Odd-Parity Topological Superconductors: Theory and Application to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Cu</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi>Bi</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Se</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>

Fu, Liang; Berg, Erez

doi:10.1103/physrevlett.105.097001

Cited by 854 publications

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“…The shape of the spectrum with the peak and the dips around it, is similar to the expected spectrum in a chiral p-wave superconductor 12 , where the andreev bound state is dispersive and wide. Fu and Berg showed in Ref 3 , that the band structure of Cu x Bi 2 Se 3 may favor an unconventional odd-parity symmetry leading to a timereversal odd-parity topological superconductor. The proposed superconductor is fully gapped in the bulk, but the surface have gapless surface Andreev bound states.…”

Section: Resultsmentioning

confidence: 99%

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Point-contact spectroscopy of Cu0.2Bi2Se3single crystals

et al. 2012

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We report point contact measurements in high quality single crystals of Cu0.2Bi2Se3. We observe three different kinds of spectra: 1) Andreev reflection spectra, from which we infer a superconducting gap size of 0.6mV. 2) Spectra with a large gap which closes above Tc at about 10K and 3) Tunnelinglike spectra with Zero Bias Conductance Peaks (ZBCP). These tunneling spectra show a very large gap of about 2meV (2∆/K b Tc ∼14).

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Section: Resultsmentioning

confidence: 99%

“…Closely related to topological insulators, topological superconductors have non-trivial topological properties and in addition are bulk superconuctors 3 . The topological superconductors caused a lot of excitement since they are predicted to host Majorana fermions which could be used for quantum computing 4 .…”

Section: Introductionmentioning

confidence: 99%

Point-contact spectroscopy of Cu0.2Bi2Se3single crystals

et al. 2012

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“…Using the Fermion anticommutation property, we show that the odd parity allows a twist of a gap function with respect to the internal degrees of freedom (e.g., orbital and spin) in systems, causing the novel temperature dependence of NMR rates. Hence, NMR rates are bulk quantities sensitive to parity closely related to defining Z 2 invariants [1,13] in a superconducting state.We formulate the NMR rate of a multi-orbital superconductor, with a mean-field approach. The meanfield Bogoliubov-de Gennes (BdG) Hamiltonian is H = (1/2) k ψ † kȞ (k)ψ k , with ψ † k = (c † k , c T −k ) and ψ T k =…”

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Inverse coherence effects in nuclear magnetic relaxation rates as a sign of topological superconductivity

2015

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We reveal that three-dimensional multi-orbital topological superconductivity can be identified by a bulk measurement, i.e., the temperature dependence of nuclear magnetic relaxation (NMR) rates. Below a critical temperature Tc, the NMR rate in the topological state exhibits an anti-peak profile, which is opposite to the conventional s-wave state. This inversion coherence effect comes from a twist of order parameters with respect to orbital and spin degrees of freedom. Our self-consistent calculations in the model for CuxBi2Se3 prove that the inverse coherence effect appears as a concave temperature dependence of the NMR rates. We propose that a time-reversal-invariant orbitalsinglet spin-triplet topological superconductivity is characterized by the temperature dependence of the NMR rate. [17][18][19]. Among these studies, although the gapless bound states on surfaces at low temperatures are actively studied [9,11,[20][21][22], observing an intrinsic behavior via bulk measurements is rarely argued. In addition, the setups of surface measurements would be sensitively affected by the characteristics of the interfaces between materials and probes. Thus, a bulk measurement sensitive to topological characters is important for supporting results in surface measurements and revealing the properties of Cooper-pair condensations.A key quantity of connecting topological characters with bulk measurements is a correlation function. Current-current correlation functions, for example, lead to the quantized conductance in integer quantum Hall effects [5]. Spin-spin correlation functions are essential for superconductivity since these quantities well reflect the spin-state properties of Cooper pairs. Nuclear magnetic relaxation (NMR) rates (T −1 1 ) are directly related to the spin-spin correlation functions. Therefore, it is interesting and important question to ask whether NMR rates contain any characteristic information on topological superconductivity. Specifically, the coherence effect is notable. The NMR rate in the presence of a spin-singlet swave superconducting state is enhanced just below a critical temperature T c , owing to the coherence factor [23]. This coherence peak (Hebel-Slichter peak) [24,25] comes from the formation of superconducting gaps. The absence of the peak and a power-law behavior of T −1 1 at low temperatures indicate the occurrence of unconventional states [26][27][28].In this paper we claim that the bulk measurements of NMR rates detect a 3D odd-parity fully-gapped topological superconducting state in time-reversal-invariant multi-orbital systems. An inverse coherence effect just below T c is the signature of this odd-parity state; the coherence factor contributes to the NMR rates with an opposite sign to that of the conventional s-wave states. Our self-consistent calculations in the model of Cu x Bi 2 Se 3 [13] show that this sign reversal leads to an anti-peak behavior of the NMR rates below T c . Using the Fermion anticommutation property, we show that the odd parity allows a twist of a gap fun...

