Distinct Quantum States in Topological Insulator Surfaces of Nanowires and Nanoribbons of Bismuth Selenide (Bi2Se3)

Topological insulators (TIs) exhibit unconventional quantum phases that can be tuned by external quantum confinements. The geometry of the surface of 3D TIs plays a crucial role. For example, the geometrical crossover from 2D surfaces to a 1D cylinder results in a novel state with a Spin‐Berry Phase (SBP). Surface‐Enhanced Raman Scattering (SERS) with a sub‐micron spatial resolution is utilized to study the quantum‐confinement effects of quasi‐relativistic electrons along the perimeter of the circular bismuth selenide (Bi2Se3) nanowires. The presence of diameter‐dependent SERS in nanowires can be attributed to the self‐interference effect of the electronic wave‐function along the circumferential direction of the TI nanowires. Nanoribbons with rectangular cross‐section do not show this effect. Further gold nanoparticles are applied as plasmonic SERS sensors attached to the distinct topological surface states to manipulate quasi‐relativistic surface states of nanoribbons and nanowires. This technique enables to discriminate between different geometries of TI surface states and also opens a novel pathway to probe the quantum properties of topological surface states.


Introduction
3] DOI: 10.1002/admi.202301109 In the TI surface, the spin of electrons is locked perpendicular to the electrons' momentum by strong spin-orbit interaction, and it is protected by timereversal symmetry. [2,4]0] With their large surface-to-volume ratio, low-dimensional TI nanostructures are expected to exhibit significantly enhanced surface conduction [11][12][13] and also enable the control and manipulation of surface states by external stimuli. [12,14][20] For instance, morphing a 3D TI such as bismuth selenide (Bi 2 Se 3 ) into a geometry, 1D cylinder leads to a curved surface in which the particle spin is tangential and circles around the perimeter of the TI nanowire.][23] 1D subbands are formed with gaps in the electronic excitation spectrum due to quantum-self interference of the electronic wave functions around the circular perimeter.Electronic bands of the TI are spin-polarized and in curved surfaces result in a Spin Berry Phase (SBP). [15]On a curved surface with a Dirac point as found in TI nanowires, a phase shift occurs because the particle spin is restricted to the curved surface of the nanowire and, thus, picks up a -Berry phase due to a 2 rotation of the spin around the curved surface. [17]For TI nanowires, the realization of a SBP opens a small gap at the gamma point, the subbands become doubly degenerate and thereby obstruct the formation of a state at the Dirac point.This gap is useful for generating Majorana zero modes.The bandgap is closed by applying an appropriate magnetic field, which inhibits the effects of the SBP and hence plays a key role in topological quantum computing. [17,19]The Dirac excitations are sensitive to geometry, since the spin is locked to the surface orientation, and hence these excitations behave like Dirac particles in TI nanowires. [19]n contrast, in a nanoribbon with a rectangular cross-section, flat surfaces are dominant. [17]When conducting local optical measurements, the size of the probe laser spot is in the range of the width of the nanoribbon and, in particular, probes the top surface of the nanoribbon.In such experiments, the surface of a nanoribbon can be viewed as a quasi-2D surface with a size of a few hundred nanometers.This situation may differ from transport studies, where the metal electrodes are in contact with the facets of nanowires and nanoribbons.26] Transport studies on 3D TI nanowires and nanoribbons have shown the presence of AB oscillations, Altshuler-Aronov-Spivak (AAS) oscillations, and even small contributions of Shubnikovde Hass (SdH) oscillations with a period of h 2e . [16,20,27,28]These oscillations have also been observed in 2D materials, [29,30] and, therefore, could not be used to discriminate the nature of topological surfaces in nanoribbons and nanowires.Moreover, understanding the geometries of nanostructures and their effects on the electronic structure would enable us to manipulate the topological phases.It was found that the surface orientation as well as local chemical composition affects the spin texture of topological surface states. [31]For instance, the most investigated surface of layered Bi 2 Se 3 TI is the (0001) surface because of its inherent cleavage plane.It implies that in low-dimensions, surfaces other than the (0001) surface are present, [31] and there is a need to understand these surfaces.However, it is difficult to grow thin films with different crystal orientations.As shown in our previous work, hot charge carrier injection from individual gold nanoparticles attached to a surface of single TI nanoribbons results in an enhanced Raman intensity. [32]This leads to a new technique using plasmonic nanoparticles in Raman spectroscopy to unmask the geometric nature of TI surfaces of 1D materials.
In this work, we present detailed studies on the local Raman response of single Bi 2 Se 3 nanowires and nanoribbons as a function of their diameter and thickness, respectively.We use Raman scattering with sub-micron spatial resolution on single crystalline Bi 2 Se 3 TI nanowires and nanoribbons to track the geometrycontrolled changes of topological surface quantum states.
We observe the appearance of surface-enhanced Raman scattering (SERS) for nanowires with diameters below 100 nm.This is due to the large surface/volume ratio, that is, an increase in surface charge density and the formation of subbands due to quantum confinement.This effect is strongly dependent on the wire diameter and agrees with novel spin-polarized excitations within the SBP.A comparable study on nanoribbons as a function of thickness shows the absence of this effect confirming different quantum confinements in nanoribbons and nanowires.Attaching a gold nanoparticle (AuNP) onto the TI surface of a nanoribbon and to the side of a nanowire leads to plasmonic SERS factors of 5 and 1.5, respectively.Contrary to this observation, we find that a gold nanoparticle attached to the sidewalls of a nanoribbon does not have such an effect.This observation can be used to discriminate between TI surfaces of nanowire and nanoribbon geometry, and it leads to a new criterion in identifying and characterizing the TI surfaces of 1D nanostructures.

