Nanomaterials of large surface area and aspect ratio are included in the family of two dimensional (2D) materials. Specifically, 2D materials consist of isolated layered structures, from a monolayer up to a few layers thickness. Here, the atoms are bonded by ionic or covalent bonds in the plane direction to form atomic layers, and those atomic layers are weakly held via van der Waals forces. Figure 1.1 shows the molecular structures of a few 2D materials. Generally, for research purposes, 2D materials are artificially derived from bulk crystals using exfoliation techniques, such as mechanical exfoliation, ultrasonic exfoliation, etc. However, many other methods such as chemical solution based synthesis, chemical etching, chemical vapor deposition, laser thinning, etc., are also available for the large area synthesis of mono or few layer thicknesses.¹  Nowadays, even for the synthesis of 2D organic crystals, many methods are available, such as floating-coffee-ring, vapor deposition, layer-by-layer deposition, self-assembly, Langmuir–Blodgett, spin-coating, patterned growth, etc.²  Figure 1.2 summarizes the some existing techniques for the growth of 2D materials including inorganic and organic materials.

The early discovered graphene^3,4  and thereafter, transition metal dichalcogenides (TMDs),^5–7  broadly opened up the novel scope of new generation 2D materials. Nowadays, the exploration of a big family of 2D semiconductors including black phosphorus (BP),^8,9  group IV monochalcogenides (MNs) such as GeS, GeSe, SnS, SnSe etc.,^10–12  main group element compounds (MECs) such as InSe, In₂Se₃, Sb₂Se₃, Sb₂O₃, Bi₂O_3, Bi₂S₃, SnP₃, etc.,^13–19  Xenes including silicene, germanene, stanene, etc.,²⁰  perovskites,²¹  and various 2D organic materials such as dioctylbenzothienobenzothiophene (C₈-BTBT), pentacene, etc.,^2,22,23  have hugely extended the technological scope of 2D materials.

Lower dielectric screening and stronger coulomb interactions within lower dimensional material systems lead to the generation of robust many-body systems in such atomically thin 2D nanomaterials,^4,6  which furthermore form the high order quasi-particles species.^7,8  The degree of interaction of quasi-particle systems is expressed in term of “binding energy”. In fact, the binding energy in 2D nanomaterials defines the extent of interaction between fundamental quasi-particles. The high binding energy quasi-particles including excitons (electron and hole pair), trions (charged excitons) and biexcitons (combination of two-excitons or exciton and trions) have been experimentally validated.^12,24  The binding energies of excitons and trions are determined in the range 400–550 and 20–34 meV, respectively, in TMD monolayers.^25–27  Such high binding energy quasi-particles can be suitably applied to design many advanced optical and optoelectronic devices. However, the development of much more advanced optical devices such as specific excitonic/trionic devices, polariton devices, etc., requires stable quasi-particles having even higher binding energies. Recent theoretical investigations on BP and a few MNs have shown higher binding energy of quasi-particles in comparison to TMDs. The exciton and trion binding energy of monolayer BP are found to be in the range 744–830 meV and 52–200 meV, respectively.^12,28  Furthermore, high binding energies have been estimated in monolayers ReSe₂, ReS₂, GeS and GeSe, which were found to be 870, 1070, 1200 and 400 meV, respectively.^29–32  In fact, excitons and trions in these 2D materials are confined into 1D space due to their puckered crystal lattices,^28,33,34  hence they possess anisotropy and higher binding energies. Table 1.1 demonstrates the binding energies values for various isotropic and anisotropic 2D systems. Higher binding energy excitons and trions were found in the 1D confined space of carbon nanotubes (CNTs) too, i.e., in the range 210–1100 meV, theoretically, and 36–200 meV, experimentally.^30,35–37  However, utilization of such higher binding energies of CNTs was critically limited due to their small cross-sectional area;³⁸  hence, the development of larger cross section 1D systems was continually in demand. The exploration of anisotropic 2D materials, BP and MNs provided an elegant way to solve the challenge of much higher binding energy quasi-particles left in TMDs as well as the issue of the large cross section left with CNTs for practical application. These new 2D anisotropic materials also exhibit the complete separation of exciton and trion PL peaks due to further reduction of dimensionality and dielectric screening.^7,39  Nowadays, such high binding energy quasi-particles with large cross-section are being greatly utilized in advanced optoelectronic and optical devices, specifically in exciton–polariton devices, polariton lasers, tunable LEDs, and other excitonic devices based on exciton condensation.⁴⁰ 

