We study odd-parity nematic superconductivity in doped topological insulators in presence of surface magnetic impurities. The peculiar surface subgap spectrum, characterized by a Majorana flatband, nodal cones and the surface states of the parent topological insulator, gives rise to an overall ferromagnetic RKKY interactions between the surface impurities. An additional coupling between the impurities and a preemptive chiral order parameter promote a surface time-reversal symmetry breaking solution at the surface of the system. We discuss the relevant scenarios and suggest to engineer surface chiral superconductivity by properly choosing magnetic adatoms with highly anisotropic exchange coupling.
The physical properties of high-$T_c$ superconductors are affected by spatial inhomogeneities introduced by impurities. In addition, superconductivity and electronic nematicity seem intertwined in these materials. To address these questions, we apply inhomogeneous cluster dynamical mean field theory to the study of superconductivity in the Hubbard model, in the presence of a repeated impurity, at zero temperature. We find that the superconducting phase is shifted slightly away from half-filling due to the presence of the impurity. This can be explained by a competition with the Mott insulating…
We study the spin-polarized spectral properties of Yu-Shiba-Rusinov resonance states induced by magnetic impurities in 2- and 3-dimensional nematic superconductors: few layer Bi$_2$Te$_3$ grown on FeTe$_{0.55}$Se$_{0.45}$ (2-dimensional) and Cu$_x$Bi$_2$Se$_3$ (3-dimensional). We focus on the relationship between pairing symmetry and the topograph of spin-polarized spectroscopy. We calculate the spin-polarized local density of states (SP LDOS) and the corresponding Fourier transformation using the $T$-matrix method for both the 2- and 3-dimensional materials. Various situations with different …
Recent experiments indicate that superconductivity in Bi$_2$Se$_3$ intercalated with Cu, Nb or Sr is nematic with rotational symmetry breaking. Motivated by this observation, we present a model study of nematic and chiral superconductivity induced by odd-parity fluctuations. We show that odd-parity fluctuations in the two-component $E_u$ representation of $D_{3d}$ crystal point group can generate attractive interaction in both the even-parity $s$-wave and odd-parity $E_u$ pairing channels, but repulsive interaction in other odd-parity pairing channels. Coulomb repulsion can suppress $s$-wave p…
We study topological excitations in two-component nematic superconductors, with a particular focus on Cu$_x$Bi$_2$Se$_3$ as a candidate material. We find that the lowest-energy topological excitations are coreless vortices: a bound state of two spatially separated half-quantum vortices. These objects are nematic Skyrmions, since they are characterized by an additional topological charge. The inter-Skyrmion forces are dipolar in this model, i.e. attractive for certain relative orientations of the Skyrmions, hence forming multi-Skyrmion bound states.
Motivated by the recent experiment indicating that superconductivity in the doped topological insulator Cu$_x$Bi$_2$Se$_3$ has an odd-parity pairing symmetry with rotational symmetry breaking, we study the general class of odd-parity superconductors with two-component order parameters in trigonal and hexagonal crystal systems. In the presence of strong spin-orbit interaction, we find two possible superconducting phases below $T_c$, a time-reversal-breaking (i.e., chiral) phase and an anisotropic (i.e., nematic) phase, and determine their relative energetics from the gap function in momentum sp…
We present a novel experimental evidence for the odd-parity nematic superconductivity in high-quality single crystals of doped topological insulator Sr$_x$Bi$_2$Se$_3$. The X-ray diffraction shows that the grown single crystals are either weakly stretched or compressed uniaxially in the basal plane along one of the crystal axis. We show that in the superconducting state, the upper critical magnetic field $H_{c2}$ has a two-fold rotational symmetry and depends on the sign of the strain: in the stretched samples, the maximum of $H_{c2}$ is achieved when the in-plane magnetic field is transverse …
In the theory of dilute magnetic impurities in superconductors, the effect of all impurity spin-components is expressed via a single magnetic scattering rate $Γ_\mathrm{m}$. In a more realistic setting, magnetic impurities are anisotropic. In this case, the spatial randomness of three spin-components of impurities gives rise to generally different scattering rates $Γ_i$ ($i=1,2,3$). We explore the effects of anisotropic magnetic impurities on the in-plane critical field in 2D superconductors. We discuss singlet, triplet and parity-mixed order parameters allowed in systems without the inversion…
It is argued that the $d_{x^2-y^2}$ superconductor exhibits the transition into $d_{x^2-y^2} + id_{xy}$ state in the presence of magnetic impurities in certain conditions. Linear coupling between impurity magnetization and the $d_{xy}$ component drives this transition. Violation of time-reversal symmetry and parity occurs spontaneously via the second order transition. In the ordered phase both impurity magnetization and $d_{xy}$ component of the order parameter develop and are proportional to each other.
