surface states. For electrons in a system with time-reversal symmetry, with this connection, we rigorously prove the correspondence between the change of Kramers degeneracy of the surface states and the bulk time-reversal $Z_2$ invariant. The theory is applicable to systems of (topological) insulators, superconductors, and semi-metals. Examples for solving the edge states of electrons with/without the spin-orbit interactions in graphene with a hard zigzag edge and that in a two-dimensional $d$-wave superconductor with a (1,1) edge are given in appendices.
We study theoretically the topological surface states (TSSs) and the possible surface Andreev bound states (SABSs) of Cu$_{x}$Bi$_{2}$Se$_{3}$ which is known to be a topological insulator at $x=0$. The superconductivity (SC) pairing of this compound
is assumed to have the broken spin-rotation symmetry, similar to that of the A-phase of $^{3}$He as suggested by recent nuclear-magnetic resonance experiments. For both spheroidal and corrugated cylindrical Fermi surfaces with the hexagonal warping terms, we show that the bulk SC gap is rather anisotropic; the minimum of the gap is negligibly small as comparing to the maximum of the gap. This would make the fully-gapped pairing effectively nodal. For a clean system, our results indicate the bulk of this compound to be a topological superconductor with the SABSs appearing inside the bulk SC gap. The zero-energy SABSs which are Majorana fermions, together with the TSSs not gapped by the pairing, produce a zero-energy peak in the surface density of states (SDOS). The SABSs are expected to be stable against short-range nonmagnetic impurities, and the local SDOS is calculated around a nonmagnetic impurity. The relevance of our results to experiments is discussed.
We present a formalism to calculate the orbital magnetization of interacting Dirac fermions under a magnetic field. In this approach, the divergence difficulty is overcome with a special limit of the derivative of the thermodynamic potential with res
pect to the magnetic field. The formalism satisfies the particle-hole symmetry of the Dirac fermions system. We apply the formalism to the interacting Dirac fermions in graphene. The charge and spin orderings and the exchange interactions between all the Landau levels are taken into account by the mean-field theory. The results for the orbital magnetization of interacting Dirac fermions are compared with that of non-interacting cases.
Two-dimensional Weyl superconductor is the most elusive member of a group of materials with Weyl fermions as low-energy excitations. Here, we propose to realize this state in a heterostructure consisting of thin films of half-metal and spin-singlet s
uperconductor. In particular, for the $d$-wave case, a very robust two-dimensional Weyl superconductor (dWSC) is realized independent of the orientation of the spontaneous magnetization of the half-metal. The quasiparticle spectra of the dWSC show interesting evolution with the direction of the magnetization, featured by a series of Lifshitz transitions in the zero-energy contour of the quasiparticle spectrum. For a general magnetization orientation of the half-metal, the state is a combination of a superconducting component and a normal fluid component and is different from all known forms of pairings. In addition, we find a transition between type-I and type-II Weyl nodes. This is also the first example of a type-II Weyl node in the presence of superconducting correlation. The symmetries and topological properties of the system are analyzed. We also study the phases in the heterostructure with the half-metal replaced by a ferromagnetic metal with a partially spin-polarized Fermi surface.
We find a series of topological phase transitions in a half-metal/superconductor heterostructure, by tuning the direction of the magnetization of the half-metal film. These include transitions between a topological superconducting phase with a bulk g
ap and another phase without a bulk gap but has a ubiquitous local gap. At the same time, the edge states change from counter-propagating Majorana edge modes to unidirectional Majorana edge modes. In addition, we find transitions between the second phase and a nodal phase which turns out to be a two-dimensional Weyl superconductor with Fermi line edge states. We identify the topological invariants relevant to each phase and the symmetry that protects the Weyl superconductivity phase.