Similar to well-explored isotropic 2D TMDs, the large aspect ratio of 2D anisotropic materials also allows the tuning of their inherent properties by applying various engineering approaches, such as strain engineering,^41,42  dielectric screening,^43,44  defect engineering,^45,46  chemical doping,^47,48  electrostatic gating,^49,50  hybridization with nanostructures^51,52  and the configuration of heterostructures, super lattices, etc.^53–56  Considering the formation of quasi-2D excitonic systems in isotropic 2D materials,^55,56  and 1D systems in anisotropic 2D materials,^28,34,57  the formation of isotropic/anisotropic 2D heterostructures can offer particle interactions in quasi-1D and 2D states. Such interaction can efficiently manipulate the high binding energy quasi-1D particle populations, which can be tuned to high performing excitonic devices. Furthermore, such unique 2D heterostructures can open up a new range of nanotechnological applications. In particular, such material designs can be important in cancer studies,⁵⁸  energy storage applications,⁵⁹  sensing⁶⁰  and quantum computing devices.⁶¹ 

The first discovered 2D material graphene exhibited outstanding electronic, optical, thermal and mechanical properties,⁶²  and showed promising application in flexible electronics, electromagnetic absorption, energy storage devices, etc.^62–67  But the absence of a band gap in graphene limited its applications for photo detection and in digital devices.^68–70  The discovery of TMDs materials filled the technological gap that graphene left.⁷¹  TMD materials possess size-tunable band gaps,^72–74  so that they can be useful in field-effect transistors (FETs), photodetectors and solar cells.^75–77  However, graphene and TMD crystal lattices are highly symmetrical, leading to in-plane isotropic physical properties.⁷⁸  In 2014, of the anisotropic 2D materials, BP was first introduced,^79,80  which initiated intensive study of anisotropic optical properties including absorption,^79–84  Raman,^85–87  photoluminescence (PL),^88–90  and anisotropic electronic,^91–93  thermal^94,95  and mechanical⁹⁶  properties of BP. Currently, many in-plane anisotropic 2D materials ranging from semimetals such as T_d WTe₂,⁹⁷  1T′ MoTe₂,⁹⁸  ZrTe₅,⁹⁹  and TaIrTe₄,^100,101  to semiconductor group IV monochalcogenides,¹⁰²  Ta₂NiS₅,¹⁰³  GaTe,¹⁰⁴  group IVB trichalcogenides,¹⁰⁵  group IV–group V compounds,^106–114  β-GeSe₂,¹¹⁵  ReS₂,^116–118  ReSe₂,^119,120  PdSe₂^121,122  and TlSe¹²³  have been explored. Table 1.2 shows the crystal structure and fundamental parameters of presently explored anisotropic 2D materials.¹²⁴ 

Nowadays, anisotropic 2D materials have greatly attracted the scientific community. The strong anisotropy and higher binding energies in such 2D materials have hugely driven the design of several novel device applications. In particular, the two important advantages of anisotropic 2D materials are different from isotropic 2D materials; i.e. (i) much richer physics of anisotropic 2D materials such as anisotropic plasmons,¹²⁵  linear dichroism,¹²⁶  etc. and (ii) the added degrees of freedom to them for adjusting their physical properties, which initiated the designing of unique semiconductor devices to explore novel applications such as high gain digital inverters,¹²⁴  polarization sensitive photodetectors,^127–130  linearly polarized pulse generators,¹³¹  high performance thermoelectric applications,¹³²  etc.

Various 2D materials of low-crystal symmetry such as monoclinic, orthorhombic and triclinic structures show anisotropic behaviors in their many physical properties. Those materials include BP, group IV MNs (SnSe, SnS, GeSe, GeS, etc.), group IVB trichalcogenides (TiS₃, TiSe₃, ZrS₃, ZrSe₃, HfS₃, HfSe₃, etc.), low-symmetry TMDs (1T′ MoTe₂, T_d WTe₂, ReS₂ and ReSe₂), low-symmetry metal chalcogenides (ZrTe₅, Ta₂NiS₅, GaTe, β GeSe₂, etc.) and MECs (GeP, GeAs, SiP, SiAs, GeAs₂, etc.).

Of the first explored anisotropic materials, BP has an orthorhombic structure with the space group Cmca (# 64), and monolayer phosphorene has the space group Pmna (# 53).¹²⁴  Each layer of BP contains two atomic layers of a puckered lattice structure, where each P atom bonds to three neighbor P atoms at two different bond angles and bond lengths of 96.34° and 102.09°, and 2.244 Å and 2.224 Å, respectively,¹³¹  and form a distorted hexagonal structure. BP consists of two distinct in-plane directions, i.e., the armchair direction and the zigzag direction with puckered structure and ridge structure, respectively, which leads to anisotropic behavior. BP exhibits high binding energies quasi-1D excitons and trions,⁹  and thus it provides a unique 2D platform for studying the dynamics of high binding energy 1D-excitons, trions and biexcitons. It also allows robust quasiparticles even at room temperature.⁹  The highly enhanced many-body interactions in BP provides strong motivation and opportunities for the development of single-photon emitters, exciton–polariton devices, tunable light emitting diodes (LEDs) and polariton lasers.

