Quantum Monte Carlo Study of Semiconductor Artificial Graphene Nanostructures G okhan Oztarhan E. Bulut Kul Emre Okcu and A. D. G u cl u Department of Physics Izmir Institute of Technology 35430 Urla Izmir Turkey

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Quantum Monte Carlo Study of Semiconductor Artiﬁcial Graphene Nanostructures

G¨okhan ¨

Oztarhan, E. Bulut Kul, Emre Okcu, and A. D. G¨u¸cl¨u

Department of Physics, ˙

Izmir Institute of Technology, 35430 Urla, ˙

Izmir, Turkey

(Dated: October 3, 2023)

Semiconductor artiﬁcial graphene nanostructures where Hubbard model parameter U/t can be of

the order of 100, provide a highly controllable platform to study strongly correlated quantum many-

particle phases. We use accurate variational and diﬀusion Monte Carlo methods to demonstrate a

transition from antiferromagnetic to metallic phases for experimentally accessible lattice constant

a= 50 nm in terms of lattice site radius ρ, for ﬁnite sized artiﬁcial honeycomb structures nanopat-

terned on GaAs quantum wells containing up to 114 electrons. By analysing spin-spin correlation

functions for hexagonal ﬂakes with armchair edges and triangular ﬂakes with zigzag edges, we show

that edge type, geometry and charge nonuniformity aﬀect the steepness and the crossover ρvalue of

the phase transition. For triangular structures, the metal-insulator transition is accompanied with

a smoother edge polarization transition.

Keywords: artiﬁcial graphene, graphene quantum dots, quantum simulators, variational Monte Carlo, diﬀu-

sion Monte Carlo

In recent years, technological advances in photonic and

condensed matter based artiﬁcial superlattices gives us

opportunities to develop practical quantum simulators

[1–14]. These quantum simulators allow us to replicate

complex systems that are hard to fabricate and pro-

vide us with a playground to verify theoretical predic-

tions. In this respect, artiﬁcial graphene (AG) nanos-

tructures, designed by imitating the 2D honeycomb pat-

tern of graphene, have been proven to be good candi-

dates for being reliable and controllable sources for both

fabrication and investigation of many physical phenom-

ena related to Dirac fermions [13–19]. In particular, AG

nanostructures can be formed using semiconductor ma-

terials. While earlier reports on nanopatterned artiﬁ-

cial graphene on GaAs quantum well (QW) structures

found no evidence of massless Dirac fermions (MDFs),

presumably because of the relatively large lattice periods

[20–22], in recent experimental works using modulation-

doped AlGaAs/GaAs quantum wells [13, 14] shrinking

down of the lattice constant of the honeycomb array to

approximately 50 nm allowed the observation of the pre-

dicted graphene-like behavior [21, 23–25].

Observation of Dirac fermions in AG also opens up a

fresh way of studying graphene quantum dots [26] where

geometry, size and edge type is expected to give rise

to several physical properties such as bandgap opening

[27], edge magnetization [28–30] and optical control [31].

However, the fabrication and reliability issues such as

edge reconstruction or presence of impurities, make it

harder to observe interesting phenomena predicted to

occur in nanostructured graphene. Semiconductor AG

nanostructures, on the other hand, oﬀer several advan-

tages such as tunability of system parameters including

lattice constant, site radius and potential depth, which,

in turn, allow to control electron-electron interactions

and tunneling strength between sites, in particular Hub-

bard parameter U/t. In experimental structures with

lattice constant a= 50 nm [14], U/t can be as high as

350 (as we will argue below) i.e. two orders of magni-

tude larger than the critical value for antiferromagnetic

Mott transition predicted by calculations based on Hub-

bard model for honeycomb lattice [32–35]. Moreover, un-

like in real graphene, long range electron repulsion does

not cancel the attraction of the artiﬁcial conﬁning po-

tential in AG even near charge neutrality. For such large

and long-ranged electron interactions, a non-perturbative

many-body approach is desirable for careful treatment of

correlation eﬀects.

Earlier theoretical work on electron interaction eﬀects

in semiconductor AG nanostructures based on density

functional theory (DFT) showed that Dirac bands were

stable against interactions [23, 24] which was also con-

ﬁrmed using path integral Monte Carlo calculations [25].

However, recent calculations using Hartree-Fock and ex-

act diagonalization approaches for a triangular zigzag ge-

ometry with a= 12.5−15 nm show that a transition from

antiferromagnetic (AF) insulator to metallic phases oc-

curs, pointing to the importance of electron interactions

[36].

In this work, we use continuum variational Monte

Carlo (VMC) and diﬀusion Monte Carlo (DMC) methods

for non-perturbative and accurate treatment of many-

body correlations within the ﬁxed-node approximation

to study GaAs based AG nanostructures. First, we con-

sider an hexagonal armchair geometry which serves as a

bridge between the ﬁnite-size samples and bulk graphene

[27], with lattice constant a= 50 nm following recent

experimental work [14]. We show that, a transition from

AF to metallic phase occurs, but is aﬀected by a nonuni-

form charge distribution in the sample due to ﬁnite size

eﬀects. This charge nonuniformity which is not present in

real graphene quantum dots, causes the phase transition

to be steeper and to occur at a smaller value of ρ. We

also investigate AG quantum dots with triangular zigzag

geometry and show that edge magnetization survives the

phase transition, in agreement with previous theoretical

arXiv:2210.14696v3 [cond-mat.mes-hall] 1 Oct 2023

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QuantumMonteCarloStudyofSemiconductorArtificialGrapheneNanostructuresG¨okhan¨Oztarhan,E.BulutKul,EmreOkcu,andA.D.G¨u¸cl¨uDepartmentofPhysics,˙IzmirInstituteofTechnology,35430Urla,˙Izmir,Turkey(Dated:October3,2023)SemiconductorartificialgraphenenanostructureswhereHubbardmodelparameterU/tcanbeoftheord...

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Quantum Monte Carlo Study of Semiconductor Artificial Graphene Nanostructures G okhan Oztarhan E. Bulut Kul Emre Okcu and A. D. G u cl u Department of Physics Izmir Institute of Technology 35430 Urla Izmir Turkey

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