Small Electron Pocket Research Articles

Ultralow lattice thermal conductivity and excellent thermoelectric performance of monolayer CdGaInS4: a first-principles investigation.

Monolayer CdGaInS4 is an excellent optoelectronic material, but its thermoelectric properties remain unexplored. Through first-principles studies, we investigate the thermoelectric transport properties of monolayer CdGaInS4. The results show that the degenerate weakly dispersive valence band results in an ultrahigh Seebeck coefficient, and the small parabolic electron pockets lead to good electron mobility and conductivity. The ultralow lattice thermal conductivity is attributed to the complete decoupling and softening of the low frequency out-of-plane mode and the strong bonding anharmonicity, giving rise to significant phonon scattering. These results provide good physical descriptors for the search for and theoretical design of excellent two-dimensional thermoelectric materials, and motivate relative measurements in monolayer CdGaInS4 and its applications as a promising thermoelectric material.

Evidence of compensated semimetal with electronic correlations at charge neutrality of twisted double bilayer graphene

Recently, magic-angle twisted bilayer graphene (MATBLG) has emerged with various interaction-driven novel quantum phases at the commensurate fillings of the moiré superlattice, while the charge neutrality point (CNP) remains mostly a trivial insulator. Here, we show an emerging phase of compensated semimetallicity at the CNP of twisted double bilayer graphene (TDBLG), a close cousin of MATBLG, with signatures of electronic correlation. Using electrical and thermal transport, we find two orders of magnitude enhancement of the thermopower at magnetic fields much smaller than the extreme quantum limit, accompanied by large magnetoresistance ( ~ 2500%) at CNP, providing strong experimental evidence of compensated semimetallicity at CNP of TDBLG. Moreover, at low temperatures, we observe unusual sublinear temperature dependence of resistance. A recent theory1 predicts the formation of an excitonic metal near CNP, where small electron and hole pockets co-exist. We understand this sublinear temperature dependence in terms of critical fluctuations in this theory.

Shift of the superconducting dome induced by a conduction band of small occupancy: Enhanced d -wave pairing in the overdoped regime

Motivated by the presence of an extremely small electron pocket in the electronic band structure of infinite-layer nickelate superconductors, we systematically explore the superconducting (SC) properties of a two-dimensional Hubbard model influenced by an additional conduction band with small occupancy (dry Fermi sea). Our dynamic cluster quantum Monte Carlo calculations demonstrated the unusual impact of this additional dry metallic layer, which shifts the SC dome of the correlated Hubbard layer towards the overdoped regime, namely the $d$-wave SC can be enhanced (suppressed) in the overdoped (underdoped) regime. Simultaneously, the pseudogap crossover line shifts to the same higher doping regime as well. Our analysis revealed the interplay of the effective pairing interaction, pair-field susceptibility, and antiferromagnetic spin fluctuation in the underlying nonmonotonic physics. We postulate on the physical picture of the SC dome shift in terms of the Kondo-type electron-hole binding in the case of a dry additional conduction band. Our investigation provided valuable insights on tuning the SC properties via external dry bands.

Enhancing thermoelectric properties in TiNiSi structure-type semimetal ZrNiSi by doping