Low-symmetry 2D TMDs materials such as 1T_d WTe₂, 1T′ MoTe₂, ReS₂ and ReSe₂ uniquely possess in-plane anisotropy. Common TMD materials such as MoS₂, WS₂, MoSe₂, WSe₂, etc. crystallize in hexagonal (2H) phases, but low symmetry TMDs present distorted octahedral (1T′ or T_d) structures. 1T_d WTe₂ has an orthorhombic structure with the space group P mn2₁ (#31) for bulk and P2_1/m (#11) for monolayer materials, while 1T′ MoTe₂ possesses a monoclinic structure and the space group P2_1/m (#11) for both bulk and monolayer. Bulk ReS₂ and ReSe₂ have triclinic symmetry and they belong to the space group P1̄ (#2).¹²⁴  Moreover, T_d WTe₂ and 1T′ MoTe₂ belong to type-II Weyl semimetals,^132,133  and may be suitable for promising spintronic applications. On the other hand, ReS₂ and ReSe₂ are semiconductors with moderate band gap, and can be appropriate for photoelectronic applications.

Group IV monochalcogenide materials, including SnSe, SnS, GeSe and GeS, consist of a puckered orthorhombic crystal structure, which causes the in-plane anisotropy in their physical properties.¹²⁴  These 2D materials belong to the Pnma (#62) D_2h¹⁶ space group.¹³⁴  This material crystallizes in double layers that are perpendicular to the direction of the largest axis of the unit cell. The unit cell contains eight atoms arranged in two adjacent double layers, and the atoms in each layer bond to their three nearest neighbor's atoms by covalent bonds of 2.441 Å forming a zigzag chain along the direction of the minor axis of the crystal.¹³⁴  In particular, this group compound consists of two elements of different electronegativity.¹³⁵  Also, odd layer number compounds belonging to this group have broken inversion symmetry, which may lead to much lower symmetry and richer physics.¹³⁵  Furthermore, theoretical studies have shown that group IV 2D monochalcogenides can exhibit giant piezoelectricity and strong ferroelectricity,^136,137  which is very distinctive from anisotropic 2D materials.

2D materials belonging to MECs have a complex layered structure, in which the d-orbitals of the elements are fully occupied, and only the electrons from S and P orbitals contribute to form the compound. Hence, these compounds are available in many forms such as MX, M₂X₃, M₃X₄, MX₂, etc., where M can be mixed oxidation states.^{13,120,138,139}  For example, indium selenide compounds belonging to this group have different stoichiometric ratios, such as InSe, In₂Se₃, In₃Se₄, In₄Se₃ and In₆Se₇. For a given stoichiometric ratio, different phase structures may also exist, such as α, β, γ, δ, and κ phases in bulk In₂Se₃, and when they turn into 2D structures, only α, β and γ phases are observed. α- and β-In₂Se₃ have tetrahedral and octahedral cages respectively, formed via packing of Se in In₂Se₃. α-In₂Se₃ and β-In₂Se₃ can be rhombohedral α/β (3R) or hexagonal α/β (2H) structures.¹⁴⁰  Combination of phase engineering and the confinement effect in these 2D materials has enriched their properties and scope of applications. For examples, monolayer β-In₂Se₃ has an indirect band structure, while monolayer α-In₂Se₃ shows direct band.^13,141  Furthermore, the continuous phase transition from Pnma to Cmcm of 2D SnSe has enriched the figure of merit value ZT up to ∼2.8.¹⁴²  The phase transition from unstable state to stable Cmcm phase state has been reported in SnSe.¹⁴³  Some 2D MECs such as Sb₂Te₃ and Bi₂Te₃ have topologically protected phases too, and they exhibit strong quantum spin Hall effect.¹⁴⁴  Thus, these 2D MECs compounds can also be well-deserving candidates for quantum computing.

Group IVB trichalcogenides include TiS₃, TiSe₃, ZrS₃, ZrSe₃, HfS₃, HfSe₃, etc., which possess a monoclinic crystal structure with the space group P2₁/m (#11).¹³⁰  The combination of one atom belonging to group IVB of the periodic table with three chalcogenide atoms creates triangular prisms, and their arrangement in a row along the zigzag direction results in quasi-one dimensional chains.¹⁴⁵  Such chains inter-connect together along the armchair direction. Among the various members belonging to this materials family, monolayer TiS₃ is a direct band gap material,¹⁴⁶  and it can be promising for future optoelectronic applications. However, detail theoretical and experimental investigations for the many other compounds belonging to this group are seriously lacking, and hence future extensive studies of this materials family are highly appealing.

2D compounds belonging to this group include ZrTe₅, Ta₂NiS₅, GaTe, GeSe₂, etc. 2D ZrTe₅ and Ta₂NiS₅ possess orthorhombic structures and belong to the space group Cmcm (# 49), while GaTe and GeSe₂ have monoclinic structures, and they are respectively allied to the space groups, C2/m (#12) and P21/c (#14).¹⁴⁷  Based on the recent progress towards the materials applications of this group, Ta₂NiS₅ has shown potential application for infrared potodetections,¹⁴⁸  fluorescence biomolecular sensing^149,150  and photoacoustic theranostics.¹⁵¹  GaTe has been used in photoelectronics for a long time.^152–154  However, extensive studies towards the various scopes of the materials of this family are limited; future study should fill this gap to broaden prospects.