A characteristic feature of Shiba impurities is the existence of a spin- and parity-changing quantum phase transition (known as "0-$π$" transition) which has been observed in scanning tunneling microscopy (STM) and transport experiments. Using the Abelian bosonization technique, here we analyze the ground-state properties and the quantum phase diagram of a classical (i.e., Ising-like) Shiba impurity. In particular, we analyze the cases of an impurity in a three- and a one-dimensional superconductor. Within the bosonization framework, the ground-state properties are determined by simple soliton…
The superconducting pairing in Sr$_2$RuO$_4$ is widely considered to be chiral $p$-wave with $\vec{d}_{\boldsymbol k} \sim (k_x + ik_y)\hat{z}$, which belongs to the $E_u$ representation of the crystalline $D_{4h}$ group. However, this superconducting order appears hard to reconcile with a number of key experiments. In this paper, based on symmetry analysis we discuss the possibility of odd-parity pairing with inherent three-dimensional (3D) character enforced by the inter-orbital interlayer coupling and the sizable spin-orbit coupling (SOC) in the material. We focus on a yet unexplored $E_u$ …
It is shown that if impurities in superfluid 3He have form of infinitely long non-magnetic strands, which are straight, parallel to each other and reflect quasi-particles specularly, the temperature of transition of liquid 3He from the normal into the polar phase coincides with that for the bulk liquid without impurities. Magnetic scattering lowers transition temperature for the polar phase in analogy with the conventional superconductors. These results are discussed in connection with the recent experimental findings.
Discovery of parity-violating chiral polar-nematic charge density wave and superconductivity in kagome metals
Beijing National Center for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Hefei National Laboratory（合肥国家实验室）；Department of Physics, Boston College（波士顿学院物理系）；Department of Applied Physics, The Hong Kong Polytechnic University（香港理工大学应用物理系）；Department of Chemistry, National University of Singapore（新加坡国立大学化学系）
CuxBi2Se3 was recently proposed as a promising candidate for time-reversal-invariant topological superconductors[1]. In this work, we argue that the unusual anisotropy of the Knight shift observed by Zheng[2], taken together with specific heat measurements, provides strong support for an unconventional odd-parity pairing in the two-dimensional E_u representation of the D3d crystal point group[1], which spontaneously breaks the three-fold rotational symmetry of the crystal, leading to a subsidiary nematic order. We predict that the spin-orbit interaction associated with hexagonal warping plays …
Due to the presence of a nontrivial three-dimensional spin-orbital entanglement, Sr$_2$RuO$_4$ may be a time-reversal invariant nematic $p$-wave superconductor with coexisting in-plane and out-of-plane pairings. Here we discuss various signatures of such a state if the out-of-plane pairing component is dominant. First, the enhancement of the superconducting $T_c$ under in-plane uniaxial strains is nearly a quadratic function of the strain, because the out-of-plane pairing lacks a linear-order coupling to the strain. Second, when the strain applies along a certain in-plane direction, the nemati…
A time-reversal (TR) invariant topological superconductor is characterized by a Kramers pair of Majorana zero-energy modes on boundaries and in a core of a TR invariant vortex. A vortex defect that preserves TR symmetry has remained primarily of theoretical interest, since typically a magnetic field, which explicitly breaks TR, needs to be applied to create vortices in superconductors. In this work, we show that an odd-parity topological superconductor with a nematic pairing order parameter can host a nematic vortex that preserves TR symmetry and binds a Majorana Kramers pair. Such a nematic s…