The orthorhombic TiNiSi structure-type compounds show interesting electronic structures comprising in most cases a pseudogap in the density of states and several small electron and hole pockets at the Fermi energy. These features are promising and can be exploited to test their potential as thermoelectric materials for waste heat conversion. Here, we investigate the effect of electron doping in the semimetallic member $\mathrm{ZrNiSi}$ of this family. We show that by doping with Sb for Si in $\mathrm{ZrNiSi}, S$ and $\ensuremath{\sigma}$ can both be increased simultaneously for initial Sb doping defying the oppositely directed trend commonly observed in most materials. In the doped samples, $\ensuremath{\sigma}$ at $300\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ increases from $1000\phantom{\rule{0.28em}{0ex}}\mathrm{S}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ to as high as $2500\phantom{\rule{0.28em}{0ex}}\mathrm{S}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$; at the same time, the peak value of $S$, which is $\ensuremath{-}20\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{V}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ in $\mathrm{ZrNiSi}$, increases by more than a factor of two. The simultaneous enhancement of $\ensuremath{\sigma}$ and $S$ has been explained using the first-principles density functional theory based band structure calculations. The as-cast (i.e., unannealed) ${\mathrm{ZrNiSi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$ samples show phase segregation due to a spinodal-type decomposition with two coexisting TiNiSi structure-type phases with different Sb/Si ratios. The thermal conductivity ($\ensuremath{\kappa}$) in the doped samples drops significantly from $12\phantom{\rule{0.28em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ ($x=0$) to nearly $2\phantom{\rule{0.28em}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ ($x=0.2$) at 300 K. As a result, the peak thermoelectric figure of merit ($zT$) increases from 0.005 $(x=0)$ to 0.023 $(x=0.2)$. Further enhancement in $zT$ is obtained by codoping of Hf (Zr site) and Sb (Si site), which improves the phase stability and chemical homogeneity while keeping the thermal conductivity still very low due to Zr-Hf point mass fluctuation, resulting in a peak $zT$ value of 0.055, i.e., almost an order of magnitude higher value than for the pristine $\mathrm{ZrNiSi}$. We show that the thermoelectric properties of TiNiSi structure-type semimetals can be enhanced by aliovalent doping. This principle can be employed on other members of the TiNiSi to improve the $zT$ in this family of compounds further.

Band Structure of Organic-Ion-Intercalated (EMIM)xFeSe Superconductor.

The band structure and the Fermi surface of the recently discovered superconductor (EMIM)FeSe are studied within the density functional theory in the generalized gradient approximation. We show that the bands near the Fermi level are formed primarily by Fe-d orbitals. Although there is no direct contribution of EMIM orbitals to the near-Fermi level states, the presence of organic cations leads to a shift of the chemical potential. It results in the appearance of small electron pockets in the quasi-two-dimensional Fermi surface of (EMIM)FeSe.

Topological pseudogap in highly polarizable layered systems with 2D hole-like dispersion

Pseudogap in hole-doped cuprate superconductors is acknowledged as a possible key to understanding their ground normal state, however, existing pseudogap models have essential inconsistencies with experiments. In our approach pseudogap emerges due to impact of autolocalized carriers on stationary states of delocalized ones and topology of the 2D hole-like dispersion. Autolocalized carriers create potential which transforms Bloch quasiparticles into distributed wave packets (DWPs) with different momentums in areas with different potential. Topology of hole-like constant energy curves in 2D-conducting cuprates forbids DWPs with average momentums near antinode. Manifestation of permitted DWPs in ARPES spectra demonstrates all known pseudogap features including midpoint shift, giant broadening and Fermi momentum misalignment. Calculated doping dependence of the pseudogap width and onset temperature agrees with experiments. The obtained ground normal state of the hole-doped cuprates, in which all the doped holes are autolocalized until high doping is reached and near-antinodal electron DWPs are absent, explains Fermi surface reconstruction from small electron pocket to large hole-like Fermi surface observed in quantum oscillation measurements. Our results open a possibility of creating systems with artificial pseudogap and switchable density of states on the base of highly polarizable layered structures with 2D conductivity and hole-like dispersion.