2D Xenes commonly represents silicene, germanene and stanene (with X being Si, Ge, Sn, etc.). 2D Xenes include group IV atoms arranged in a honeycomb buckled lattice due to interplay of sp² and sp³ hybrid bonds.²⁰  These materials are very similar to graphene, but vary with degrees of buckling. The electronic structure of 2D Xenes can be hugely tuned with functionalization chemistry or a variety of substrates. The electronic structure of Xenes includes a wide range, from insulators to semiconductors with tunable band gaps and semi-metals, based on the substrate used, their chemical functionalization and applied strain.¹⁵⁵  Spin–orbit coupling (SOC) in silicene and germanene predicted their 2D topological insulating behavior with bulk energy gaps of about 1.5–2 and 23.9–30 meV, respectively.¹⁵⁶  Stanene owns stronger SOC, and incorporates a 2D topological insulating state with a sizeable energy gap of about 0.1 eV.^157,158  Looking ahead, theoretical studies have predicted a dozen different topological insulating states from the Xene family. Hence, 2D Xenes can enable promising nanodevices including topological field-effect transistors.

2D organic semiconductors have attracted comprehensive interest as an active component in electronics and optoelectronics. Due to their low cost, chemical synthesis versatility, easiness of processing, low weight, etc., 2D organic semiconductors possess great advantages in nanotechnological applications. The anisotropic physical property is a very important parameter to determine the device performance of 2D organic materials to a large extent. More specially, anisotropic charge-carrier mobility directly defines the quality of 2D organic devices. Hence, the particular crystal structure of 2D organic materials and their relation to the physical property is a great of research interest.^159,160  The orientation dependent field-effect mobility on a rubrene single crystal relative to the crystallographic axes has been reported.¹⁶¹  Also, several theoretical studies have presented qualitative simulation towards anisotropy in charge transport behavior in organic crystals.^162–164  Recently, much experimental attention is being paid to demonstrate anisotropic charge transfer behavior in organic single crystals.^165–167  However, the relationship of molecular and structural characteristics to the charge transport mobility, PL yield, etc., in 2D organic materials is still much less studied; hence, extended future studies are required to fully understand 2D organic material anisotropy.

Optical anisotropies generally deal with anisotropies in absorption, photoluminescence and Raman scattering phenomena. Optical absorption in 2D materials strongly relies on the electron–photon interaction, and low symmetry 2D materials particularly possess orientation dependent electronic structures, which lead to anisotropic optical absorption onto them. The band structure of these low symmetry 2D materials also has in-plane anisotropy electronic dispersion.¹²³  Towards particular anisotropic materials, BP has exhibited anisotropy in the complex dielectric function.⁹¹  Later, Xia et al. reported the orientation-dependent optical absorption of BP film (30 nm thick) in the infrared range.⁷⁹  This result showed the highest extinction of light along the armchair direction.⁷⁹  Similar absorption anisotropy was also recognized in the visible range of light.^80,128  Furthermore, the different thicknesses of BP also performed polarization-dependent absorption in the visible light range,⁸⁹  which showed stronger absorption in armchair polarization than in zigzag polarization and no evidential absorption peaks in zigzag polarization.^81,123  However, GeSe showed the opposite trend to BP; a higher absorption was observed along the zigzag direction than along the armchair direction. This showed an absorption ratio along the zigzag to armchair of up to ∼1.09, 1.26 and 3.02 at 532, 638 and 808 nm, respectively.¹⁶⁸  The different electronic distribution and the overlap of wave functions of the valence band maximum with the conduction band minimum along the armchair and zigzag directions in GeSe are attributed to such anisotropic optical absorption.¹⁶⁸  Furthermore, GeS exhibited analogic anisotropic optical absorption on sets of 1.58 eV along the armchair direction and 1.66 eV along the zigzag direction.⁵⁷  Moreover, TiS₃ exhibited a much bigger anisotropic absorption ratio compared to BP, GeS and GeSe.¹⁶⁹  Whereas the transmittance of TiS₃ has strong polarization dependence, the transmission ratio between the zigzag direction and the armchair direction can up to be 30.¹⁶⁹  Moreover, calculation showed a much stronger absorption spectra for the bulk TiS₃ with electric field along the zigzag axis than along the armchair axis. Later on, the anisotropic optical absorption was also demonstrated in triclinic ReS₂ and ReSe₂.^81,170  Polarization resolved reflection spectra for 3L ReS₂ exhibited three exciton peaks, and two peaks showed maximum absorption values at polarization angles of 15° and 50° with the zigzag axis, respectively.

