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

Instituto de Ciencia Molecular (ICMol), Universidad de Valencia,Paterna, Spain

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

J. A. Galvis et al., Phys. Rev. B 89, 224512 (2014)

giovedì 9 ottobre 14

Transition metal dichalcogenides

Report STM measurements on single layer of 2H-TaS2

each layer : three atomic planes X - M - XM

Xlayered materials: van der Waals forces between layers

X = S, SeM = Ta, Nb metallicM = W, Mo semiconducting 2H polytype

Fermi surface has a strong Ta character

5 d orbitals from Ta2x3 p orbitals from S

strong spin-orbit

2H polytype parity symmetric

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STM measurement of surface of 2H-TaS2

scanning the bulk surface: BCS like gap

scanning the single layer surface: Zero Bias Conductance Peak

Similar results for 2H-TaSe2 J. A. Galvis et al., Phys. Rev. B 87, 094502 (2013)

not compatible with BCS theory

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Tight binding model

two Ta orbitals on a triangular lattice dx

2�y

2 dxy

H0 = �X

R,�

3X

i=1

c†R,�hicR+ai,� +H.c.

nearest-neighbour hoppingtdd�

tdd⇡

KK’

!

3!/2

3!/2

!3!/2!3!/2

kxa

kya

effective model:

two orbitals two bands � K

K0K inequivalent points in the BZ

three bands

H0k = �2

3X

i=1

hi cos(k · ai)

tdd� > tdd⇡

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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

�K0 = ��Kfavors a odd-momentum gap

tight-binding imaginary nearsest neighbour pairing

HSC = �i�X

R,↵

3X

s=±,j=1

s(�1)jc†R↵"c†R+saj ,↵# +H.c. �i

i

�i

�i

i

i

�k = 2�3X

i=1

(�1)i sin(k · ai)��k = ��k

odd-momentum gap

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Nodal odd-momentum superconductivity

Bogoliubov de Gennes Hamiltonian

k =

✓ckT ck

◆T = isyKtime-reversal operatorNambu spinor

HBdG =1

2

X

k

†kHBdG

k k

HBdGk = (H0

k � µ)⌧z

+�ksz⌧xtriplet f-wave pairing

KK’

!

+"

+"

+"

#"

#"

#"

+$ #$

+$

#$+$

#$

3!/2

3!/2

!3!/2!3!/2

kxa

kya

pocket

pocket

pocket �

K0

K �

��

nodal

six nodes: symmetry robustness

nodal gap induced by the K,K’’

�

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STM local density of states

usually the STM measures the unperturbed density of states

Bardeen theory

dI

dV/

Zd!

X

�,�

|T�|2A�(�,!)f0(! � eV )

perturbative in tunnelingunperturbed

spectral function

A�(�,!) = � 1

⇡ImG�(�,! + i0+)

local DOS

|T�|2 =X

⇢

|M�⇢|2Atip(⇢,!)

dI(r)

dV/ ⇢(eV, r) = � 1

⇡

X

�

Im G�(r, r; eV + i0+)

t0

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Effective Dirac BdG Hamiltonian

Expand BdG Hamiltonian around nodal points

✏Q

(k) 'qv2�k

2x

+ v2F

k2y

tdd� � tdd⇡

v� ' a�HBdGQ

' vF

ky

⌧z

+ v�kx⌧x

gr(✏) ' NfAc

2⇡vF v�

�2✏ ln

�

|✏| � i⇡|✏|�

retarded Green’sfunction

cutoff of the liner dispersion�

Nf = 12

6 spin-degenerates nodes

⇢(✏) ⇠ NfAc

2⇡vF v�|✏| V-shaped gap around the Fermi energy

this is not what is measured

vF ' atdd�

analogous to graphene

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Possible explanation

within the theoretical model two assumptions: nodal odd-momentum superconductivity

perturbative tip-sample coupling

simple s-wave BCS superconductivity cannot expalin a ZBCP no magnetic impurities

{

odd-momentum superconductivity strong short range interaction

Can we relax the perturbative tip-sample coupling assumption?

two gaps:pocket

pocket �

K0K � ��

nodal �{ � ⌧ �

tip-sample couplingperturbative

non-perturbative �

K0K{ tip-modified local DOS

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gsc(z) =X

k

(z �HBdGk )�1SC Green’s function

��k = ��kodd gapX

k

�k

Ek= 0

No Andreev currentanalogous to tunneling to a semiconductor

Non-perturbative tip-sample coupling

�(!) =e2

h

4⇡2t20⇢tip(! � eV )⇢sc(!)

|1� t20gtip(! � eV )gsc(!)|2differential conductance

assume point-like tunneling t0

analogous to tunneling to a graphene

t0 + +....

⌃tip(!) = t20gtip(!) ' �i⇡t20⇢tiptip self-energy

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1� ⌃tipgsc(⌦) = 0

gsc(z) = Cz ln(�iz) z = ✏/�

C =NfAc�

⇡v�vF� = t20⇢tipC effective coupling1 + i�z ln(�iz) = 0

z = ix

retarded Green’s function defined in the upper half of complex energy plane

x lnx = 1/�

Resonant behaviour

for strong coupling solution compatible with cutoff

purely imaginary resonance

broad resonance at zero energy

compatible with experimental observation

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Zero Bias Conductance Peak

the tip-sample coupling is usually perturbative

effective coupling � = Nf �

� = t20⇢tip⇢sysmicroscopic coupling

⇢sys = Ac/avF

for a large N the effective coupling can become non-perturbative

� ⌧ 1 perturbative

conductance with the full tight-binding

valid at all energies

broad ZBCP

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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

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