Zero-bias conductance peak in detached flakes of superconducting 2H-TaS2 probed by STS J. A. Galvis, L. C., I. Guillamon, S. Vieira, E. Navarro-Moratalla, E. Coronado, H. Suderow, F. Guinea Laboratorio de Bajas Temperaturas, Instituto de Ciencia de Materiales Nicolás Cabrera Universidad Autónoma de Madrid, Spain Instituto de Ciencia de Materiales de Madrid (CSIC), Madrid, Spain Instituto de Ciencia Molecular (ICMol), Universidad de Valencia,Paterna, Spain J. A. Galvis et al., Phys. Rev. B 89, 224512 (2014)
Transition metal dichalcogenides layered materials: van der Waals forces between layers each layer: three atomic planes X - M - X X M X = S, Se M = Ta, Nb metallic M = W, Mo semiconducting 2H polytype Report STM measurements on single layer of 2H-TaS2 Fermi surface has a strong Ta character 5 d orbitals from Ta 2x3 p orbitals from S strong spin-orbit 2H polytype parity symmetric
STM measurement of surface of 2H-TaS2 scanning the bulk surface: BCS like gap scanning the single layer surface: Zero Bias Conductance Peak not compatible with BCS theory Similar results for 2H-TaSe2 J. A. Galvis et al., Phys. Rev. B 87, 094502 (2013)
Tight binding model two Ta orbitals on a triangular lattice d x 2 y 2 d xy effective model: nearest-neighbour hopping t dd t dd >t dd H 0 = X R, 3X c R, h i c R+ai, +H.c. t dd i=1 3π/2 H 0 k = 2 3X h i cos(k a i ) i=1 two orbitals two bands K k y a Γ K K 0 inequivalent points in the BZ three bands 3π/2 3π/2 K k x a K 3π/2
Possible odd-momentum superconductivity Fermi surface has a strong Ta 5d character non-negligible role of Coulomb interaction Strong K, K interband scattering due to short range Coulomb repulsion favors a odd-momentum gap K 0 = K tight-binding imaginary nearsest neighbour pairing H SC = i X R, 3X s( 1) j c R " c R+sa j, # +H.c. i s=±,j=1 3X k =2 ( 1) i sin(k a i ) i=1 odd-momentum gap k = k i i i i i
Nodal odd-momentum superconductivity Bogoliubov de Gennes Hamiltonian Nambu spinor k = ck T c k H BdG = 1 2 X k k HBdG k k time-reversal operator T = is y ˆK H BdG k =(H 0 k µ) z + k s z x triplet f-wave pairing 3π/2 K K 0 pocket pocket +Δ +δ Δ δ pocket nodal k y a Δ δ Γ +δ +Δ nodal gap induced by the K,K +δ δ six nodes: symmetry robustness 3π/2 3π/2 K +Δ k x a Δ K 3π/2
STM local density of states usually the STM measures the unperturbed density of states Bardeen theory di dv / Z d! X, T 2 A (,!)f 0 (! ev ) t 0 perturbative in tunneling unperturbed spectral function local DOS T 2 = X M 2 A tip (,!) A (,!) = 1 ImG (,! + i0+ ) di(r) dv / (ev, r) = 1 X Im G (r, r; ev + i0 + )
Effective Dirac BdG Hamiltonian Expand BdG Hamiltonian around nodal points t dd t dd H BdG Q ' v F k y z + v k x x Q (k) ' q v 2 k 2 x + v 2 F k2 y v F ' at dd v ' a retarded Green sfunction g r ( ) ' N f A c 2 v F v apple 2 ln i N f = 12 cutoff of the liner dispersion 6 spin-degenerates nodes ( ) N f A c 2 v F v V-shaped gap around the Fermi energy analogous to graphene this is not what is measured
Possible explanation within the theoretical model two assumptions: { nodal odd-momentum superconductivity perturbative tip-sample coupling no magnetic impurities strong short range interaction simple s-wave BCS superconductivity cannot expalin a ZBCP odd-momentum superconductivity Can we relax the perturbative tip-sample coupling assumption? two gaps: { K K 0 pocket pocket nodal tip-sample coupling { K K 0 perturbative tip-modified non-perturbative local DOS
Non-perturbative tip-sample coupling assume point-like tunneling t 0 SC Green s function ĝ sc (z) = X k (z H BdG k ) 1 t 0 + +... odd gap k = k X k k E k =0 analogous to tunneling to a semiconductor analogous to tunneling to a graphene No Andreev current differential conductance (!) = e2 h 4 2 t 2 0 tip (! ev ) sc (!) 1 t 2 0 g tip(! ev )g sc (!) 2 tip self-energy tip (!) =t 2 0g tip (!) ' i t 2 0 tip
Resonant behaviour 1 tip g sc ( ) =0 retarded Green s function defined in the upper half of complex energy plane g sc (z) =Cz ln( iz) z = / 1+i z ln( iz) =0 = t 2 0 tip C effective coupling C = N f A c v v F z = ix purely imaginary resonance x ln x =1/ for strong coupling solution compatible with cutoff broad resonance at zero energy compatible with experimental observation
Zero Bias Conductance Peak the tip-sample coupling is usually perturbative effective coupling = N f sys = A c /av F microscopic coupling = t 2 0 tip sys 1 perturbative for a large N the effective coupling can become non-perturbative conductance with the full tight-binding valid at all energies broad ZBCP
Summary and Conclusions experimentally observed Zero Bias Conductance Peak in single layer 2H-TaS2 ZBCP found in a large area ruled out any local mechanism such as magnetic impurity non-compatible with BCS-like theory strong short range Coulomb repulsion can induce odd-parity gao at K and K nodal induced gap on the Gamma pocket perturbative STM cannot explain measurements on the Gamma pocket a weak tip-sample coupling can become non-perturbative