We consider the effects of magnetic impurities on the surface of superconducting Cu doped $Bi_{2}Se_{3}$ in the odd parity pairing phase which support topologically protected Majorana fermions surface states with linear spectrum. We show that a single magnetic impurity on the surface may induce a pair of in-gap localized bound states. The energy of the in-gap state is extremely sensitive to the orientation of the magnetic impurity due to the so-called Ising properties of Majorana fermions. The magnetic impurity induced spin-texture, which can be measured using spin sensitive STM, is calculated…
We show that the interference between scattering by impurities and by critical spin fluctuations gives rise to anisotropic transport in the Ising-nematic state of the iron pnictides. The effect is closely related to the non-Fermi liquid behavior of the resistivity near an antiferromagnetic quantum critical point. Our theory not only explains the observed sign of the resistivity anisotropy $Δρ$ in electron doped systems, but also predicts a sign change of $Δρ$ upon sufficient hole doping. Furthermore, our model naturally addresses the changes in $Δρ$ upon sample annealing and alkaline-earth sub…
We theoretically study the spectrum induced by one and two magnetic impurities near the boundary of a one-dimensional nanowire in proximity to a conventional $s$-wave superconductor and extract the ground state magnetic configuration. We show that the energies of the subgap states, supported by the magnetic impurities, are strongly affected by the boundary for distances less than the superconducting coherence length. In particular, when the impurity is moved towards the boundary, multiple quantum phase transitions periodically occur in which the parity of the superconducting condensate oscilla…
Recent experimental and theoretical studies have highlighted the possible role of a electronic nematic liquid in underdoped cuprate superconductors. We calculate, within a model of d-wave superconductor with Hubbard correlations, the spin susceptibility in the case of a small explicitly broken rotational symmetry of the underlying lattice. We then exhibit how the induced spin response asymmetry is strongly enhanced by correlations as one approaches the instability to stripe order. In the disorder-induced stripe phase, impurities become spin nematogens with a C_2 symmetric impurity resonance st…
Crystalline FeSe is known to display strong nematic order below a weak tetragonal-orthorhombic structural transition around $T_s\sim 90$K, and a superconducting transition at $T_c\sim 9K$. Recently, it was shown that electron irradiation, which creates pointlike potential scattering defects, has the surprising effect of enhancing $T_c$ while suppressing $T_s$. Here we discuss a possible scenario for such an effect, which postulates a competition between $s_\pm$ superconductivity and nematic order. The transition to the nematic state is modeled by a mean field theory of a $d$-wave Pomeranchuk i…
Recent experiments show strong evidences of nematic triplet superconductivity in doped Bi$_2$Se$_3$ and in Bi$_2$Te$_3$ thin film on a superconducting substrate, but with varying identifications of the direction of the $d$-vector of the triplet that is essential to the topology of the underlying superconductivity. Here we show that the $d$-vector can be directly visualized by scanning tunneling measurements: At subgap energies the $d$-vector is along the leading peak wave-vector in the quasi-particle-interference pattern for potential impurities, and counter-intuitively along the elongation of…
We study the problem of two local potential scatterers in a d-wave superconductor, and show how quasiparticle bound state wave functions interfere. Each single-impurity electron and hole resonance energy is in general split in the presence of a second impurity into two, corresponding to one even parity and one odd parity state. We calculate the local density of states (LDOS), and argue that scanning tunneling microscopy (STM) measurements should be capable of extracting information about the Green's function in the pure system by a systematic study of 2-impurity configurations. In some configu…
We study the physics of the Josephson effect in nematic superconductors with $E_u$ odd parity in the Ginzburg-Landau approach. Two-component vector superconducting order parameter makes this effect rather unusual. We get that the Meissner kernel has off-diagonal components. We derive current-phase relations for different configurations of the junction, crystallographic axes of the sample, and nematicity direction. We show that an anomalous Josephson Hall effect can be observed in such a system without any magnetization. That is, for definite orientations of the junction and crystal axes, a com…