Low thermal conductivity and semimetallic behavior in some TiNiSi structure-type compounds

Motivated by recent advances in half-Heusler based thermoelectric materials, we investigated the phase stability and thermoelectric properties of compounds ZrNiSi, ZrNiGe, HfNiSi, NbCoSi, and ZrNiSb, some of which were recently reported in literature as promising half-Heuslers for thermoelectric applications using the first-principles density functional theory based calculations. Here, we show that all the named compounds actually crystallize with the orthorhombic TiNiSi structure type, which remains stable above room temperature up to at least 1100 K. In ZrNiSb, $5%$ excess Zr is required to obtain the pure orthorhombic phase. Our first-principles electronic band structure calculations reveal that they are semimetals. In ZrNiSi, ZrNiGe, and HfNiSi, the Fermi surface consists of small electron and hole pockets with electrons as the majority charge carriers. In NbCoSi and ZrNiSb, the majority carriers are holes. A pseudogaplike feature is observed in the electronic density of states with Fermi energy (${E}_{F}$) located either slightly below (ZrNiSi, ZrNiGe, and HfNiSi) or above the pseudogap (NbCoSi). In ZrNiSb no pseudogap is observed; however, the density of states at ${E}_{F}$ is still small. The electrical conductivity ($\ensuremath{\sigma}$) near room temperature is of the order of ${10}^{3}\phantom{\rule{4pt}{0ex}}\mathrm{S}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, which is intermediate between that of the degenerate semiconductors and metallic alloys. Near room temperature the thermopower is negative for $\mathrm{ZrNi}X$ ($X$ = Si, Ge) and HfNiSi, and positive for NbCoSi and ZrNiSb as predicted theoretically. The average value of Seebeck coefficient is small, of the order of $10\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{V}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$. Despite reasonably high electrical conductivity, the thermal conductivity ($\ensuremath{\kappa}$) of these compounds is found to be generally low ($<15\phantom{\rule{4pt}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ near $300\phantom{\rule{4pt}{0ex}}\mathrm{K}$). In ${\mathrm{Zr}}_{1.05}\mathrm{Ni}\mathrm{Sb}$, which has the highest electrical conductivity ($\ensuremath{\approx}4000\phantom{\rule{4pt}{0ex}}\mathrm{S}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$), $\ensuremath{\kappa}$ is as low as $\ensuremath{\approx}4\phantom{\rule{4pt}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$ at $300\phantom{\rule{4pt}{0ex}}\mathrm{K}$, of which almost 70% is estimated to be due to the electronic contribution resulting in a lattice contribution which is $<1\phantom{\rule{4pt}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}1}$. This uncommon combination of high electrical conductivity and low thermal conductivity is interesting and invites further attention.

Fermi Surface Reconstruction and Electron Dynamics at the Charge-Density-Wave Transition in TiSe_{2}.

The evolution of the charge carrier concentrations and mobilities are examined across the charge-density-wave (CDW) transition in TiSe_{2}. Combined quantum oscillation and magnetotransport measurements show that a small electron pocket dominates the electronic properties at low temperatures while an electron and hole pocket contribute at room temperature. At the CDW transition, an abrupt Fermi surface reconstruction and a minimum in the electron and hole mobilities are extracted from two-band and Kohler analysis of magnetotransport measurements. The minimum in the mobilities is associated with the overseen role of scattering from the softening CDW mode. With the carrier concentrations and dynamics dominated by the CDW and the associated bosonic mode, our results highlight TiSe_{2} as a prototypical system to study the Fermi surface reconstruction at a density-wave transition.

Transport properties of topologically non-trivial bismuth tellurobromides BinTeBr.

Temperature-dependent transport properties of the recently discovered layered bismuth-rich tellurobromides BinTeBr (n = 2, 3) are investigated for the first time. Dense homogeneous polycrystalline specimens prepared for different electrical and thermal measurements were synthesized by a ball milling-based process. While the calculated electronic structure classifies Bi2TeBr as a semimetal with a small electron pocket, its transport properties demonstrate a semiconductorlike behavior. Additional bismuth bilayers in the Bi3TeBr crystal structure strengthens the interlayer chemical bonding thus leading to metallic conduction. The thermal conductivity of the semiconducting compositions is low, and the electrical properties are sensitive to doping with a factor of four reduction in resistivity observed at room temperature for only 3% Pb doping. Investigation of the thermoelectric properties suggests that optimization for thermoelectrics may depend on particular elemental substitution. The results presented are intended to expand on the research into tellurohalides in order to further advance the fundamental investigation of these materials, as well as investigate their potential for thermoelectric applications.