Raman Characterization of Nanowires and Nanoribbons
Bi 2 Se 3 is a layered TI material with a rhombohedral crystal structure and belongs to the space group D 5 3d (R 3m).The unit cell of Bi 2 Se 3 consists of three quintuple layers with each quintuple layer made up of five atoms with two equivalent Se atoms, two equivalent Bi atoms, and a third Se atom that are covalently bound together as shown in Figure 1c.Each quintuple layer is ≈1 nm thick and bound to neighboring quintuple layers by van der Waals forces.According to Group theory predictions, five atoms in the primitive cell of Bi 2 Se 3 have 15 zone center phonon branches and 12 optical phonon modes.The 12 optical phonon modes have 4 symmetry Raman active and 4 symmetry infrared active modes, respectively.Therefore, phonon properties can be used as sensors for the characterization of the quasi-relativistic electronic surface states due to electron -phonon interaction in Bi 2 Se 3 TI.The Raman tensors in Bi 2 Se 3 and the atomic displacements of the Raman-active modes are well known. [32]he commonly grown morphologies of Bi 2 Se 3 G1D nanostructures are nanowires (NWs) and nanoribbons (NRs) as shown in Figure 1a,b.We earlier mentioned the observation of AB oscillations originating from the surface state of G1D TI.At low energies, the degenerate subbands are formed as a result of circumferential confinement of the TI surface states.Accordingly, the nontrivial -Berry phase shows a clear dependence on the wire diameter. [31]The dispersion of the 1D subbands in circumferential confinement is a function of angular and circumferential momenta, given by [31] P where , P, k c ,  and  F are the angular momentum number, circumference of the nanostructure, circumferential momentum, Berry phase, and Fermi velocity, respectively.Due to the halfinteger shift in the -Berry phase, the electronic spectrum of 1D nanostructures is gapped [18,33] and increases with decreasing 1D circumference.The spin polarization vector in G1D TI has been discussed. [21,34]Considering the lowest energy subbands, the spin helicity is a direct consequence of the 2D surface Dirac cone, which gives rise to spin orientation in real space. [31]For a G1D nanowire, the spin-polarization vector lies along the direction tangential to its circumference as shown in Figure 1a.In G1D nanoribbons, due to its distinct facets, the spin polarization vector lies on the surface as shown in Figure 1b.The grown G1D nanostructures were characterized by scanning electron microscopy (SEM), atomic force microscopy (AFM), and highresolution transmission electron microscopy (HRTEM) as shown in the supporting information (SI).SEM, AFM, and HRTEM confirm the shape, the height, and single crystallinity/growth direction of the G1D nanostructures, respectively.Furthermore, the HRTEM in combination with energy-filtered TEM reveals a 1-2 nm thick amorphous oxide shell that protects the surface states.The stoichiometry (Bi:Se = 2:3) of the G1D nanostructures is confirmed within experimental errors by energy dispersive X-ray (EDX) studies as shown in the SI.We decorated nanowires and nanoribbons with AuNPs (selected SEM images are shown in Figure 1d,f in order to discriminate the different topological surface states in both G1D nanostructures.In Figure 1d, we attached a single AuNP on the circumference of the nanowire.In nanoribbons, the AuNPs are attached in two different facets: on the top-facet and by the side-facet as shown in Figure 1e,f, respectively. The Raman measurements as a function of nanowire diameter are shown in Figure 2. In Figure 2a, we observe two distinct phonon modes that we can assign to E 2 g and A 2 1g symmetry in line with the Raman tensor. [35]The spectra were fitted with the generalized Fano equation, [32] (Equation 2). and where Ā, y, q,  0 , Γ, g and T represent the amplitude, electronics background, ratio between imaginary and real parts of the electronic susceptibility, frequency, width of phonon line, electronphonon coupling, and electron-photon coupling, respectively. im and  re are the imaginary and real part of electronic susceptibility while A 2 is the non-resonant Raman-matrix element. [36]he measurement of the 411 nm wire and 2D flake show comparable phonon modes which agree with the stacking of the quintuple layers perpendicular to the length of the nanowire.We observe a decrease in Raman intensity, which is proportional to the nanowire diameter.The observed decrease in Raman intensity is a result of decreasing scattering volume.The signal strength of the nanowires is lost at ≈ 200 nm.In order to confirm this observation, different nanowires with diameters between 180 and 225 nm were measured.Interestingly, the intensity of the Raman signal from nanowires, with a diameter less than 100 nm, starts to increase again and peaks ≈ 60 nm.This clearly shows a crossover from a 2D to a 1D behavior.The plot of the mode difference (E 2 g -A 2 1g ) as a function of nanowire diameter is shown in Figure 2b.The dashed line is the 2D limit obtained from nanowires with diameter >200 nm.Within the 1D behavior, the mode difference changes by ∼3 cm −1 as the nanowire diameter is decreased.Figure 2c shows the plot of the intensities of the E 2 g and A 2 1g modes divided by the nanowire diameter.The intensities are normalized to the susceptibility of the 2D limit.The intensities of the E 2 g and A 2 1g modes peak at different nanowire diameters, with the E 2 g mode and A 2 1g mode peaking at ≈ 57.4 and 53.6 nm, respectively.This observation suggests a coupling of these phonons to low-energy electronic excitations, which is dependent on TI nanowire diameter.To further elucidate on this dependency, we plotted the Fano parameter q as a function of nanowire diameter (Figure 2d).The Fano parameter q results from the interference between discrete phonon states and low-energy electronic degrees of freedom. [37]he smaller the absolute value of q the stronger the effective interference between electrons and phonons.This is due to the contribution of the imaginary part of the electronic susceptibility. [32]ur results therefore show an electron-phonon interaction as the nanowire diameter is decreased.This observation can be explained partially as follows: for a nanowire, the surface charge builds up with decreasing diameter [15] and the resulting electric field can couple to the photon field in Raman scattering, thereby enhancing the Raman intensity and leading to a diameterdependent SERS effect.In general, a diameter-dependent SERS effect in semiconductor nanowires is not uncommon. [38,39]How-ever, we attribute our observation to the interaction of the optical photons with the surface charges in the subbands of the quantum-confined TI.For simplicity, we will refer to this interaction between surface charges and optical photons as surface charges.
The E 2 g and A 2 1g modes of Bi 2 Se 3 have energies of 15.6 (125.8 cm −1 ) and 20.86 meV (168.2 cm −1 ), matching the expected energy scale of the surface charge in the 1D confined surface state. [15]The largest diameter-dependent SERS effect is expected when the energy of the surface charge matches the phonon energy.Since this energy scale is two orders of magnitude smaller than our photon energy, we effectively observe a non-resonant Raman effect.Furthermore, the same surface charge that is responsible for the enhancement of the non-resonant Raman process in nanostructures also couples to the phonons and yields a renormalization of the phonon frequencies as observed in Figure 2b.
Figure 3a shows the result of our Raman study as a function of nanoribbon thickness.As in the nanowires, we can assign the two distinct phonon modes to E 2 g and A 2 1g symmetry.The spectra 1g modes as a function of nanoribbon thickness normalized to the susceptibility at 180 nm.d) Fano parameter q as a function of nanoribbon thickness.The dashed lines represent the 2D limit obtained from nanowires with diameter >200 nm.
were again fitted with the generalized Fano equation (Equation 2).We further observed a decrease in Raman intensity as the thickness of the nanoribbon decreased from 180 down to 33 nm.Unlike in nanowires, we could not observe the loss and reappearance of Raman signal as a function of nanoribbon thickness.The line-shape analysis of the Raman spectra from nanoribbons is plotted in Figure 3b,d.In Figure 3b, we show the plot of mode difference as a function of nanoribbon thickness.The graph shows that the mode difference is scattered within the 2D limit and therefore has no noticeable dependence on the nanoribbon thickness.This is evidenced in the plot of the normalized Raman susceptibility as a function of nanoribbon thickness as shown in Figure 3c.The Raman susceptibility is normalized to the susceptibility at 180 nm thickness and the plot shows similar behavior to the 2D limit.Figure 3d displays the plot of the Fano parameter q as a function of nanoribbon thickness.As indicated by the Fano parameter that is decreasing with decreasing nanowire diameter/nanoribbon thickness, we can clearly identify an enhanced electronic susceptibility as a result of thickness dependent carrier concentration.Recall that Fano parameter q mea-sures the interference between phononic states and electronic degrees of freedom.We show that the electron-phonon interaction is much stronger when measuring on thin nanoribbons.42][43] The fact that we observe strong electron-phonon interaction and no loss or appearance of thickness-normalized signal strength with reducing thickness of the nanoribbons, clearly hints at a geometric effect of the 1D nanostructures.Note that the direct consequence of the quantum confinement effect is the splitting of the surface states into subbands.There have been numerical studies and theoretical interpretations of electronic states in G1D TI nanostructures with circular and square (rectangular) cross-sections. [15,21,31]Each of these studies recognizes the existence of different surfaces (facets) in 1D nanoribbon and each surface has different electronic states.For instance, the opening of a gap at the Dirac point in the electronic states of nanoribbons is attributed to the interference of the surface states of the two faces (top and bottom interface). [44]This effect is observed when the thickness of the nanoribbon is ≤7 nm.In contrast, for 1D nanowires, the opening of the gap at the Dirac point is observed even for nanowire diameters of up to 800 nm. [15,21]This effect is a direct consequence of the spin-Berry phase.For TI materials, the electronic bands are spinpolarized, and consequently a Spin Berry Phase (SPB) is formed.
The cylindrical nanowire has one curved surface and the electron spin in such a system is constrained in the tangent plane of the nanowire.The 2 rotation of the electron spin along the curved surface, just like a closed loop, leads to a -Berry phase. [21,45]Due to the self-interference of the electronic wave functions around the cylinder perimeter, 1D energy bands with gaps in the electronic excitation spectrum are formed.In order to probe these quasi-relativistic surface electrons in G1D TI nanostructures further, we conducted a Raman study on G1D TI decorated with AuNPs.