Unconventional symmetry-breaking phenomena due to nontrivial order parameters attract increasing attention in strongly correlated electron systems. Here, we predict theoretically the occurrence of nanoscale spontaneous spin-current, called the spin loop-current (sLC) order, as a promising origin of the pseudogap and electronic nematicity in cuprates. We reveal that the sLC is driven by the odd-parity electron-hole condensation that are mediated by transverse spin fluctuations around the pseudogap temperature $T^*$. At the same temperature, odd-parity magnon pair condensation occurs. The sLC or…
We study the effects of random nonmagnetic impurities on superconducting transition temperature $T_c$ in a Cu-doped Bi$_2$Se$_3$, for which four types of pair potentials have been proposed. Although all the candidates belong to $s$-wave symmetry, two orbital degree of freedom in electronic structures enriches the symmetry variety of a Cooper pair such as even-orbital-parity and odd-orbital-parity. We consider realistic electronic structures of Cu-doped Bi$_2$Se$_3$ by using tight-binding Hamiltonian on a hexagonal lattice and consider effects of impurity scatterings through the self-energy of …
Unconventional superconductivity is characterized by the spontaneous symmetry breaking of the macroscopic superconducting wavefunction in addition to the gauge symmetry breaking, such as rotational-symmetry breaking with respect to the underlying crystal-lattice symmetry. Particularly, superconductivity with spontaneous rotational-symmetry breaking in the wavefunction amplitude and thus in bulk properties, not yet reported previously, is intriguing and can be termed "nematic" superconductivity in analogy to nematic liquid-crystal phases. Here, based on specific-heat measurements of the single-…
Microscopic origin of the nemato-elastic coupling and dynamics of hybridized collective nematic-phonon excitations
Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Carl Zeiss SMT GmbH（卡尔蔡司SMT有限公司）；Ariel University（阿里埃勒大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
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…
We investigate emergent odd-frequency pairs and proximity effect in nematic and chiral states of superconducting topological insulators (STIs), such as $M_x$Bi$_2$Se$_3$ ($M=$ Cu, Sr, Nb). The interplay of superconducting gap symmetry, the orbital degrees of freedom, and strong spin-orbit interaction generates a variety of odd-frequency pairs in the bulk and surface of STIs. The nematic and chiral states are the prototypes of topological superconductors with and without time-reversal symmetry, respectively. We find that the Fermi surface evolution from a closed spheroidal to an open cylindrica…
Cu$_x$Bi$_2$Se$_3$ hosts both topological surface states and bulk superconductivity. It has been identified recently as a topological superconductor (TSC) with an extraordinary nematic, i. e. C2-symmetric, superconducting state and odd-parity pairing. Here, using scanning tunneling microscopy (STM), we directly examine the response of the superconductivity of CuxBi2Se3 to magnetic field. Under out-of-plane fields, we discover elongated magnetic vortices hosting zero-bias conductance peaks consistent with the Majorana bound states expected in a TSC. Under in-plane fields, the average supercondu…
Paramagnetic effects are shown to result in the appearance of a triplet component of order parameter in a vortex phase of a d-wave superconductor in the absence of impurities. This component, which breaks both parity and time-reversal symmetries of Cooper pairs, is expected to be of the order of unity in a number of modern superconductors such as organic, high-Tc, and some others. A generic phase diagram of such type-IV superconductors, which are singlet ones at H=0 and characterized by singlet-triplet mixed Copper pairs with broken time-reversal symmetry in a vortex phase, is discussed.