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“…We emphasize the flexibility of this composite structure, which enables to reach an interesting regime where the inter-sub-band interaction may be dominant mechanism for interlayer coupling. The current structures offer a model system to control the bilayer degree of freedom in multi-component superconductors, which has been theoretically proposed to synthesize unconventional superconductivity [35][36][37]. …”

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Tunable coupling of two-dimensional superconductors in bilayer SrTiO3heterostructures

et al. 2013

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Interlayer coupling effects between high mobility two-dimensional superconductors are studied in bilayer δ-doped SrTiO3 heterostructures. By tuning the undoped SrTiO3 spacer layer between the dopant planes, clear tunable coupling is demonstrated in the variation of the sheet carrier density, Hall mobility, superconducting transition temperature, and the temperature-and angle-dependences of the superconducting upper critical field. Systematic variation is found between one effective (merged) two-dimensional superconductor to two decoupled two-dimensional superconductors. In the intermediate coupled regime, a crossover is observed due to coupling arising from inter-sub-band interactions.Interlayer coupling between two-dimensional (2D) planes in layered materials is a key parameter which dramatically influences their physics and functionality. Paradigmatic examples in the field of superconductivity include the high temperature superconducting cuprates [1, 2], and the iron pnictides [3], as well as artificially created superlattices, in which the Josephson coupling between the layers can be tunable continuously using thin film control [4,5]. There have also been extensive studies of coupled bilayer 2D systems, where exotic phases arise from the interlayer interactions [6][7][8][9][10][11][12].Among the various 2D systems currently under investigation, SrTiO 3 (STO) is of particular interest since it is a rare example of a high mobility doped semiconductor that is simultaneously superconducting. By confining electrons in STO two-dimensionally using field effect gating [13], heterointerfaces with LaTiO 3 [14], or LaAlO 3 [15,16], and δ-doping [17], the interplay between subband quantization and superconductivity can be investigated. Here we exploit interlayer coupling in a δ-doped bilayer system to spatially and flexibly control the subbands. By systematically tuning the interlayer coupling by varying the spacer layer thickness, we can examine the effects of the sub-band quantization on superconductivity.The bilayer samples consist of two Nb:STO δ-doped layers, with an undoped STO spacer of thickness d inter , as well as 100 nm thick undoped STO cap and buffer layers. All samples were fabricated using pulsed laser deposition using growth conditions as reported elsewhere [18]. The thickness of each of the two δ-layers was fixed at a constant value of d doped = 5.4 ± 1 nm, as calibrated from the total thickness and the laser pulse count. The interlayer undoped STO thickness d inter was varied in the range 3.7 ≤ d inter ≤ 272 nm. The dopant concentration of the δ-doped layers was 1 at.%. A schematic of the bilayer samples is shown in Fig.

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Odd-Parity Topological Superconductors: Theory and Application toCuxBi2Se3

Cited by 854 publications

References 31 publications

Point-contact spectroscopy of Cu0.2Bi2Se3single crystals

Point-contact spectroscopy of Cu0.2Bi2Se3single crystals

Inverse coherence effects in nuclear magnetic relaxation rates as a sign of topological superconductivity

Tunable coupling of two-dimensional superconductors in bilayer SrTiO3heterostructures

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