Raman Characterization of Nanowire and Nanoribbon Decorated with AuNPs
Figure 4 shows the exemplary spectra of G1D TI nanostructures decorated with AuNPs.The red, blue, and green markers represent the spectra acquired from bare TI, TI with AuNP on the surface, and TI with AuNP at the sidewall, respectively.As mentioned earlier, the two distinct phonon modes are assigned to E 2 g and A 2 1g symmetry.The spectra were fitted with the generalized Fano equation (Equation 2).The insets in Figure 4a,b is the SEM images of nanowire and nanoribbon, respectively.The scale bar represents a length of 100 nm.For the TI nanowire (Figure 4a), the AuNP is attached at the curved surface.Note that this geometry has only one curved surface.We are comparing the Raman signal obtained from ON the AuNP to OFF the AuNP by an enhancement factor (EF) = Raman Intensity ON Raman Intensity OFF .We observe a susceptibility enhancement of 1.5 when measuring on the AuNP.For TI nanoribbons with two facets (Figure 4b), we attach an AuNP at the top surface (0001) and another AuNP at the sidewall.The susceptibility enhancement of ≈ 5.0 was observed when measuring on the AuNP attached to the top surface.Interestingly, there is no noticeable effect when measuring on the AuNP attached to the sidewall of the nanoribbon.Our observation can be explained as follows: For the lowest energy degenerate subband in G1D TI, the real space spin density is localized entirely around the nanowire circumference [31] with a pronounced 2 rotation around the nanowire perimeter.The decay of the surface plasmons in AuNP generates hot carriers and the Raman enhancement associated with this decay is referred to as the plasmonic SERS effect.[48] Injection of hot electrons into the nanowire perimeter increases the density of topological electrons and consequently, enhances the Raman scattering cross-section on the curved surface of the nanowire.As a direct consequence of different facets in nanoribbons, the real-space electron density is not distributed uniformly over the nanoribbon surface but rather localized on the facets. [31]In this case, the 2 rotation of connected TI surfaces is not evident. [31]This explains why we have different enhancement factors when the AuNP is attached at different facets in nanoribbons.The different spin-polarized subbandsplitting between nanowires and nanoribbons might well explain different enhancement factors due to hot carrier injection from AuNPs. [31]