Pressure-induced phase transitions and superconductivity in a quasi–1-dimensional topological crystalline insulator α-Bi4Br4

Great progress has been achieved in the research field of topological states of matter during the past decade. Recently, a quasi-1-dimensional bismuth bromide, Bi4Br4, has been predicted to be a rotational symmetry-protected topological crystalline insulator; it would also exhibit more exotic topological properties under pressure. Here, we report a thorough study of phase transitions and superconductivity in a quasihydrostatically pressurized α-Bi4Br4 crystal by performing detailed measurements of electrical resistance, alternating current magnetic susceptibility, and in situ high-pressure single-crystal X-ray diffraction together with first principles calculations. We find a pressure-induced insulator-metal transition between ∼3.0 and 3.8 GPa where valence and conduction bands cross the Fermi level to form a set of small pockets of holes and electrons. With further increase of pressure, 2 superconductive transitions emerge. One shows a sharp resistance drop to 0 near 6.8 K at 3.8 GPa; the transition temperature gradually lowers with increasing pressure and completely vanishes above 12.0 GPa. Another transition sets in around 9.0 K at 5.5 GPa and persists up to the highest pressure of 45.0 GPa studied in this work. Intriguingly, we find that the first superconducting phase might coexist with a nontrivial rotational symmetry-protected topology in the pressure range of ∼3.8 to 4.3 GPa; the second one is associated with a structural phase transition from monoclinic C2/m to triclinic P-1 symmetry.

Phase stiffness in an antiferromagnetic superconductor

We analyze the suppression of the phase stiffness in a superconductor by antiferromagnetic order. The analysis is based on a general expression for the phase stiffness in a mean-field state with coexisting spin-singlet superconductivity and spiral magnetism. Neel order is included as a special case. Close to half-filling, where the pairing gap is much smaller than the magnetic gap, a simple formula for the phase stiffness in terms of magnetic quasi-particle bands is derived. The phase stiffness is determined by charge carriers in small electron or hole pockets in this regime. The general analysis is complemented by a numerical calculation for the two-dimensional Hubbard model with nearest and next-to-nearest neighbor hopping amplitudes at a moderate interaction strength. The resulting phase stiffness exhibits a striking electron-hole asymmetry. In the ground state, it is larger than the pairing gap on the hole-doped side, and smaller for electron doping. Hence, in the hole-doped regime near half-filling the ground state pairing gap sets the scale for the Kosterlitz-Thouless temperature T_c^{KT}, while in the slightly electron-doped regime T_c^{KT} is determined essentially by the ground state phase stiffness.

Visualizing Dirac nodal-line band structure of topological semimetal ZrGeSe by ARPES

As a member of ZrHM (H = Si/Ge/Sn; M = O/S/Se/Te) family materials, which were predicted to be the candidates of topological Dirac nodal-line semimetals, ZrGeSe exhibited particular properties, such as magnetic breakdown effect in the transport measurement, different from its other isostructural compounds, informing an unique topology of the electronic band structure. However, the related experimental research is insufficient until now. Here, we present a systematic study of the band structure and Fermi surfaces (FS) of ZrGeSe by angle-resolved photoemission spectroscopy (ARPES). Our Brillouin zone (BZ) mapping shows multiple Fermi pockets such as the diamond-shaped FS around the zone center Γ point, small electron pocket encircling the X point of the BZ, and lenses-shaped FS in the Γ-M direction. The obtained Fermi velocities and effective masses were up to 9.2 eV·Å and 0.42 me, and revealing an anisotropic electronic property along different high-symmetry k-space directions. Moreover, a kink appears near the Fermi level in the linear Dirac bands along the M-X direction, probably originated from the band hybridization and has not been reported in other ZrHM-type materials. Our findings support that the ZrHM-type material family can be a new platform on which to explore exotic states of quantum matter.

