Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to the combination of spin-orbit interactions and time-reversal symmetry. The two-dimensional (2D) topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A three-dimensional (3D) topological insulator supports novel spin-polarized 2D Dirac fermions on its surface. In this Colloquium the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topological insulators have been observed. Transport experiments on $\mathrm{Hg}\mathrm{Te}∕\mathrm{Cd}\mathrm{Te}$ quantum wells are described that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. Experiments on ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$, ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, and ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$ are then discussed that establish these materials as 3D topological insulators and directly probe the topology of their surface states. Exotic states are described that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions and may provide a new venue for realizing proposals for topological quantum computation. Prospects for observing these exotic states are also discussed, as well as other potential device applications of topological insulators.

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Colloquium: Topological insulators

Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by ${Z}_{2}$ topological invariants, which characterize the ground state. In two dimensions, there is a single ${Z}_{2}$ invariant that distinguishes the ordinary insulator from the quantum spin-Hall phase. In three dimensions, there are four ${Z}_{2}$ invariants that distinguish the ordinary insulator from ``weak'' and ``strong'' topological insulators. These phases are characterized by the presence of gapless surface (or edge) states. In the two-dimensional quantum spin-Hall phase and the three-dimensional strong topological insulator, these states are robust and are insensitive to weak disorder and interactions. In this paper, we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the ${Z}_{2}$ invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wave functions at the time-reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials that are strong topological insulators, including the semiconducting alloy ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$ as well as $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ and HgTe under uniaxial strain. This paper also includes an expanded discussion of our formulation of the topological insulators in both two and three dimensions, as well as implications for experiments.

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Topological insulators with inversion symmetry

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Infrared detectors: status and trends

We describe here a simple, all-inorganic metal/NC/metal sandwich photovoltaic (PV) cell that produces an exceptionally large short-circuit photocurrent (>21 mA cm -2 ) by way of a Schottky junction at the negative electrode. The PV cell consists of a PbSe NC film, deposited via layer-by-layer (LbL) dip coating that yields an EQE of 55-65% in the visible and up to 25% in the infrared region of the solar spectrum, with a spectrally corrected AM1.5G power conversion efficiency of 2.1%. This NC device produces one of the largest short-circuit currents of any nanostructured solar cell, without the need for sintering, superlattice order or separate phases for electron and hole transport.

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Schottky Solar Cells Based on Colloidal Nanocrystal Films

This article reviews the history, the present status and possible future developments of HgCdTe ternary alloy for infrared (IR) detector applications. HgCdTe IR detectors have been intensively developed since the first synthesis of this material in 1958. This article summarizes the fundamental properties of this versatile narrow gap semiconductor, and relates the material properties to its successful applications as an IR photoconductive and photovoltaic detector material. An emphasis is put on key developments in the crystal growth and their influence on device evolution. Competitive technologies to HgCdTe ternary alloy are also presented. Recent advances of backside illuminated HgCdTe heterojunction photodiodes have enabled a third generation of multispectral instruments for remote sensing applications and have led to the practicality of multiband IR focal plane array technology. Finally, evaluation of HgCdTe for room temperature long wavelength IR applications is presented. (Some figures in this article are in colour only in the electronic version)

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HgCdTe infrared detector material: history, status and outlook

Narrow-gap semiconductors

The properties and applications of the Hg 1−x Cd x Te alloy system

The temperature dependence of the Auger-lifetime of n-Hg1−xCdxTe is investigated both theoretically and experimentally for several values of bandgap and of extrinsic carrier-concentration nex in the whole range between room and He-temperatures. For semiconducting compounds a pronounced minimum of the lifetime between 10 and 50K and an exponential increase at still lower temperatures are found. The position of the minimum and the exponent depend mainly on the value of the bandgap and on the ratio of the conduction- and valenceband effective masses. Apart from the extended temperature range, which does not allow the use of classical statistics, our calculation differs from earlier work in so far, as we take the band energies and the overlap integrals of conduction- and valenceband Bloch-functions from a k·p-calculation. For semiconducting compounds, we compare the results with those obtained from an estimate of the overlap integrals given by Antoncik and Landsberg. Whereas both results are compatible at high temperatures, characteristic differences occur at low temperatures, where we find the lifetime to be proportional to n ex −8 3 rather than to nex−2. For semimetallic compounds we calculate a weakly temperature dependent Auger-time of the order of 0.1–1 nsec.

The Auger-effect in Hg1−xCdxTe

Drastic long‐term changes of transport properties and the recombination behavior of a Hg1−xCdxTe crystal are reported. Being pure n‐type material immediately after fabrication the crystal showed a p‐type conduction after a five‐year storage under room‐temperature conditions. The lifetime—formerly dominated by Auger recombination—dropped by about two orders of magnitude. A model of Hg vacancy diffusion is suggested to explain the observed data.

Long‐term Hall‐type conversion by vacancy diffusion in Hg1−xCdxTe at room temperature

Experimental life time data of n-type PbTe and Pb0.8Sn0.2Te epitaxial layers are reported. Experiments were carried out with photoionized and impact ionized excess carriers between 6 and 300 K. Both materials show a strongly increasing life time with decreasing temperature. With PbTe an extremely non-exponential excess carrier decay was observed. Measurements of carrier sweep out and time resolved photo Hall effect have shown that in PbTe a strong minority carrier trapping occurs, whereas in PbSnTe, both electrons and holes, have nearly equal decay times. Comparing the experimental data with theory it can be concluded that in PbTe a Shockley-Read mechanism dominates the recombination at low temperatures. Auger recombination might become efficient only at temperatures above 200 K. The recombination behaviour in PbSnTe cannot be explained by one of the well-known models. An Auger recombination theory taking into account degeneracy might describe the observed data.

Ralf Dornhaus

Papers

Narrow-gap semiconductors

The properties and applications of the Hg 1−x Cd x Te alloy system

The Auger-effect in Hg1−xCdxTe

Long‐term Hall‐type conversion by vacancy diffusion in Hg1−xCdxTe at room temperature

Life time measurements in PbTe and PbSnTe