Electron-Phonon Interaction in TI Nanostructures
Figure 5a illustrates the electron-phonon interaction in TI nanostructures.The solid horizontal black lines represent the phonon states which couple to the subbands of the TI surface states.The gray dispersion lines are the subbands of the surface states' conduction band (CB) and valence band (VB), while the black parabolic dispersion lines are associated with the bulk states' CB and VB.The red dashed line represents the Fermi energy (EF) for the bare TI and the Dirac point is represented by DP. Figure 5b,c shows the surfaces and the accompanying electronic states of TI nanowire and nanoribbon, respectively.Note the existence of two distinct types of facets and two structural degrees of freedom [31] in nanoribbons unlike in nanowires.We mentioned earlier that due to circumferential confinement of the TI surface states in nanowires, the electronic states are composed of evenly spaced degenerate subbands as depicted in Figure 5b.The accompanying bandgaps at the Dirac point are due to a non-trivial SBP which is dependent on the circumferential confinement of topological surface states.From the schematic diagram (Figure 5a), it is observed that low-energy phonons (black horizontal lines) excited by optical photons can couple to the quasi-relativistic electrons that populate the surface states (surface plasmons) of the TI (blue parabola), in contrast, low-energy phonons cannot interfere with the bulk electrons provided that the Fermi surface lies between the bulk CB and VB. [32]The coupling between the low-energy phonons and the surface plasmons in TI enhances the phonon Raman intensity.As mentioned earlier, the maximum enhancement is expected when the energy of the surface plasmons matches the phonon energy.Again, the same spin-polarized surface plasmon that is responsible for the enhancement of the Raman process interacts with the phonon and causes renormalization of the phonon frequencies.This scheme supports our observation of the coupling between low-energy phonons and the surface plasmons in TI and it is evidenced by the decrease in Raman intensity with the nanowire diameter which increases again for very thin wires (Figure 2a).