Furthermore, the low symmetry and much reduced dielectric screening in anisotropic 2D materials result in anisotropic PL originating from 1D excitonic recombination. An anisotropic PL pattern was first observed in BP, which yielded highly polarized PL intensity trends despite the excitation polarization.¹⁷¹  However, the highest PL intensity ratio was achieved while the excitation polarization was along the armchair direction. Also, different thicknesses of BP, including 1L, 2L and 3L, all yielded strong polarization dependent PL.⁸⁹  After BP, monoclinic GaTe exhibited anisotropic PL; both the band edge PL emission at 1.66 eV and sub band PL emission at 1.39 eV showed polarization dependent behavior.¹⁷²  Both these PL emission intensities were maximized with the excitation polarization along the zigzag direction. Furthermore, ZrS₃ is another 2D material with a quasi-one dimensional structure that shows PL anisotropy. With polarization along the zigzag direction, PL of ZrS₃ reached its maximum intensity value.¹⁷³  Interestingly, with linear polarization along the armchair direction, the PL of ZrS₃ showed maximum intensities apart from the excitation polarization direction.¹⁷³  The small anisotropy difference in the values of effective mass may show the PL intensity of ZrS₃.⁸  Recently, anisotropic PL in few-layer triclinic ReS₂ has also been demonstrated;¹⁷⁰  maximum PL was observed at 15° and 50°, respectively, similar to its anisotropic optical absorption.

Much interestingly, in low symmetry 2D materials, Raman modes associated with the anisotropic vibrations are found to be highly polarization dependent. The mathematical equation following the Raman scattering is, l∝le_iRe_sl², where e_i, e_s and R are the unit polarization vectors of incident light, scattered light and the Raman tensor, respectively. Since Raman spectroscopy follows both electron–phonon and electron–photon interactions in an absorptive material,^80,102,174  only the imaginary parts of R are considered for the calculation. Towards the study in specific materials, Raman scattering intensities, A_g in Ta₂NiS₅ under parallel polarization configuration showed maximum intensity at 0°, with some at 180°.¹⁰¹  BP also exhibited polarization dependent Raman spectra for the modes: A$g1$, A$g2$, and B_2g in both parallel and cross-polarization configurations.⁸⁵  These materials have also shown Raman anisotropy to the wavelength of an excitation laser as well as the material thickness.^{80,85,101,175}  Such Raman anisotropy may arise due to linear dichroism and linear birefringence of the materials.^86,175  The Raman anisotropy can also be explained by quantum theory,⁸⁰  based on the anisotropy in the optical absorption. Such Raman response includes three consecutive processes; namely (i) electron excitement by incident photon, (ii) electronic transition from via electron–phonon interaction and (iii) photon emission.¹⁷⁶ 

The anisotropy in the carrier effective mass of low symmetry 2D materials results in anisotropic electronic transport properties. For the first time, the Hall measurements on bulk BP exhibited anisotropy in electronic transport that showed the highest mobility along the armchair direction.¹⁷⁷  Furthermore, BP flakes exhibited similar electronic anisotropy on their electrical conductance, which showed higher values along the armchair direction.^87,178  In bulk and few-layer BP, the calculated values of the carrier effective mass of both holes and electrons were found to be about 10 times smaller along the armchair direction than along the zigzag direction, which can result in two times higher carrier mobility along the armchair direction.⁹¹  Recently, SnS also exhibited anisotropic mobility; it was found to be about 1.7 times higher along the zigzag than along the armchair direction.¹³⁵  Such experimental observation of anisotropy in mobility was found to be consistent with the theoretically calculated value of the effective mass anisotropy.^179,180  Furthermore, ReS_2, SnSe and TiS₃ also exhibited similar anisotropic electronic behaviors.^129,181,182  30 nm thick TiS₃ exhibited the mobility along the zigzag axis to be about twice that of the value along the armchair axis. A recent observation in a 6.4 nm TiS₃ flake showed a greater anisotropic ratio of mobility of up to 7.6.¹⁶⁹  Moreover, an anisotropic conductivity ratio up to 3.9 has been observed in SnSe,¹⁸¹  and ReS₂ flakes exhibited an anisotropic mobility ratio of 3.1.¹²⁹ 

Low symmetry 2D materials possess orientation dependent phonon dispersions, which causes anisotropy in their thermal conductivities.^183,184  Thermal anisotropy in such 2D anisotropic materials can be determined by many methods including Raman thermometry,¹⁸³  thermal reflectance,^185,186  time-resolved magneto-optical Kerr effect,¹⁸⁷  etc. Towards the experimental illustration of anisotropic thermal transport, anisotropic thermal conductivity was first demonstrated in BP,¹⁸³  which delivered higher thermal conductivity along the zigzag direction. Moreover, it was observed that the decrease in thickness along both the armchair and zigzag directions leads to a decrease in the thermal conductivity due to effective boundary scattering.¹⁰⁹  Recently, many studies have demonstrated anisotropic thermal conductivity values in BP using various techniques including electro-thermal measurement,¹⁸⁴  Raman thermometry and thermal reflectance measurements.^185,186  Moreover, theoretical calculations have predicted similar anisotropic thermal behavior of BP analog group IV monochalcogenides (MNs).¹⁸⁷  The calculation predicted the anisotropy in thermal conductivity for the four MN monolayers in the order SnS < SnSe < GeSe < GeS, which are attributed to different phonon dispersions.¹⁸⁷  The largest phonon gap in the GeS monolayer, the small gap in the GeSe monolayer, and no phonon gaps in the SnSe and SnS monolayers are mainly responsible for such responsive orders of anisotropic thermal conductivity.¹⁸⁷  However, anisotropic thermal behaviors of group IV MNs requires further experimental verification. Moreover, low-symmetry TMD materials, T_d WTe₂ and ReS₂, also performed thermal anisotropy.^188,189  T_d WTe₂ flakes performed thermal conductivity 15 times higher along the in-plane direction than through the plane.¹⁸⁸  The thermal conductivity of ReS₂ reached 70 ± 18 W m⁻¹ K⁻¹ along the through plane and 50 ± 13 W m⁻¹ K⁻¹ along the transverse direction at different thicknesses flakes.¹⁸⁹ 

