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arXiv2018

Derivation of a Ginzburg-Landau free energy density containing mixed gradient terms of a $p+ip$ superconductor with spin-orbit coupling

A Ginzburg-Landau free energy for a superconducting chiral p-wave order parameter is derived from a two-dimensional tight binding lattice model with weak spin-orbit coupling included as a general symmetry-breaking field. Superconductivity is accounted for by a BCS-type nearest neighbor opposite-spin interaction where we project the potential onto the $p$-wave irreducible representation of the square lattice symmetry group and assume this to be the dominating order. The resulting free energy contains kinetic terms that mix components of the order parameter as well as directional gradients --- so called mixed gradient terms --- as a virtue of the symmetry of the order parameter. Spin-orbit coupling and electron-hole anisotropy lead to additional contributions to the coefficients of these terms, increasing the number of necessary phenomenological parameters by one compared to previous work, and leading to an increase in the coefficient measuring Fermi surface anisotropy for Rashba spin-orbit coupling in the continuum limit.

cond-mat.supr-con↗

arXiv2018

Spontaneous surface current in multi-component cubic superconductors with time-reversal symmetry breaking

In this work we present a comprehensive study of the spontaneous currents in time-reversal symmetry breaking (TRSB) multi-component superconductors with cubic crystalline symmetry. We argue, not limiting to cubic lattices, that spontaneous current on certain high-symmetry surfaces can exist only if the TRSB pairing simultaneously breaks a certain pair of mirror symmetries. This is shown to have exact correspondence with the Gingzburg-Landau (GL) theory and is verified by numerical Bogoliubov de-Gennes (BdG) calculations. In the course we extend the BdG to include effects of gap anisotropy and surface disorder, both of which could lead to a much suppressed current. The GL theory has been known to describe well the spontaneous current. However, we highlight a special case where it becomes less adequate, and show that a refined effective theory for low temperatures is needed. These results could shed light on the phenomenology of cubic superconductors such as U$_{1-x}$Th$_x$Be$_{13}$, the filled skutterudites PrOs$_4$Sb$_{12}$, PrPt$_4$Ge$_{12}$ and related compounds.

cond-mat.supr-con↗

arXiv2018

Majorana bound states in hybrid 2D Josephson junctions with ferromagnetic insulators

We consider a Josephson junction consisting of superconductor/ferromagnetic insulator (S/FI) bilayers as electrodes which proximizes a nearby 2D electron gas. By starting from a generic Josephson hybrid planar setup we present an exhaustive analysis of the the interplay between the superconducting and magnetic proximity effects and the conditions under which the structure undergoes transitions to a non-trivial topological phase. We address the 2D bound state problem using a general transfer matrix approach that reduces the problem to an effective 1D Hamiltonian. This allows for straightforward study of topological properties in different symmetry classes. As an example we consider a narrow channel coupled with multiple ferromagnetic superconducting fingers, and discuss how the Majorana bound states can be spatially controlled by tuning the superconducting phases. Following our approach we also show the energy spectrum, the free energy and finally the multiterminal Josephson current of the setup.

cond-mat.supr-con↗

arXiv2018

Tailoring $T_c$ by symmetry principles: The concept of Superconducting Fitness

We propose a generalization of the concept of superconducting fitness, which allows us to make statements analogous to Anderson's theorems concerning the stability of different superconducting states. This concept can be applied to complex materials with several orbital, layer, sublattice or valley degrees of freedom. The superconducting fitness parameters $F_A(\bf{k})$ and $F_C(\bf{k})$ give a direct measure of the robustness of the weak coupling instability and of the presence of detrimental terms in the Hamiltonian, respectively. These two parameters can be employed as a guide to engineer normal state Hamiltonians in order to favour or suppress superconducting order parameters with different symmetries and topological properties. To illustrate the applicability and power of this concept we study three cases: the non-centrosymmetric heavy fermion $\text{CePt}_3\text{Si}$, the hole doped iron pnictide $\text{KFe}_2\text{As}_2$ and the doped topological insulator $\text{Cu}_x\text{Bi}_2\text{Se}_3$.

