S. Heun

NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore,

Pisa, Italy

Dephasing in strongly anisotropic

black phosphorous

S. Roddaro

M. Peruzzini

T. Szkopek

S. Xiang

G. Gervais

M. Serrano-Ruiz

F. Telesio

V. Tayari

A. Ienco

N. Hemsworth

M. Caporali

Phosphorus

Each P atom has 5 outer shell electrons in 3p

orbitals (sp3)

1669

Symbolic representation of the Philosopher’s

stone. Elias Ashmole's Theatrum Chemicum

Brittanicum (1652)

“Lapis Philosphicus” from a manuscript

(N° 416) by Sir Isaac Newton.

Particular from the

Alchemist’s

laboratory (1570 ca.), by

Giovanni Stradano for the

“Studiolo” of Francesco I

Medici, Florence)

1669 Hennig Brand(t) (1630 – 1692) alchemist in Hamburg discovered elemental phosphorus while searching for the Philosopher’s stone

Partington`s Text Book of Inorganic Chemistry 1946

Retort (XVIII Century)

“The Discovery of Phosphorus”

by the English painter,

Joseph Wright (1734-1797)

1669 Hennig Brand(t)

alchemist in Hamburg discovered the

“Phosphorus mirabilis” while searching for the

Philosopher’s Stone

How can White Phosphorus be produced from Urine?

A human adult contains

ca. 0.7 kg ”P” Urine contains

about 1-3 g/day of “P”

From 1000 liters of rotted urine

Brand(t) got about 55 g of Φωσφόρος

Phosphorus

Orthorhombic black Phosphorus (bP or o-P): most

stable and least reactive allotrope of the

phosphorus element

F. Bachhuber et al., Angew. Chem. Int. Ed. 53 (2014) 11629

Phosphorus

F. Bachhuber et al., Angew. Chem. Int. Ed. 53 (2014) 11629

White P

Phosphorus

F. Bachhuber et al., Angew. Chem. Int. Ed. 53 (2014) 11629

White P Black P

Phosphorus

F. Bachhuber et al., Angew. Chem. Int. Ed. 53 (2014) 11629

White P Black P

Red P (amorphous)

Phosphorus

F. Bachhuber et al., Angew. Chem. Int. Ed. 53 (2014) 11629

White P Black P

Red P (amorphous)

Violet P

monoclinic, m-P

violet Hittorf’s P

Phosphorus

Wikipedia

bP crystallographic structure

Layered structure with orthorhombic symmetry

X. Ling et al., PNAS 112 (2015) 4523

P-P (A-B) = 2.224 Å

P-P (B-C) = 2.244 Å

Top view: hexagonal structure

Unit

cell

bP crystallographic structure Red: 3 covalent s-bonds with

neighboring P atoms.

Blue: Out-of-plane lone pair orbital

Rediscovery of black phosphorus

1914: First successful synthesis (Bridgman)

1953 (Keyes) and 1963 (Warschauer): p-type

semiconductor

1983 (Narita): n-type doping by Te

High hole mobility: 64,000 cm2/Vs @ 20 K

In-plane anisotropy

A. Morita, Appl. Phys. A 39 (1986) 227

Rediscovery of black phosphorus

1914: First successful synthesis (Bridgman)

1953 (Keyes) and 1963 (Warschauer): p-type

semiconductor

1983 (Narita): n-type doping by Te

High hole mobility: 64,000 cm2/Vs @ 20 K

In-plane anisotropy

2014: First publications on bP layered thin films

New 2d materials

H. O. H. Churchill and P. Jarillo-Herrero, Nat. Nano 9 (2014) 330

New 2d materials

X. Ling et al., PNAS 112 (2015) 4523

Band gap of bP

Direct band gap of

0.3 eV in the bulk

L. Li et al., Nat. Nano 9 (2014) 372

Band gap of bP

Direct band gap of

0.3 eV in the bulk

2 eV for monolayer

R. Fei et al., Nano Lett. 14 (2014) 6393

armchair zigzag

dispersive

flat

Band gap of bP

Direct band gap of

0.3 eV in the bulk

2 eV for monolayer

Gap can be tuned by

bP thickness, from 0.3

eV (bulk) to 1 to 2 eV

(ML)