Counter-thermal flow of holes in high-mobility LaNiO3 thin films

Measurements of electronic structure and theoretical models indicate that the Fermi surface of ${\mathrm{LaNiO}}_{3}$ (LNO) is predominantly holelike, with a small electron pocket. However, measurements of the Hall and Seebeck effects yield nominally opposite signs for the dominant charge carrier type, making charge transport in LNO puzzling. Here, we combine measurements of the Hall, Seebeck, and Nernst coefficients in high-mobility epitaxial LNO thin films, and resolve this puzzle by demonstrating that the negative Seebeck coefficient is generated by the diffusion of holes from cold to hot regions of LNO. We further examine this counter-thermal flow of holes by measuring the evolution of the Nernst coefficient from the diffusive to the ballistic regime, where the suppression of energy-dependent scattering leads to a reversal of the flow of holes.

Fermi surface reconstruction in underdoped cuprates: Origin of electron pockets

A new phenomenological model is proposed to describe the evolution of the Fermi surface (FS) in a wide range of dopings. It reproduces the key features of the cuprates in the underdoped phase above the superconducting temperature $T_c$. It is shown that the explicit accounting of strong electron correlation in the framework of the $t-J$ model taken in complementary to the translational symmetry breaking induced by the charge density wave (CDW) gives rise to the Fermi surface reconstruction (FSR) into small electron pockets. While the strong Coulomb repulsion leads to an emergence of the arc-like Fermi surface in the pseudogap (PG) phase, the Bragg reflection on the boundaries of the reduced Brillouin zone (BZ) opens up a possibility to close the quasiparticle orbits. Direct calculation of the FS properties allows us to unveil the scenario of the experimentally observed transition to the CDW phase that sets in at the doping level $\delta\approx0.08$ and is accompanied by a divergence of the carriers effective mass and the sign reversals of the Hall and Seebeck coefficients.

Carrier dynamics in doped bilayer iridates near magnetic quantum criticality

Motivated by experiments on the carrier-doped bilayer iridate $(\text{Sr}_{1-x}\text{La}_x)_3\text{Ir}_2\text{O}_7$, we study the dynamics of a single doped electron in a bilayer magnet in the presence of spin-orbit coupling, taking into account the spatially staggered rotation of IrO$_6$ octahedra. We employ an effective single-orbital bilayer $t$-$J$ model, concentrating on the quantum paramagnetic phase near the magnetic quantum critical point. We determine the carrier dispersion using a combination of self-consistent Born and bond-operator techniques. Extrapolating to finite small carrier density we find that, for experimentally relevant parameters, the combination of octahedral rotation and spin-orbit coupling induces a band folding which results in a Fermi surface of small double electron pockets, in striking agreement with experimental observations. We also determine the influence of spin-orbit coupling on the location of the quantum critical point in the undoped case, and discuss aspects of the global phase diagram of doped bilayer Mott insulators.

Revealing the hidden heavy Fermi liquid in CaRuO3

The perovskite ruthenate has attracted considerable interest due to reports of possible non-Fermi-liquid behavior and its proximity to a magnetic quantum critical point, yet its ground state and electronic structure remain enigmatic. Here we report the first measurements of the Fermi surface and quasiparticle dispersion in CaRuO3 through a combination of oxide molecular beam epitaxy and in situ angle-resolved photoemission spectroscopy. Our results reveal a complex and anisotropic Fermi surface consisting of small electron pockets and straight segments, consistent with the bulk orthorhombic crystal structure with large octahedral rotations. We observe a strongly band-dependent mass renormalization, with prominent heavy quasiparticle bands which lie close to the Fermi energy and exhibit strong temperature dependence. These results are consistent with a heavy Fermi liquid with a complex Fermiology and small hybridization gaps near the Fermi energy. Our results provide a unified framework for explaining previous experimental results on CaRuO3, such as its unusual optical conductivity, and demonstrate the importance of octahedral rotations in determining the quasiparticle band structure, and electron correlations in complex transition metal oxides.