Conclusion
In summary, we have used Raman scattering to study the coupling between low-energy electronic excitations and lattice de-grees of freedom in Bi 2 Se 3 TI nanostructures.We have demonstrated a geometrical crossover of topologically protected surface state in 2D to 1D Bi 2 Se 3 TI nanostructures.Bi 2 Se 3 TI nanowires with circular cross-sections exhibit a SERS effect that is strongly dependent on the diameter of the nanowires.In such a system, the spin-polarized surface charge excitations dominate the electronic excitation spectrum.We showed that the coupling between spin-polarized 1D surface charge excitations in Bi 2 Se 3 TI nanowires are different from that in Bi 2 Se 3 TI nanoribbons.This is attributed to a difference in geometrical quantum confinement between nanowires and nanoribbons.In nanoribbons, we can differentiate two distinct surfaces.The essential role of the electron and associated spin polarization density and magnitude on each facet, [31] is seen in the different enhancement factors of a TI nanoribbon when a plasmonic AuNP is attached at either facet.Thus, Raman scattering is a powerful tool to locally probe the TI surface states in structurally distinct facets on the nanoscale.By hot carrier injection, we can occupy spin-polarized bands of TI nanowires which might prove useful for engineering advanced spintronic devices made from TI surfaces.

Experimental Section
Single crystalline Bi 2 Se 3 nanostructures (nanowires and nanoribbons) were fabricated inside a two-zone tube furnace.The furnace was equipped with a quartz tube of a diameter of 2.5 cm to increase the vapor pressure.The nanostructures were grown on 〈100〉 silicon substrates.A general approach was followed in oven synthesis [20,49,50] and with a detailed optimization study for the growth of nanowires and nanoribbons (see Supporting Information).A custom-made x, y, z -positioner micro-manipulator, with a wire shaft diameter of 10 μm, 51 mm long tungsten picoprobe tips and a point radius of ∼0.1 μm, was used to transfer the nanowires and nanoribbons to a custom-made silicon finder grid.The finder grid has 225 fields of 100 μm × 100 μm.All nanostructures were characterized individually before the Raman study.The nanostructures were decorated with a single AuNP before the Raman measurement.Detailed information on the synthesis and characterization of the AuNPs has been reported previously. [32,51]Exemplary SEM and TEM images of the studied nanostructures are shown in the Supporting Information.A custom-made piezo-controlled micro-Raman setup was used (see Supporting Information). [52,53]The measurements were conducted in a back-scattering configuration while employing the Porto configuration. [54]All measurements were carried out at room temperature.To exclude laser heating of the samples, the measurements were done with low laser power (see Supporting Information).