Furthermore, the high anisotropy in crystal structures of low symmetric 2D materials also results in mechanical anisotropy. The anisotropic mechanical strength was initially evidentially realized in mechanically exfoliated BP,¹²³  TiS₃¹⁸²  and Ta₂NiS₅¹⁰¹  flakes. The mechanical anisotropic property of BP demonstrated based on Young's modulus measurements via the AFM technique showed its value to be about twice along the zigzag direction compared to the value along the armchair direction.¹⁷⁸  Furthermore, on the basis of nanomechanical multimode resonance spectromicroscopy, the anisotropic mechanical properties of BP were demonstrated,⁹⁵  which stimulated an anisotropic factor of ∼2 in BP for elastic modulus along the zigzag rather than along the armchair direction. Moreover, tuning of the mechanical anisotropy is also possible via electrostatic gating, application of strain (∼1%), etc.⁹⁵ 

Figure 1.3 briefly summarizes the observed or calculated anisotropic properties of low symmetry 2D materials.

The electrical and optical anisotropies of low symmetry 2D materials can be suitably applied to design the next generation electronic and optoelectronic applications. In this regard, Tian et al. first introduced the neuromorphic applications of BP FETs with the utilization of its anisotropic properties,¹⁹⁰  where the post-synaptic current signals are directed along the in plane and plane through directions subject to sequential pulses. Such anisotropic electronic properties can be utilized to engineer a prototype logic device. Further, Liu et al. designed the digital inverter from anisotropic ReS₂ FETs,¹²⁹  which delivered a high gain |dV_out/dV_in| of 4.4 at V_DD = 3 V. Also, another research team, Liu et al., presented a monolithically integrated flexible complementary inverter based on BP.¹⁹¹  Interestingly, the origination of a p–n homojunction with a gain higher than unity has been realized via partial aluminum doping onto BP. Another significant application of anisotropic 2D semiconducting materials can be a photodetector. The optical anisotropy can be utilized into two ways; the first way can be to choose isotropic electrodes and polarized light and the second way can be to choose anisotropic electrodes and normal light. The first type of photodetector follows anisotropic optical absorption, while the second type utilizes anisotropic electrical transport. Towards the experimental success in an anisotropic photodetector, Yuan et al. first demonstrated a BP photodetector with a ring-shaped photocurrent collector.¹²³  Afterwards, a polarization light-sensitive BP phototransistor was introduced for infrared light at around 3.39 μm wavelength in the picowatt range.¹²⁷  More recently, polarization-sensitive photodetectors based on GeAs₂, ReS₂, GeSe and ReSe₂ have also been illustrated.^110,125,192  Cui et al. introduced Re-based dichalcogenides photodetectors, showing maximum and minimum values of photocurrent with the incident light polarized along the zigzag axis, and perpendicular to that axis.¹¹²  Later on, Lai et al. designed a self-powered polarization photodetector of type-II Weyl semimetal, TaIrTe₄,¹⁹³  to be worked in broadband wavelengths in the range 532–10.6 μm. Moreover, that photodetector can obtain an anisotropy ratio up to 1.88 for mid-infrared wavelength light of 10.6 μm. Liu et al. introduced a 2D heterostructure based polarization dependent photodiode from a ReS₂–ReSe₂ lateral heterostructure.¹⁹⁴  This heterojunction photodiode displayed an unusual linear dichroism under different growth modes. Currently, anisotropic photo detection has been reported on other materials such as b-AsP,¹⁹⁵  SnS,¹⁹⁶  Sb₂Se₃¹⁸  and GeP.¹⁰⁶ 

Moreover, formation of 2D heterostructures of anisotropic and isotropic semiconducting materials can open up the scope of novel and high performing opto-electronic devices. Usually, this type of 2D semiconducting heterostructure follows two types of band alignments including type-I and type-II.^197–199  Type-I band alignment is suitably applied to design such optical devices that supply spatially confined electrons and holes. Hence, isotropic/anisotropic 2D heterostructures following a type I band alignment can be very suitable for designing excellent performance polarization-dependent optical devices. Heterostructures of BP–WS₂ or BP–WSe₂ may be very appropriate for broad range wavelength photoemitters tunable from the visible to infrared.²⁰⁰  Furthermore, BP can offer a suitable platform for exciton–polariton devices working in infrared regime,^28,33,34,38  and layer thickness dependent direct band gaps of BP also allow flexibility in choosing a suitable emission wavelength. Moreover, isotropic/anisotropic 2D heterostructures consisting of BP and TMDs following the type-II band alignment can be suitable for amplifying the efficiency of the exciton–polariton system. Furthermore, enhanced many-body interactions in such 2D heterostructures can enhance the high binding energy 1D quasi-particle populations. Hence, such a 2D heterostructure can be an idyllic platform to obtain a high performance electronically pumped exciton–polariton laser system.

