Recent experiments have observed bulk superconductivity in doped topological insulators. Here we ask whether vortex Majorana zero modes, previously predicted to occur when s-wave superconductivity is induced on the surface of topological insulators, survive in these doped systems with metallic normal states. Assuming inversion symmetry, we find that they do but only below a critical doping. The critical doping is tied to a topological phase transition of the vortex line, at which it supports gapless excitations along its length. The critical point depends only on the vortex orientation and a suitably defined SU(2) Berry phase of the normal state Fermi surface. By calculating this phase for available band structures we determine that superconducting p-doped Bi(2)Te(3), among others, supports vortex end Majorana modes. Surprisingly, superconductors derived from topologically trivial band structures can support Majorana modes too.

Superconductivity (SC) in so-called "unconventional superconductors" is nearly always found in the vicinity of another ordered state, such as antiferromagnetism, charge density wave (CDW), or stripe order. This suggests a fundamental connection between SC and fluctuations in some other order parameter. To better understand this connection, we used high-pressure x-ray scattering to directly study the CDW order in the layered dichalcogenide TiSe 2 , which was previously shown to exhibit SC when the CDW is suppressed by pressure [1] or intercalation of Cu atoms [2]. We succeeded in suppressing the CDW fully to zero temperature, establishing for the first time the existence of a quantum critical point (QCP) at P c = 5.1 ± 0.2 GPa, which is more than 1 GPa beyond the end of the SC region. Unexpectedly, at P = 3 GPa we observed a reentrant, weakly first order, incommensurate phase, indicating the presence of a Lifshitz tricritical point somewhere above the superconducting dome. Our study suggests that SC in TiSe 2 may not be connected to the QCP itself, but to the formation of CDW domain walls. *The term "unconventional superconductor" once referred to materials whose phenomenology does not conform to the Bardeen-Cooper-Schrieffer (BCS) paradigm for superconductivity. It is now evident that, by this definition, the vast majority of known superconductors are unconventional, notable examples being the copper-oxide, iron-arsenide, and iron-selenide high temperature superconductors, heavy Fermion materials such as CeIn 3 and CeCoIn 5 , ruthenium oxides, organic superconductors such as ϰ-(BEDT-TTF)2X, filled skutterudites, etc.Despite their diversity in structure and phenomenology, the phase diagrams of these materials all exhibit the common trait that superconductivity (SC) resides near the boundary of an ordered phase with broken translational or spin rotation symmetry. For example, SC resides near antiferromagnetism in CeIn 3 [3], near a spin density wave in iron arsenides [4], orbital order in ruthenates [5], and stripe and nematic order in the copper-oxides [6]. The pervasiveness of this "universal phase diagram" suggests that there exists a unifying framework -more general than BCS -in which superconductivity can be understood as coexisting with some ordered phase, and potentially emerging from its fluctuations.A classic example is the transition metal dichalcogenide family, MX 2 , where M=Nb, Ti, Ta, and X=Se, S, which exhibit a rich competition between superconductivity and Peierls-like charge density wave (CDW) order [7]. A recent, prominent case is 1T-TiSe 2 , which under ambient pressure exhibits CDW order below a transition temperature T CDW = 202 K [8]. This CDW phase can be suppressed either with intercalation of Cu atoms [2,9], or through the application of hydrostatic pressure [1,10], causing SC to emerge. These studies suggest that the emergence of SC coincides with a quantum critical point (QCP) at which T CDW goes to zero, suggesting that TiSe 2 exemplifies the universal phenomenon of superconductivity em...

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Several small-band-gap semiconductors are now known to protect metallic surface states as a consequence of the topology of the bulk electron wave functions. The known "topological insulators" with this behavior include the important thermoelectric materials Bi₂Te₃ and Bi₂Se₃, whose surfaces are observed in photoemission experiments to have an unusual electronic structure with a single Dirac cone. We study in-plane (i.e., horizontal) transport in thin films made of these materials. The surface states from top and bottom surfaces hybridize, and conventional diffusive transport predicts that the tunable hybridization-induced band gap leads to increased thermoelectric performance at low temperatures. Beyond simple diffusive transport, the conductivity shows a crossover from the spin-orbit-induced antilocalization at a single surface to ordinary localization.

We show that strained or deformed honeycomb lattices are promising platforms to realize fractional topological quantum states in the absence of any magnetic field. The strained induced pseudo magnetic fields are oppositely oriented in the two valleys [1][2][3] and can be as large as 60-300 Tesla as reported in recent experiments [4,5]. For strained graphene at neutrality, a spin or a valley polarized state is predicted depending on the value of the onsite Coulomb interaction. At fractional filling, the unscreened Coulomb interaction leads to a valley polarized Fractional Quantum Hall liquid which spontaneously breaks time reversal symmetry. Motivated by artificial graphene systems [5][6][7][8] Fractional Quantum Hall (FQH) phases are macroscopic scale manifestations of quantum phenomena with unique features including the fractional charge and statistics (abelian or nonabelian) of elementary excitations. This topological order originates from the strong Coulomb interactions between electrons moving in a partially filled Landau level induced by a strong magnetic field. Recently Chern insulator models with a nontrivial flat band [9][10][11] were also shown to exhibit topological order in the absence of any magnetic field [12][13][14][15][16][17]. Those so-called Fractional Chern Insulators (FCIs) explicitely break time-reversal symmetry T as did the original Haldane model [18]. In contrast, fractional topological insulators (FTIs) [19][20][21][22] can be naively thought of as two copies of time-reversed Laughlin FQH states, thereby obeying time reversal symmetry T . In spite of few proposals [23,24], the experimental implementation of FCIs and FTIs remains very challenging.Motivated by recent experimental advances [4,5], we introduce another route towards fractional topological phases making use of the gauge fields that can be generated in a deformed honeycomb lattice [1][2][3]. The associated effective magnetic fields are opposite in the two different valleys and therefore they do not break the time reversal symmetry T [1]. Indeed, a scanning tunneling spectroscopy study [4] confirmed that straining graphene could yield flat Pseudo Landau Levels (PLLs) [2,3] with effective fields as high as 300 T in each valley. Most recently by designing a molecular honeycomb grid of carbon monoxide molecules on top of a copper surface, Gomes at al. [5] were able to observe the linear dispersion of Dirac fermions in graphene, and furthermore to generate nearly uniform pseudo-magnetic fields as high as 60 T by deforming this grid [5]. Finally other realizations of artifical graphene systems, in patterned GaAs quantum wells [6] or with cold atoms trapped in hexagonal optical lattices [7,8], also provide experimental platforms to create strong valley-dependent effective magnetic fields.In this Letter, we first consider real graphene under strong pseudo-magnetic fields generated by a mechanical strain. We investigate the interaction-driven phases in the n = 0 PLL using mean field and numerical exactdiagonalization. The unscreened Cou...

