Tunable spin and transport in porphyrin-graphene nanoribbon hybrids Fei GaoyRodrigo E. Mench onzAran Garcia-Lekuezand Mads Brandbygey

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Tunable spin and transport in porphyrin-graphene

nanoribbon hybrids

Fei Gao,†Rodrigo E. Mench´on,‡Aran Garcia-Lekue,∗,‡,¶and Mads Brandbyge∗,†

†Department of Physics, Technical University of Denmark, DK-2800 Kongens Lyngby,

Denmark

‡Donostia International Physics Center (DIPC), 20018 Donostia-San Sebasti´an, Spain

¶IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain

E-mail: wmbgalea@ehu.es; mabr@dtu.dk

Abstract

Recently, porphyrin units have been attached to graphene nanoribbons (Por-GNR)

enabling a multitude of possible structures. Here we report ﬁrst principles calculations

of two prototypical, experimentally feasible, Por-GNR hybrids, one of which displays

a small band gap relevant for its use as electrode in a device. Embedding a Fe atom

in the porphyrin causes spin polarization with a spin ground state S= 1. We employ

density functional theory and nonequilibrium Green’s function transport calculations

to examine a 2-terminal setup involving one Fe-Por-GNR between two metal-free, small

band gap, Por-GNR electrodes. The coupling between the Fe-dand GNR band states

results in a Fano anti-resonance feature in the spin transport close to the Fermi energy.

This feature makes transport highly sensitive to the Fe spin state. We demonstrate

how mechanical strain or chemical adsorption on the Fe give rise to a spin-crossover

to S= 1 and S= 0, respectively, directly reﬂected in a change in transport. Our

theoretical results provide a clue for the on-surface synthesis of Por-GNRs hybrids,

which can open a new avenue for carbon-based spintronics and chemical sensing.

arXiv:2210.13610v1 [cond-mat.mes-hall] 24 Oct 2022

Introduction

Graphene nanoribbons (GNRs) with extensive π-delocalized electrons have attracted atten-

tion due to their electronic properties like width-dependent band gaps, edge states and long

spin relaxation time, turning these one-dimensional (1D) materials into promising building

blocks for nanoelectronic and spintronic devices in the carbon family.1–5 One of the most

signiﬁcant pigments in nature, porphyrin, exhibits tunable spin properties in its conjugated

arrays, depending on the central metal ion and the surrounding ligand ﬁeld.6–8 Therefore,

it would be a highly appealing strategy to synthesize porphyrin-graphene nanoribbon (Por-

GNR) hybrids with well-ordered atomic arrangements and possibilities of tailoring the band

gap, topological phases, and detecting magnetic signals in transport.

During the last decade, on-surface synthesis has become a powerful technique to form

atomically precise nanostructures by linking small precursor molecules9–12 or porphyrin

building blocks13,14 in a bottom-up approach. This makes the fabrication of quasi 1D Por-

GNR hybrids feasible, avoiding problems such as random molecular placement and metal

clusters formation.15,16 Recently, several research groups have attempted to expand the syn-

thetic 1D complexes including porphyrin cores in diﬀerent ways.17,18 The structures con-

sidered so far, both in experimental and theoretical works, have mainly been porphyrin

oligomers/polymers,19 or porphyrin nanotapes,20 which lack the GNRs segments as a back-

bone. However, Mateo et al., have synthesized structures with two metal-free (H2) Pors

connected by a short GNR segment.21 This naturally poses the question of how electronic

transport takes places in GNRs with incorporated Pors, and especially spin transport for

Pors with magnetic centers.

In this letter, we propose two Por-GNRs hybrids which might be experimentally feasible

using two existing carbon-based precursor molecules22,23 and a porphyrin center. Combining

such molecular units gives rise to the straight hybrid1 and “S-shape” hybrid2 structures

shown in Fig. 1. Our ﬁrst principles calculations reveal that hybrid2 has a small electronic

band-gap (∼0.1−0.2 eV), which is highly desirable for potential spintronic devices. Em-

bedding an iron atom in the porphyrin center in both 1D nanostructures gives rise to spin

polarization with a spin ground state of S= 1. Employing the nonequilibrium Green’s

function (NEGF) formalism, we consider a 2-terminal device setup including one Fe-hybrid2

linked between two H2-hybrid2. The coupling between the electronic states of the GNR

segments and those states with matching symmetry in the Fe-porphyrin center, leads to

spin-polarized Fano anti-resonances close to the Fermi energy in the transmission. A switch-

ing of the spin-state to S= 2 can be achieved by mechanical strain, while the adsorption of a

CO molecule on top of the Fe center fully quenches the magnetism. Our work highlights the

potential of Por-GNRs as a highly tunable and ﬂexible platform for spintronics and sensing

applications.