Recent experimental evidences point to rotation symmetry breaking superconductivity in doped Bi$_2$Se$_3$, where the relevant order parameter belongs to a two-component odd-parity representation $E_u$ of the crystal point group. The $E_u$ channel admits two possible phases, the chiral phase, that breaks time-reversal symmetry, and nematic phase, that well explains the reported rotation symmetry breaking. In weakly anisotropic three-dimensional systems the nematic phase is the stable one. We study the stability of the nematic phase versus the chiral phase as a function of the anisotropy of the …
We present resistivity and magnetization measurements on proton-irradiated crystals demonstrating that the superconducting state in the doped topological superconductor Nb$_x$Bi$_2$Se$_3$ (x = 0.25) is surprisingly robust against disorder-induced electron scattering. The superconducting transition temperature $T_c$ decreases without indication of saturation with increasing defect concentration, and the corresponding scattering rates far surpass expectations based on conventional theory. The low-temperature variation of the London penetration depth $Δλ(T)$ follows a power law ($Δλ(T)\sim T^2$) …
We clarify topology of $^3P_2$ superfluids which are expected to be realized in the inner cores of neutron stars and cubic odd-parity superconductors. $^3P_2$ phases include uniaxial/biaxial nematic phases and nonunitary ferromagnetic and cyclic phases. We here show that all the phases are accompanied by different types of topologically protected gapless fermions: Surface Majorana fermions in nematic phases and a quartet of (single) itinerant Majorana fermions in the cyclic (ferromagnetic) phase. Using the superfluid Fermi liquid theory, we also demonstrate that dihedral-two and -four biaxial …
Superconductors with noncentrosymmetric crystal structures such as Li2T3B(T:Pd,Pt) have been the focus of in-depth research with their parity mixing nature. In this study, we focused our research on non-magnetic impurity effect in Li2T3B (T: Pd, Pt). The nature of the pair breaking by non-magnetic impurity in the parity mixing superconducting state is still unclear. We prepared different quality samples of Li2Pd3B and Li2Pt3B by changing conditions in synthesizing, and sample qualities were estimated by residual resistivity. Spin singlet dominant superconductor Li2Pd3B exhibits the weak Tc sup…
If the topological insulator Bi$_{2}$Se$_{3}$ is doped with electrons, superconductivity with $T_{\rm c}\approx3-4\:{\rm K}$ emerges for a low density of carriers ($n\approx10^{20}{\rm cm}^{-3}$) and with a small ratio of the superconducting coherence length and Fermi wave length: $ξ/λ_{F}\approx2\cdots4$. These values make fluctuations of the superconducting order parameter increasingly important, to the extend that the $T_{c}$-value is surprisingly large. Strong spin-orbit interaction led to the proposal of an odd-parity pairing state. This begs the question of the nature of the transition i…
Spin-orbit coupled superconductors are potentially interesting candidates for realizing topological and potentially non-Abelian states with Majorana Fermions. We argue that time-reversal broken spin-orbit coupled superconductors generically can be characterized as having sub-gap states that are bound to localized non-magnetic impurities. Such bound states, which are referred to as Shiba states, can be detected as sharp resonances in the tunneling spectrum of the spin-orbit coupled superconductors. The Shiba state resonance can be tuned using a gate-voltage or a magnetic field from being at the…
An anapole state that breaks inversion and time reversal symmetries with preserving translation symmetry of underlying lattice has aroused great interest as a new quantum state, but only a few candidate materials have been reported. Recently, in a spin-orbit coupled Mott insulator \SIR, the emergence of a possible hidden order phase with broken inversion symmetry has been suggested at $T_Ω$ above the Néel temperature by optical second harmonic generation measurements. Moreover, polarized neutron diffraction measurements revealed the broken time reversal symmetry below $T_Ω$, which was supporte…
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$_{2}$…
Unconventional features in superconductivity are revealed by responses to impurity scattering. We study non-magnetic impurity effects in a three-dimensional topological superconductor, focusing on an effective model (massive Dirac Hamiltonian with s-wave on-site pairing) of Copper-doped bismuth-selenium compounds. Using a self-consistent T-matrix approach for impurity scattering, we examine in-gap states in density of states. We find that the results are well characterized by a single material variable, which measures relativistic effects in the Dirac Hamiltonian. In non-relativistic regime, a…