Thermoelectric devices generate electrical power based on temperature gradient.²⁰¹  The figure of merit of a thermoelectric material, ZT = S²σT/κ, defines the efficiency of such thermoelectric devices, where the parameters S, σ, T and κ represent the Seebeck coefficient, electrical conductivity, absolute temperature and thermal conductivity respectively. This thermo-electric equation indicates that the ZT value can be maximized via low thermal and high electrical conductivities. Towards a specific material based study, the monolayer BP has resulted in a strong thermal anisotropic nature; it delivered a maximum ZT value along the armchair direction. Such peculiar thermal and electrical properties of BP suggest its potential use in thermoelectric devices. Later, a highly thermoelectric anisotropy was predicated in monolayer MNs.²⁰²  Furthermore, other low-symmetry 2D materials including WTe₂^203,204  and TiS₃²⁰⁵  were also found to be potential candidates for promising thermoelectric application. Few theoretical studies have suggested a technique of strain engineering to increase the ZT value of such 2D anisotropic materials.^93,206  Hence, a novel design of 2D heterostructures consisting of isotropic and anisotropic 2D materials may also be suitable for thermoelectric applications due to the possible lattice mismatch on this type of heterostructure. Such crystal lattice mismatch may provide mutual self-strain to increase the ZT value; however, comprehensive studies are a requirement for future real life thermoelectric applications of such 2D heterostructures.

Piezoelectricity is the interconversion of electricity and mechanical force; inversion symmetry breaking in materials allows such interconversion.²⁰⁷  Reducing the dimensionality of conventional piezoelectric materials can enhance the piezoelectricity.²⁰⁸  Some specific 2D materials such as h-BN, TMDs and group III MNs have shown to be stable piezoelectric structures;^209,210  however, the piezoelectric coefficients of these materials are found to be very low; i.e. in the order of 10⁻¹⁰ C m⁻¹.^208,211  However, theoretical calculations have surprisingly estimated the giant piezoelectric effect in group-IV MNs due to their non-centrosymmetric and puckered structures.^100,212  The calculated piezoelectric coefficients of these materials are found to be in the order of 100 pm V⁻¹, which is higher (∼100 times)than many other materials including h-BN, AlN, GaN, MoS₂, etc.¹⁰⁰  Such outstanding piezoelectric values may widen opportunities for nanoscale chemicals sensing. Also, the formation of vertical 2D heterostructures from the isotropic and anisotropic materials may tailor the inherent electronic polarization of complementary material components to amplify the piezoelectric potential of material. Such designs may offer novel scopes to generate the piezoelectric response for harvesting nano energy.

Ferroelectrics are pyroelectrics, an external electric field that can tune the direction of spontaneous polarization.²¹³  Currently, ferroelectrics have extensive applications in many modern devices including field effect transistors and sensors, non-volatile memories, etc.²¹⁴  However, in traditional ferroelectric materials, the competition between the internal depolarization field and the external polarization field often ruins the ferroelectricity.^136,215  Interestingly, the first principle calculation has predicted that low-symmetric monolayer group IV MNs have strong in-plane spontaneous polarization.¹³⁶  Hence, in-plane anisotropic 2D materials may offer an opportunity to beat the challenges existing in traditional ferroelectrics. Moreover, the low switching barriers as well as high curie temperatures on such anisotropic 2D materials suggest their potential for non-volatile ferroelectric memory devices.^137,216 

The light irradiation inducing generation of strain is known as the photostrictive effect. This effect can be generalized as the phenomenon of mechanical motion in materials driven by light. Indeed, possible coupling in between the optically excited excitonic systems with ionic polar lattices in 2D semiconducting materials induces a photostrictive effect. This photostrictive effect has been illustrated in the monolayer of group IV MNs.²¹⁷  However, extensive studies of the photostrictive effect in the broader materials family have been seriously limited to date. However, earlier observations in MNs can be a strong motivation for future studies to design efficient photostrictive devices based on low symmetric anisotropic 2D materials including MNs and others. Also, the design of heterostructures of such anisotropic 2D materials may lead to an increased photostrictive effect from the increased population of excitonic density due to many-body interactions. Such 2D heterostructure can be effective to obtain highly efficient remotely switchable memory devices, light-induced actuators, etc.¹² 