Results and discussion

Figure 1a and b show two existing carbon-based precursor units (1,2) and the porphyrin

building block, respectively, with M representing either a metal-free (H2) or a metallized

(e.g. with a Fe atom) unit. The precursors we select here have already been synthesized and

successfully used to grow atomically precise 7-AGNRs (unit 1)24 and 13-AGNRs25 (unit 2) on

surface. In Fig 1c we show how the combination of Por with units 1 or 2 can give rise to a quasi

1D Por-GNR structure which may be repeated periodically or joined by additional “pristine”

1 or 2 units, respectively. Moreover, the diﬀerent precursors produce GNR segments of

distinct morphology, resulting in a straight-shaped hybrid1 and a “S-shaped” hybrid2. The

previous successful bottom-up synthesis of GNRs and Por-GNR connections indicates that

these proposed systems should be feasible.

The DFT optimized structures in Fig. 2a are planar for the two periodically repeated

H2-Por-GNR hybrids, and both are non-spin polarized, as seen in the band structures in

Fig. 2b. Besides, the bands shown in the left and middle panels in Fig. 2b indicate that

diﬀerent edge conformations lead to diﬀerent frontier bands and, importantly, reveal a band

gap closing in hybrid2 at the Y-point (zone-boundary). Although this result depends on the

DFT exchange functional employed, the trend is the same: the straight hybrid1 has a larger

gap of 0.75 eV for PBE and 0.9 eV for HSE06, whereas the “S-shape” hybrid2 displays a

small electronic gap of 0.1 eV for PBE and 0.25 eV for HSE06. This band-gap “closing”

is likely to be caused by the presence of wider GNR segments in hybrid2, as the band gap

of the pristine 13-AGNRs is around 1 eV larger than that of 7-AGNRs.25 The small band

gap exhibited by hybrid 2 would be highly useful for potential applications in quantum

transport nanodevices. To gain a deeper insight into the properties of the Por-GNR hybrids,

we calculate the Z2topological invariant for non-metallized hybrid1 and hybrid 2, using the

supercells shown in left and middle panels of Fig 2a. We obtain Z2= 1 for both structures,

indicating that they are both in a topologically non-trivial phase and that localized end

states at the interface to vacuum are be expected. Moreover, as shown in Fig. S1, we do

not observe any symmetry inversion when inspecting the wavefunctions of the conduction

and valence bands at Γ and Y for both Por-GNR structures, also conﬁrming that such two

hybrids belong to the same topological family.

In an attempt to realize future spintronics in these novel nanostructures, we embed an iron

atom in the porphyrin center in hybrid2 (Fe-hybrid2). This gives rise to spin polarization,

the ground state being the S= 1 solution. The atomic structure of D4hsymmetry remains

planar and the four equivalent Fe-N bonds have a length of 2 ˚

A. For comparison, we also

introduce a Fe atom into hybrid1 and the relaxed ﬂat structure has the same occupation

of Fe-3dorbitals as Fe-hybrid2 (see Fig. S2), with a slightly decrease Fe-N bond length of

1.97 ˚

A. The ground state of the isolated iron tetraphenyl porphyrin (FeTPP), which contains

the same central macrocycle, has a S= 1 ground state (3

A2g) and the occupancy of the 3d

shell is (dx2

−y2)2(dz2)2(dxz)1(dyz )1, where the last two orbitals are degenerate as a consequence

of the molecular symmetry.26,29 However, for the ground state of the hybrid2 we obtain the

Egelectronic conﬁguration, in which the 3doccupation is (dx2

−y2)2(dz2)(dxz)2(dyz )1, despite

the total spin moment being still 2 µB. It is the breaking of symmetry and the coupling

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TunablespinandtransportinporphyringraphenenanoribbonhybridsFeiGaoRyRodrigoEbMenchonRz2ranGarciaLekueRRzR{andMadsBrandbygeRyyDepartmentofPhysicsRTechnicalUniversityofDenmarkRDKc1ssKongensLyngbyRDenmarkzDonostiaInternationalPhysicsCenternDIPC-Rcss(1DonostiaSanSebastianRSpain{IKERB2SQUERBasqueFound...

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Tunable spin and transport in porphyrin-graphene nanoribbon hybrids Fei GaoyRodrigo E. Mench onzAran Garcia-Lekuezand Mads Brandbygey

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