cond-mat.supr-con↗

arXiv2018

Vortex lattice and vortex bound states in CsFe$_2$As$_2$ investigated by scanning tunneling microscopy/spectroscopy

We investigate the vortex lattice and vortex bound states in CsFe$_2$As$_2$ single crystals by scanning tunneling microscopy/spectroscopy (STM/STS) under various magnetic fields. A possible structural transition or crossover of vortex lattice is observed with the increase of magnetic field, i.e., the vortex lattice changes from a distorted hexagonal lattice to a distorted tetragonal one at the magnetic field near 0.5 T. It is found that a mixture of stripelike hexagonal and square vortex lattices emerges in the crossover region. The vortex bound state is also observed in the vortex center. The tunneling spectra crossing a vortex show that the bound-state peak position holds near zero bias with STM tip moving away from the vortex core center. The Fermi energy estimated from the vortex bound state energy is very small. Our investigations provide experimental information to both the vortex lattice and the vortex bound states in this iron-based superconductor.

cond-mat.supr-con↗

arXiv2018

Nodeless superconductivity in type-II Dirac semimetal PdTe2: low-temperature London penetration depth and symmetry analysis

Superconducting gap structure was probed in type-II Dirac semimetal PdTe$_2$ by measuring the London penetration depth using tunnel diode resonator technique. At low temperatures, the data for two samples are well described by weak coupling exponential fit yielding $λ(T=0)=230$~nm as the only fit parameter at a fixed $Δ(0)/T_c\approx 1.76$, and the calculated superfluid density is consistent with a fully gapped superconducting state characterized by a single gap scale. Electrical resistivity measurements for in-plane and inter-plane current directions find very low and nearly temperature-independent normal- state anisotropy. The temperature dependence of resistivity is typical for conventional phonon scattering in metals. We compare these experimental results with expectations from a detailed theoretical symmetry analysis and reduce the number of possible superconducting pairing states in PdTe$_2$ to only three nodeless candidates: a regular, topologically trivial, $s$-wave pairing, and two distinct odd-parity triplet states that both can be topologically non-trivial depending on the microscopic interactions driving the superconducting instability.

cond-mat.supr-con↗

arXiv2018

Non-Fermi liquid at the FFLO quantum critical point

When a 2D superconductor is subjected to a strong in-plane magnetic field, Zeeman polarization of the Fermi surface can give rise to inhomogeneous FFLO order with a spatially modulated gap. Further increase of the magnetic field eventually drives the system into a normal metal state. Here, we perform a renormalization group analysis of this quantum phase transition, starting from an appropriate low-energy theory recently introduced by Piazza et al. (Ref.1). We compute one-loop flow equations within the controlled dimensional regularization scheme with fixed dimension of Fermi surface, expanding in $ε= 5/2 - d$. We find a new stable non-Fermi liquid fixed point and discuss its critical properties. One of the most interesting aspects of the FFLO non-Fermi liquid scenario is that the quantum critical point is potentially naked, with the scaling regime observable down to arbitrary low temperatures. In order to study this possibility, we perform a general analysis of competing instabilities, which suggests that only charge density wave order is enhanced in the vicinity of the quantum critical point.

cond-mat.str-el↗

arXiv2018

Vibrational anomalies in AFe$_\mathbf{2}$As$_\mathbf{2}$ (A$\,=\,$Ca, Sr, and Ba) single crystals