Recent quantum oscillation experiments on SmB6 pose a paradox, for while the angular dependence of the oscillation frequencies suggest a 3D bulk Fermi surface, SmB6 remains robustly insulating to very high magnetic fields. Moreover, a sudden low temperature upturn in the amplitude of the oscillations raises the possibility of quantum criticality. Here we discuss recently proposed mechanisms for this effect, contrasting bulk and surface scenarios. We argue that topological surface states permit us to reconcile the various data with bulk transport and spectroscopy measurements, interpreting the low temperature upturn in the quantum oscillation amplitudes as a result of surface Kondo breakdown and the high frequency oscillations as large topologically protected orbits around the X point. We discuss various predictions that can be used to test this theory.SmB 6 , discovered 50 years ago [1,2], has attracted recent interest due to its unusual surface transport properties: while its insulating gap develops around T K 50K, the resistivity saturates below a few Kelvin[3]. The renewed interest derives in part from from the possibility that SmB 6 is a topological Kondo insulator, developing topologically protected surface states at low temperatures [4][5][6][7]. Experiments [8][9][10] have confirmed that the plateau conductivity derives from surface states, and these states have been resolved by angle-resolved photoemission spectroscopy (ARPES) [11][12][13][14]. Furthermore, spin-ARPES experiments have revealed the spinmomentum locking of the surface quasiparticles expected from topologically protected Dirac cones [15].Yet despite this progress, some important experimental results are unresolved. In particular, quantum oscillation experiments on SmB 6 have given rise to two dramatically different interpretations [16,17]. Ref [16] observes low frequency (small Fermi surface) oscillations with the characteristic 1/ cos(φ) dependence on field orientation expected from 2D topological surface states. On the other hand Ref [17] detects a wide range of frequencies (both high and low frequency oscillations) which have been interpreted in terms of angularly isotropic three dimensional quasiparticle orbits, resembling a metallic hexaboride without a hybridization gap (such as LaB 6 ). A striking aspect of these measurements, is that the oscillations strongly deviate from a classic Lifshitz-Kosevich formula below ∼ 1K. Two recent theoretical proposals have been advanced to account for this bulk behavior, as a consequence of magnetic breakdown [18], of the formation of non-conducting Fermi surfaces [19].Another aspect of recent measurements, is the wide disparity in the reported effective masses of the carriers. The effective mass observed in both quantum oscillation experiments, m * /m ∼ 0.1 − 0.2 is an order of magnitude smaller than effective mass observed in ARPES [11][12][13][14] [17]. Error bars are the size of symbols which include both experimental errorbars and also errors from extracting data from a logarithmic plot. Given...

arXiv:0812.0015v1 [cond-mat.supr-con] 30 Nov 2008Andreev Bound states as a phase sensitive probe of the pairing symmetry of the iron pnictide superconductors. A leading contender for the pairing symmetry in the Fe-pnictide high temperature superconductors is extended s-wave s±, a nodeless state in which the pairing changes sign between Fermi surfaces. Verifying such a pairing symmetry requires a special phase sensitive probe that is also momentum selective. We show that the sign structure of s± pairing can lead to surface Andreev bound states at the sample edge. In the clean limit they only occur when the edge is along the nearest neighbor Fe-Fe bond, but not for a diagonal edge or a surface orthogonal to the c-axis. In contrast to dwave Andreev bound states, they are not at zero energy and, in general, do not produce a zero bias tunneling peak. Consequences for tunneling measurements are derived, within a simplified two band model and also for a more realistic five band model.

We study the finite temperature properties of quantum magnets close to a continuous quantum phase transition between two distinct valence bond solid phases in two spatial dimension. Previous work has shown that such a second order quantum 'Lifshitz' transition is described by a free field theory and is hence tractable, but is nevertheless non-trivial. At T > 0, we show that while correlation functions of certain operators exhibit ω/T scaling, they do not show analogous scaling in space. In particular, in the scaling limit, all such correlators are purely local in space, although the same correlators at T = 0 decay as a power law. This provides a valuable microscopic example of a certain kind of 'local' quantum criticality. The local form of the correlations arise from the large density of soft modes present near the transition that are excited by temperature. We calculate exactly the autocorrelation function for such operators in the scaling limit. Going beyond the scaling limit by including irrelevant operators leads to finite spatial correlations which are also obtained.