Figure 1 .
Figure 1.Graphical illustration of topological surfaces in Bi 2 Se 3 a) NW and b) NR.In NW, the electrons in the surface band are confined tangentially along the circumferential direction of the wire whereas in NR, electrons are moving in a 2D surface.The laser-spot with a Gaussian intensity profile (red line) is focused on a single Bi 2 Se 3 NW/NR.The spin-momentum locking is depicted via blue and red arrows.The gradient in color between the red and blue spin states shows intermediate spin states.c) Schematic illustration of the crystalline structure of Bi 2 Se 3 .The shaded area depicts one quintuple layer (QL).The shown orientation corresponds to the growth directions of the studied nanowires and nanoribbons, as confirmed exemplarily by TEM (see Supporting Information for details).d) SEM image of a Bi 2 Se 3 nanowire with a gold nanoparticle attached.The nanowire is 116 nm in diameter and the gold NP has a diameter of 137 nm.As given by the geometry of a wire, the AuNP is attached to the curved surface of the NW.e) SEM image of an AuNP (131 nm) on top of a Bi 2 Se 3 nanoribbon with a height of 83 nm and a width of 300 nm.In this configuration, the AuNP is placed on the top surface of the TI.(f) SEM image of an AuNP (120 nm) attached to the side of a Bi 2 Se 3 nanoribbon (height = 54 nm, width = 460 nm).Please note, that due to the geometrical properties of 2D surfaces of nanoribbons, e) and f) represent different surface states due to different facets.

Figure 2 .
Figure 2. a) Experimental Raman spectra of Bi 2 Se 3 nanowires with diameters ranging from 411 nm down to 42 nm as well as the spectra of reference Bi 2 Se 3 nanoflakes with a thickness of 10 nm.Vertical dashed lines represent the positions of E 2 g and A 2 1g modes in the Bi 2 Se 3 and the solid black lines represent the fit to the spectra.b) Plot of the frequency difference E 2 g -A 2 1g as a function of nanowire diameter.c) Amplitude of the Raman susceptibility of the E 2 g and A 2 1g modes as a function of nanowire diameter normalized to the susceptibility at 411 nm.A 2 1g mode (blue marker).d) Fano parameter qas a function of nanowire diameter.The dashed lines are the 2D limit obtained from nanowires with diameter >200 nm.

Figure 3 .
Figure 3. a) Experimental Raman spectra of Bi 2 Se 3 nanoribbons with thickness ranging from 180 nm down to 33 nm.The positions of E 2 g and A 2 1g modes in the Bi 2 Se 3 are represented with vertical dashed lines.The spectra were corrected for the beam spot size and the solid black lines represent the fit to the spectra.b) The plot of mode difference E 2 g -A 2 1g as a function of nanoribbon thickness.c) The Raman intensity of the E 2 g and A 21g modes as a function of nanoribbon thickness normalized to the susceptibility at 180 nm.d) Fano parameter q as a function of nanoribbon thickness.The dashed lines represent the 2D limit obtained from nanowires with diameter >200 nm.

Figure 4 .
Figure 4. Raman studies of single Bi 2 Se 3 a) nanowire and b) nanoribbon decorated with AuNPs.The insets in (a) and (b) show the SEM images of the Bi 2 Se 3 NW and NR, respectively.Each scale bar represents a length of 100 nm.The positions of E 2 g and A 2 1g modes in the Bi 2 Se 3 are represented with a vertical dashed line.The red, green, and blue markers represent the spectra acquired from Bi 2 Se 3 without AuNP, with AuNP attached at the side of the ribbon, and with AuNP attached on the surface of the nanoribbon, respectively.Note that for the nanowire, the AuNP is attached to the curved surface of the nanowire.

Figure 5 .
Figure 5. Schematic illustration of coupling between quasi-relativistic electronic states and phonons.a) The energy dispersion E as a function of momentum k showing the surface subbands.The Fermi energy (EF) is represented by the dashed horizontal red line, and the black and gray dispersions represent the conduction (CB) and the valence band (VB) of bulk and surface states of TI, respectively.The red parabola represents the populated electrons and DP is the Dirac point.b) TI nanowire showing gapped subbands as a direct consequence of the SBP.c) TI nanoribbon showing gapless Dirac cones at two different facets as indicated in lightbrown (front facet) and in gray (side facet).