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Register a new userRevealing puddles of electrons and holes in compensated topological insulators
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Added by
Markus Gr\\\"uninger
Publication date
2015
fields
Physics
and research's language is
English
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Three-dimensional topological insulators harbour metallic surface states with exotic properties. In transport or optics, these properties are typically masked by defect-induced bulk carriers. Compensation of donors and acceptors reduces the carrier density, but the bulk resistivity remains disappointingly small. We show that measurements of the optical conductivity in BiSbTeSe$_2$ pinpoint the presence of electron-hole puddles in the bulk at low temperatures, which is essential for understanding DC bulk transport. The puddles arise from large fluctuations of the Coulomb potential of donors and acceptors, even in the case of full compensation. Surprisingly, the number of carriers appearing within puddles drops rapidly with increasing temperature and almost vanishes around 40 K. Monte Carlo simulations show that a highly non-linear screening effect arising from thermally activated carriers destroys the puddles at a temperature scale set by the Coulomb interaction between neighbouring dopants, explaining the experimental observation semi-quantitatively. This mechanism remains valid if donors and acceptors do not compensate perfectly.
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Compensation of intrinsic charges is widely used to reduce the bulk conductivity of 3D topological insulators (TIs). Here we use low temperature electron irradiation-induced defects paired with in-situ electrical transport measurements to fine-tune the degree of compensation in Bi2Te3. The coexistence of electrons and holes at the point of optimal compensation can only be explained by bulk carriers forming charge puddles. These need to be considered to understand the electric transport in compensated TI samples, irrespective of the method of compensation.
Existence of a protected surface state described by a massless Dirac equation is a defining property of the topological insulator. Though this statement can be explicitly verified on an idealized flat surface, it remains to be addressed to what extent it could be general. On a curved surface, the surface Dirac equation is modified by the spin connection terms. Here, in the light of the differential geometry, we give a general framework for constructing the surface Dirac equation starting from the Hamiltonian for bulk topological insulators. The obtained unified description clarifies the physical meaning of the spin connection.
High surface-mobility, which is attributable to topological protection, is a trademark of three-dimensional topological insulators (3DTIs). Exploiting surface-mobility indicates successful application of topological properties for practical purposes. However, the detection of the surface-mobility has been hindered by the inevitable bulk conduction. Even in the case of high-quality crystals, the bulk state forms the dominant channel of the electrical current. Therefore, with electrical transport measurement, the surface-mobility can be resolved only below-micrometer-thick crystals. The evaluation of the surface-mobility becomes more challenging at higher temperatures, where phonons can play a role. Here, using spectroscopic techniques, we successfully evaluated the surface-mobility of Bi2Te3 (BT) at room temperature (RT). We acquired the effective masses and mean scattering times for both the surface and bulk states using angle-resolved photoemission and terahertz time-domain spectroscopy. We revealed a record-high surface-mobility for BT, exceeding 33,000 cm^2/(Vs) per surface sheet, despite intrinsic limitations by the coexisting bulk state as well as phonons at RT. Our findings partially support the interesting conclusion that the topological protection persists at RT. Our approach could be applicable to other topological materials possessing multiband structures near the Fermi level.
We use first principles calculations to study the electronic properties of rock salt rare earth monopnictides La$X$ ($X=$N, P, As, Sb, Bi). A new type of topological band crossing termed `linked nodal rings is found in LaN when the small spin-orbital coupling (SOC) on nitrogen orbitals is neglected. Turning on SOC gaps the nodal rings at all but two points, which remain gapless due to $C_4$-symmetry and leads to a 3D Dirac semimetal. Interestingly, unlike LaN, compounds with other elements in the pnictogen group are found to be topological insulators (TIs), as a result of band reordering due to the increased lattice constant as well as the enhanced SOC on the pnictogen atom. These TI compounds exhibit multi-valley surface Dirac cones at three $bar{M}$-points on the $(111)$-surface.
Systems of free fermions are classified by symmetry, space dimensionality, and topological properties described by K-homology. Those systems belonging to different classes are inequivalent. In contrast, we show that by taking a many-body/Fock space viewpoint it becomes possible to establish equivalences of topological insulators and superconductors in terms of duality transformations. These mappings connect topologically inequivalent systems of fermions, jumping across entries in existent classification tables, because of the phenomenon of symmetry transmutation by which a symmetry and its dual partner have identical algebraic properties but very different physical interpretations. To constrain our study to established classification tables, we define and characterize mathematically Gaussian dualities as dualities mapping free fermions to free fermions (and interacting to interacting). By introducing a large, flexible class of Gaussian dualities we show that any insulator is dual to a superconductor, and that fermionic edge modes are dual to Majorana edge modes, that is, the Gaussian dualities of this paper preserve the bulk-boundary correspondence. Transmutation of relevant symmetries, particle number, translation, and time reversal is also investigated in detail. As illustrative examples, we show the duality equivalence of the dimerized Peierls chain and the Majorana chain of Kitaev, and a two-dimensional Kekule-type topological insulator, including graphene as a special instance in coupling space, dual to a p-wave superconductor. Since our analysis extends to interacting fermion systems we also briefly discuss some such applications.
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