The detailed behavior of the in-plane infrared-active vibrational modes has been determined in AFe$_2$As$_2$ (A$\,=\,$Ca, Sr, and Ba) above and below the structural and magnetic transition at $T_N=$172, 195 and 138 K, respectively. Above $T_N$, two infrared-active $E_u$ modes are observed. In all three compounds, below $T_N$ the low-frequency $E_u$ mode is observed to split into upper and lower branches; with the exception of the Ba material, the oscillator strength across the transition is conserved. In the Ca and Sr materials, the high-frequency $E_u$ mode splits into an upper and a lower branch; however, the oscillator strengths are quite different. Surprisingly, in both the Sr and Ba materials, below $T_N$ the upper branch appears be either very weak or totally absent, while the lower branch displays an anomalous increase in strength. The frequencies and atomic characters of the lattice modes at the center of the Brillouin zone have been calculated for the high-temperature phase for each of these materials. The high-frequency $E_u$ mode does not change in position or character across this series of compounds. Below $T_N$, the $E_u$ modes are predicted to split into features of roughly equal strength. We discuss the possibility that the anomalous increase in the strength of the lower branch of the high-frequency mode below $T_N$ in the Sr and Ba compounds, and the weak (silent) upper branch, may be related to the orbital ordering and a change in the bonding between the Fe and As atoms in the magnetically-ordered state.

cond-mat.str-el↗

arXiv2017

Dynamical susceptibility of a near-critical non-conserved order parameter and B2g Raman response in Fe-based superconductors

We analyze the dynamical response of a two-dimensional system of itinerant fermions coupled to a scalar boson $ϕ$, which undergoes a continuous transition towards nematic order with $d-$wave form-factor. We consider two cases: (a) when $ϕ$ is a soft collective mode of fermions near a Pomeranchuk instability, and (b) when it is an independent critical degree of freedom, such as a composite spin order parameter near an Ising-nematic transition. In both cases, the order-parameter is not a conserved quantity and the $d-$wave fermionic polarization $Π(q, Ω)$ remains finite even at $q=0$. The polarization $Π(0, Ω)$ has similar behavior in the two cases, but the relations between $Π(0, Ω)$ and the bosonic susceptibility $χ(0, Ω)$ are different, leading to different forms of $χ^{\prime \prime} (0, Ω)$, as measured by Raman scattering. We compare our results with polarization-resolved Raman data for the Fe-based superconductors FeSe$_{1-x}$S$_x$, NaFe$_{1-x}$Co$_x$As and BaFe$_2$As$_2$. We argue that the data for FeSe$_{1-x}$S$_x$ are well described within Pomeranchuk scenario, while the data for NaFe$_{1-x}$Co$_x$As and BaFe$_2$As$_2$ are better described within the "independent" scenario involving a composite spin order.

cond-mat.str-el↗

arXiv2018

Discrete lattice symmetry breaking in a two-dimensional frustrated spin-1 Heisenberg model

Spontaneous discrete symmetry breaking can be described in the framework of Projected Entangled Pair States (PEPS) by linearly superposing local tensors belonging to two (or more) symmetry classes of tensors. This is illustrated in the case of a frustrated spin-1 Heisenberg model on the square lattice, which hosts a nematic spin liquid spontaneously breaking lattice $π/2$-rotation symmetry. A superposition of SU(2)-symmetric PEPS tensors belonging to two irreducible representations of the lattice point group is shown to capture accurately the properties of the nematic phase, as shown from a comparison to Exact Diagonalisations and Density Matrix Renormalization Group results.

cond-mat.str-el↗

arXiv2011

Spectral probes of the holographic Fermi groundstate: dialing between the electron star and AdS Dirac hair

We argue that the electron star and the AdS Dirac hair solution are two limits of the free charged Fermi gas in AdS. Spectral functions of holographic duals to probe fermions in the background of electron stars have a free parameter that quantifies the number of constituent fermions that make up the charge and energy density characterizing the electron star solution. The strict electron star limit takes this number to be infinite. The Dirac hair solution is the limit where this number is unity. This is evident in the behavior of the distribution of holographically dual Fermi surfaces. As we decrease the number of constituents in a fixed electron star background the number of Fermi surfaces also decreases. An improved holographic Fermi groundstate should be a configuration that shares the qualitative properties of both limits.