Absence of Dirac states in BaZnBi2 induced by spin-orbit coupling

We report magnetotransport properties of ${\mathrm{BaZnBi}}_{2}$ single crystals. Whereas electronic structure features Dirac states, such states are removed from the Fermi level by spin-orbit coupling (SOC) and consequently electronic transport is dominated by the small hole and electron pockets. Our results are consistent with not only three-dimensional, but also with quasi-two-dimensional portions of the Fermi surface. The SOC-induced gap in Dirac states is much larger when compared to isostructural ${\mathrm{SrMnBi}}_{2}$. This suggests that not only long-range magnetic order, but also mass of the alkaline-earth atoms $A$ in ${ABX}_{2}\phantom{\rule{4pt}{0ex}}(A=$ alkaline-earth, $B=$ transition-metal, and $X=$ Bi/Sb) are important for the presence of low-energy states obeying the relativistic Dirac equation at the Fermi surface.

Lifshitz transition from valence fluctuations in YbAl3

In mixed-valent Kondo lattice systems, such as YbAl3, interactions between localized and delocalized electrons can lead to fluctuations between two different valence configurations with changing temperature or pressure. The impact of this change on the momentum-space electronic structure is essential for understanding their emergent properties, but has remained enigmatic. Here, by employing a combination of molecular beam epitaxy and in situ angle-resolved photoemission spectroscopy we show that valence fluctuations can lead to dramatic changes in the Fermi surface topology, even resulting in a Lifshitz transition. As the temperature is lowered, a small electron pocket in YbAl3 becomes completely unoccupied while the low-energy ytterbium (Yb) 4f states become increasingly itinerant, acquiring additional spectral weight, longer lifetimes, and well-defined dispersions. Our work presents a unified picture of how local valence fluctuations connect to momentum-space concepts such as band filling and Fermi surface topology in mixed valence systems.

Tunability of the topological nodal-line semimetal phase in ZrSiX -type materials ( X=S, Se, Te )

The discovery of a topological nodal-line (TNL) semimetal phase in ZrSiS has invigorated the study of other members of this family. Here, we present a comparative electronic structure study of ZrSiX (where X = S, Se, Te) using angle-resolved photoemission spectroscopy (ARPES) and first-principles calculations. Our ARPES studies show that the overall electronic structure of ZrSiX materials comprises of the diamond-shaped Fermi pocket, the nearly elliptical-shaped Fermi pocket, and a small electron pocket encircling the zone center ($\Gamma$) point, the M point, and the X point of the Brillouin zone, respectively. We also observe a small Fermi surface pocket along the M-$\Gamma$-M direction in ZrSiTe, which is absent in both ZrSiS and ZrSiSe. Furthermore, our theoretical studies show a transition from nodal-line to nodeless gapped phase by tuning the chalcogenide from S to Te in these material systems. Our findings provide direct evidence for the tunability of the TNL phase in ZrSiX material systems by adjusting the spin-orbit coupling (SOC) strength via the X anion.

Observation of topological nodal fermion semimetal phase in ZrSiS

Unveiling new topological phases of matter is one of the current objectives in condensed matter physics. Recent experimental discoveries of Dirac and Weyl semimetals prompt to search for other exotic phases of matter. Here we present a systematic angle-resolved photoemission spectroscopy (ARPES) study of ZrSiS, a prime topological nodal semimetal candidate. Our wider Brillouin zone (BZ) mapping shows multiple Fermi surface pockets such as the diamond-shaped Fermi surface, ellipsoidal-shaped Fermi surface, and a small electron pocket encircling at the zone center (G) point, the M point and the X point of the BZ, respectively. We experimentally establish the spinless nodal fermion semimetal phase in ZrSiS, which is supported by our first-principles calculations. Our findings evidence that the ZrSiS-type of material family is a new platform to explore exotic states of quantum matter, while these materials are expected to provide an avenue for engineering two-dimensional topological insulator systems.