We study the effect of strong spin-orbit coupling (SOC) on bound states induced by impurities in superconductors. The presence of spin-orbit coupling breaks the $\mathbb{SU}(2)$-spin symmetry and causes the superconducting order parameter to have generically both singlet (s-wave) and triplet (p-wave) components. We find that in the presence of SOC the spectrum of Yu-Shiba-Rusinov (YSR) states is qualitatively different in s-wave and p-wave superconductor, a fact that can be used to identify the superconducting pairing symmetry of the host system. We also predict that in the presence of SOC the…
We consider mixed symmetry superconducting phases in Dirac materials in the odd parity channel, where pseudoscalar and vector order parameters can coexist due to their similar critical temperatures when attractive interactions are of finite range. We show that the coupling of these order parameters to unordered magnetic dopants favors the condensation of novel time-reversal symmetry breaking (TRSB) phases, characterized by a condensate magnetization, rotation symmetry breaking, and simultaneous ordering of the dopant moments. We find a rich phase diagram of mixed TRSB phases characterized by p…
The low-temperature variation of the London penetration depth $λ(T)$ in the candidate topological superconductor Nb$_x$Bi$_2$Se$_3$ (x = 0.25) is reported for several crystals. The measurements were carried out by means of a tunnel-diode oscillator (TDO) technique in both field orientations ($H_{rf} \parallel$ $c$ and $H_{rf} \parallel$ $ab$ planes). All samples exhibited power law behavior at low temperatures ($Δλ\sim T^2$) clearly indicating the presence of point nodes in the superconducting order parameter. The results presented here are consistent with a nematic odd-parity spin-triplet $E_…
A rare combination of strong spin-orbit coupling and electron-electron correlations makes the iridate Mott insulator Sr$_2$IrO$_4$ a promising host for novel electronic phases of matter. The resemblance of its crystallographic, magnetic and electronic structures to La$_2$CuO$_4$, as well as the emergence upon doping of a pseudogap region and a low temperature $d$-wave gap, has particularly strengthened analogies to cuprate high-$T_c$ superconductors. However, unlike the cuprate phase diagram that features a plethora of broken symmetry phases in a pseudogap region that include charge density wa…
We study theoretically the effects of random nonmagnetic impurities on the superconducting transition temperature $T_c$ in a two-band superconductor characterized by an equal-time s-wave interband pairing order parameter. The Fermi-Dirac statistics of electrons allows a spin-triplet s-wave pairing order as well as a spin-singlet s-wave order parameter due to the two-band degree of freedom. In a spin-singlet superconductor, $T_c$ is insensitive to the impurity concentration when we estimate the self-energy due to the random impurity potential within the Born approximation. On the other hand in …
The impact of superconducting correlations on localized electronic states is important for a wide range of experiments in fundamental and applied superconductivity (SC). This includes scanning tunneling microscopy of atomic impurities at the surface of superconductors, as well as superconducting-ion-chip spectroscopy of neutral ions and Rydberg states. Moreover, atom-like centers close to the surface are currently believed to be the main source of noise and decoherence in qubits based on superconducting devices. The proximity effect is known to dress atomic orbitals in Cooper-pair-like states …
Unlike anomalous quantum Hall insulators, clean single-band chiral superconductors do not exhibit intrinsic Hall effect at the one-loop approximation. Finite ac Hall conductance was found to emerge beyond one-loop, such as with vertex corrections associated with extrinsic random impurity scatterings. In this paper, we investigate the effect of impurities embedded in single-band chiral superconductors in a superlattice pattern, instead of in random distributions. The impurity-induced Bogoliubov quasiparticle bound states hybridize to form subgap bands, constituting an emergent low-energy effect…
We investigate a chiral d-density wave (CDDW) mean field Hamiltonian in momentum space, which also includes the in-plane hopping anisotropy parameter e, for the under-doped YBCO to explore the possibility of quantum oscillations (QO) in the specific heat in the presence of a changing magnetic field (B). The inclusion is motivated by the experimental signature of nematic order found in cuprates in neutron scattering experiments of Hinkov et al. (see Ref.[10]). We obtain the Fermi surface topologies, without and with magnetic field background, including the elastic scattering by impurities in th…
Sr$_x$Bi$_2$Se$_3$ and the related compounds Cu$_x$Bi$_2$Se$_3$ and Nb$_x$Bi$_2$Se$_3$ have attracted considerable interest, as these materials may be realizations of unconventional topological superconductors. Superconductivity with T$_c$ ~ 3 K in Sr$_x$Bi$_2$Se$_3$ arises upon intercalation of Sr into the layered topological insulator Bi$_2$Se$_3$. Here we elucidate the anisotropy of the normal and superconducting state of Sr$_{0.1}$Bi$_2$Se$_3$ with angular dependent magnetotransport and thermodynamic measurements. High resolution x-ray diffraction studies underline the high crystalline qua…