hep-th↗

arXiv2012

A Holographic Chiral p_x + ip_y Superconductor

Using a string inspired model we construct gravity duals generalizing px and p_x + ip_y superconductors. Introducing a Chern-Simons coupling in the gravity side we demonstrate the ability to control which phase dominates at low temperatures, and focus on the chiral p_x + ip_y phase. We study the fermionic spectral function and establish that the behavior is rather different from the standard p-wave two-nodes model.

hep-th↗

arXiv2012

Generalized index theorem for topological superconductors with Yang-Mills-Higgs couplings

We investigate an index theorem for a Bogoliubov-de Gennes Hamiltonian (BdGH) describing a topological superconductor with Yang-Mills-Higgs couplings in arbitrary dimensions. We find that the index of the BdGH is determined solely by the asymptotic behavior of the Higgs fields and is independent of the gauge fields. It can be nonvanishing if the dimensionality of the order parameter space is equal to the spatial dimensions. In the presence of point defects there appear localized zero energy states at the defects. Consistency of the index with the existence of zero energy bound states is examined explicitly in a vortex background in two dimensions and in a monopole background in three dimensions.

hep-th↗

arXiv2013

Oscillons and oscillating kinks in the Abelian-Higgs model

We study the classical dynamics of the Abelian Higgs model employing an asymptotic multiscale expansion method, which uses the ratio of the Higgs to the gauge field amplitudes as a small parameter. We derive an effective nonlinear Schrodinger equation for the gauge field, and a linear equation for the scalar field containing the gauge field as a nonlinear source. This equation is used to predict the existence of oscillons and oscillating kinks for certain regimes of the ratio of the Higgs to the gauge field masses. Results of direct numerical simulations are found to be in very good agreement with the analytical findings, and show that the oscillons are robust, while kinks are unstable. It is also demonstrated that oscillons emerge spontaneously as a result of the onset of the modulational instability of plane wave solutions of the model. Connections of the results with the phenomenology of superconductors is discussed.

hep-th↗

arXiv2013

Magnetic-field-induced superconductivity and superfluidity of W and Z bosons: in tandem transport and kaleidoscopic vortex states

We show that in a background of a sufficiently strong magnetic field the electroweak sector of the quantum vacuum exhibits superconducting and, unexpectedly, superfluid properties due to the magnetic-field-induced condensation of, respectively, W and Z bosons. The phase transition to the "tandem" superconductor-superfluid phase -- which is weakly sensitive to the Higgs sector of the standard model -- occurs at the critical magnetic field of 10^{20} T. The superconductor-superfluid phase of the electroweak vacuum has anisotropic transport properties as both charged and neutral superflows may propagate only along the magnetic field axis. The ground state possesses an unusual "kaleidoscopic" structure made of a hexagonal lattice of superfluid vortices superimposed on a triangular lattice of superconductor vortices.

hep-ph↗

arXiv2014

A Holographic Model of Two-Band Superconductor

We construct a holographic two-band superconductor model with interband Josephson coupling. We investigate the effects the Josephson coupling has on the superconducting condensates and the critical temperature for their formation numerically, as well as analytically where possible. We calculate the AC conductivity and find it qualitatively similar to the single band superconductor. We investigate the nodal structure of our holographic two-band superconductor from the low temperature behavior of the thermal conductivity and find it nodeless.

hep-th↗

arXiv2013

Non-Abelian statistics of vortices with non-Abelian Dirac fermions

We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core, to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities, and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, a genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined non-locally by Majorana fermions located at two spatially separated vortices.

cond-mat.supr-con↗

arXiv2013

Dynamics of self-organized driven particles with competing range interaction

Non-equilibrium self-organized patterns formed by particles interacting through competing range interaction are driven over a substrate by an external force. We show that, with increasing driving force, the pre-existed static patterns evolve into dynamic patterns either via disordered phase or depinned patterns, or via the formation of non-equilibrium stripes. Strikingly, the stripes are formed either in the direction of the driving force or in the transverse direction, depending on the pinning strength. The revealed dynamical patterns are summarized in a dynamical phase diagram.

cond-mat.soft↗