Zero-bias conductance peak in detached flakes of...
Transcript of Zero-bias conductance peak in detached flakes of...
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)
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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 �
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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