V. Tran et al., PRB 89 (2014) 235319

In-plane anisotropy

F. Xia et al., Nat. Comm. 5 (2014) 4458

Angle-dependent Raman

S. Zhang et al., ACS Nano 8 (2014) 9590

Effective mass anisotropy

R. Fei et al., Nano Lett. 14 (2014) 6393

armchair zigzag

dispersive

flat

𝑚𝑒𝑓𝑓 = ℏ2𝑑2𝐸

𝑑𝑘2

−1

Anisotropic thermal conductance

R. Fei et al., Nano Lett. 14 (2014) 6393

𝜅𝑥𝜅𝑦 ≈ 0.4

Angle-resolved DC conductivity

F. Xia et al., Nat. Comm. 5 (2014) 4458

𝜎𝑥𝜎𝑦 ≈ 1.5

Angle-resolved Hall mobility

F. Xia et al., Nat. Comm. 5 (2014) 4458

𝜇𝑥𝜇𝑦 ≈ 1.8

Aging of bP flakes

A. Castellanos-Gomez et al., 2D Mater. 1 (2014) 025001

bP Field Effect Transistor

Rxx: 1-2

Rxy: 1-3

Flake thickness:

65 ± 2 nm

N. Hemsworth et al., arXiv:1607.08677.

Transport Characterization

N. Hemsworth et al., arXiv:1607.08677.

p ~ Vg for Vg < -30 V

p = 1013 cm-2 for Vg = -30 V

Field-effect mobility µ:

300 cm2/Vs at Vg = -70 V

Negligible T-dependence in µ

for 0.26 K < T < 20 K

Weak Localization

Weak localization is a quantum effect related to coherent scattering at low temperatures.

Picture from Bergmann, Weak localization in thin films,

Physics Reports 107, 1984

Amplitude A1 Amplitude A2

Normal Diffusion Model:

P = |A1|2 + |A2|

2 = 2 |A|2

Koherent Addition:

P = |A1 + A2|2 = |2 A|2 = 4 |A|2

Weak Localization

N. Hemsworth et al., arXiv:1607.08677.

Weak Localization

S. Hikami, A. I. Larkin, and Y. Nagaoka,

Prog. Of Theor. Phys. 63 (1980) 707.

Weak Localization

N. Hemsworth et al., arXiv:1607.08677.

T = 0.26 K

Scattering Lengths

N. Hemsworth et al., arXiv:1607.08677.

𝐵𝐿2 = ℎ4𝑒

𝐿𝜙,𝑚𝑎𝑥 = 55 𝑛𝑚

Scattering Lengths

• Dephasing length vs. inelastic scattering

time: 𝐿𝜙 = 𝐷𝜏𝜙 with D diffusion coefficient

• Ballistic transport: 𝜏𝜙 ∝ 𝑇−2 or 𝐿𝜙 ∝ 𝑇−1

• Diffusive transport (𝐿0 < 𝐿𝜙):

𝜏𝜙 ∝ 𝑇−1 or 𝐿𝜙 ∝ 𝑇−12

N. Hemsworth et al., arXiv:1607.08677.

Scattering Lengths

N. Hemsworth et al., arXiv:1607.08677.

Saturation

most likely

due to

impurities.

𝐿𝜙 does not

follow a 𝑇−12

behaviour.

quasi-1D systems

Comparison with quasi-1D wire

N. Hemsworth et al., arXiv:1607.08677.

𝜏𝜙 ∝ 𝑇−2 3

𝐿𝜙 ∝ 𝑇−1 3

D. Natelson et al.:

quasi-1D:

𝐿𝜙, 𝐿𝑇 > 𝑤, 𝑡

width w

thickness t

𝐿𝜙 = 55 𝑛𝑚

thermal length:

𝐿𝑇 = ℏ𝐷𝑘𝐵𝑇

= 10 – 60 nm

Conclusions

• Weak localization oberved in a bP FET

• Excellent agreement with HLN model

• Dephasing length 𝐿𝜙 reaches 55 nm

• T-dependence of 𝐿𝜙 close to quasi-1D

• We attribute this to puckered bP structure

N. Hemsworth et al., arXiv:1607.08677.

Funding