Recent research progress in anisotropic 2D materials has shown their remarkable performance for energy storage. The most studied material, BP, exhibited a storage capacity of 2596 mA h g⁻¹ for Li ions,²¹⁸  and also, a reversible capacity of 433 mA h g⁻¹ was achieved by monolayer BP.²¹⁹  Furthermore, Li et al. observed an ultrafast and highly anisotropic diffusion of Li ions in monolayer BP; the anisotropy was found to be 1.6 × 10⁹ times faster along the zigzag direction in comparison with the armchair direction.²²⁰  A lower energy barrier of ∼0.09 eV for Li ion diffusion in monolayer BP²²⁰  has inspired the use of BP for energy storage purposes, but the weak binding energy of Li in BP, i.e. ∼1.9 eV, has inhibited the use of BP for real life applications. However, more recent studies have resolved the issue of weak binding energy by introducing the concept of point defects in the host BP, which increases the binding energy of Li ions in BP.¹⁸⁰  Furthermore, Kulish et al. proposed the application of BP for Na ion storage;²²¹  a theoretical study estimated that monolayer BP has a specific storage capacity of 2600 mA h g⁻¹ and an energy barrier of 0.04 eV.²²¹  Moreover, Neupane et al. sketched the possibility of much higher capacity Li and Na ion batteries by choosing BP or other anisotropic 2D MNs, including SnS, SnSe etc., hetero-structured with in-plane isotropic TMDs.¹² 

2D anisotropic materials are found to be suitable candidates for sensing applications. In a specific materials based study, BP has been shown to have exciting potential to be used as a gas sensor due to the presence of naturally existing lone pairs in phosphorus atoms in BP.²²²  Furthermore, to use BP for highly efficient chemical sensing, some additional strategies have also been proposed. For example, Zhao et al. illustrated that the introduction of ripples can increase the charge transfer phenomenon in between physio-absorbed gas molecules and BP.²¹⁹  Kistanov et al. introduced the concept of doping to improve the binding affinity of BP towards the guest gas molecules.²²³  Hence combing both ripples and doping can be very effective to deliver a highly efficient chemical gas sensor. Suitable design of a BP–TMD heterostructure is important for designing such gas sensors, where lattice mismatch can cause self-existent strain to satisfy rippling and band alignments that can cause possible doping. However, recent progress towards the application of anisotropic 2D materials for sensing applications has not been satisfactory. Hence, many future studies are seriously required for a wide class of anisotropic 2D materials and various engineering approaches should be investigated to enhance the performance.

Figure 1.4 Sketches the wide device scope of anisotropic 2D materials.

The newly explored anisotropic 2D materials family has rapidly expanded into a big family. These 2D materials are allied to the materials family of low-symmetry crystal structures including orthorhombic, monoclinic and triclinic crystals. Such low symmetry in their crystal structures causes a unique anisotropy in optical, electronic, thermal, mechanical, etc. properties. These various anisotropic natures can be useful for the various nanotechnological applications. For example, anisotropic FETs, neuromorphic devices, digital inverters, etc. in electronics and polarization-sensitive photodetectors, polariton–exciton lasers, etc., in optoelectronics. These 2D materials can be furthermore utilized in thermoelectric, piezoelectric and ferroelectric device applications. Despite the high potential for a wide variety of emerging nanotechnological uses for these 2D anisotropic materials, some challenges remain, which always drag their real life application. The anisotropic ratio of many of these 2D materials is found to be extremely low, hence that ratio must be improved to a certain extent for their practical use. In such a context, some techniques can be suitably applied to enhance their in-plane anisotropy. For example, optical anisotropy can be improved by careful engineering of phonon polaritons with the heterostructures. Applying a gate voltage to these materials can also tune their electronic anisotropic properties. However, much research will be required to trace the effective techniques for significant improvement in the anisotropy ratio of the particular material. Addressing the long time stability concern of these materials can be another big challenge for their device applications. Many anisotropic 2D materials are found to be easily degradable in ambient atmosphere, hence action towards improving their stability can be a serious concern to be addressed. However, some attempts, such as chemical passivation or encapsulation of these materials, have been introduced in this direction, which partially increase their ambient stability, but investigating the techniques for the significant improvement in their ambient stability is seriously demanding. Furthermore, the determination of the band structures of these 2D materials with different thickness is essential for fundamental understanding as well as design effective device applications, but research on this has been seriously lacking. Moreover, the application of these 2D materials in thermoelectric, piezoelectric, ferroelectric, etc. devices are at a very early stage, hence their exploration is highly demanding. In conclusion, the uniquely inherent anisotropic physical properties of low symmetry 2D materials and further various possibilities of engineering to tune their properties have provided an important benchmark for the discovery of a series of novel nanotechnological applications in electronics, optics and optoelectronics. The unique anisotropic properties of these 2D materials can also be effectively implemented to obtain high performing thermoelectric, piezoelectric and photostrictive device applications. Indeed, these materials can revolutionize the existing technological achievements towards nano energy storage, chemical sensing, quantum computing, etc.