Superconductivity at very low density: The case of strontium titanate

Ruhman, Jonathan; Lee, Patrick A.

doi:10.1103/physrevb.94.224515

Title: Superconductivity at very low density: The case of strontium titanate

Abstract

Doped strontium titanate becomes superconducting at a density as low as n = 5 × 10¹⁷ cm^-3, where the Fermi energy is orders of magnitude smaller than the longitudinal-optical-phonon frequencies. In this limit, the only optical mode with a frequency which is smaller than the Fermi energy is the plasmon. In contrast to metals, the interaction strength is weak due to screening by the crystal, which allows the construction of a controllable theory of plasmon superconductivity. We show that plasma mediated pairing alone can account for the observed transition temperatures only if the dielectric screening by the crystal is reduced in the slightly doped samples compared with the insulating ones. We also discuss unique features of the plasmon mechanism, which appear in the tunneling density of states above the gap.

Authors:

Ruhman, Jonathan ^[1]; Lee, Patrick A. ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Publication Date:: Thu Dec 22 00:00:00 EST 2016

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1535810

Alternate Identifier(s):: OSTI ID: 1337441

Grant/Contract Number:: FG02-03ER46076

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. B

Additional Journal Information:: Journal Volume: 94; Journal Issue: 22; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics; Electron-phonon coupling; Fermi surface; Ferroelectricity; Multiband superconductivity; Semiconductors; Superconducting phase transition; BCS theory; Condensed Matter & Materials Physics; Plasma Physics

Citation Formats


                    Ruhman, Jonathan, and Lee, Patrick A. Superconductivity at very low density: The case of strontium titanate.  United States: N. p., 2016. 
Web.  doi:10.1103/physrevb.94.224515.

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                    Ruhman, Jonathan, & Lee, Patrick A. Superconductivity at very low density: The case of strontium titanate.  United States.  https://doi.org/10.1103/physrevb.94.224515

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                    Ruhman, Jonathan, and Lee, Patrick A. Thu .  
"Superconductivity at very low density: The case of strontium titanate".  United States.  https://doi.org/10.1103/physrevb.94.224515.  https://www.osti.gov/servlets/purl/1535810.

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@article{osti_1535810,

  title        = {Superconductivity at very low density: The case of strontium titanate},

  author       = {Ruhman, Jonathan and Lee, Patrick A.},

  abstractNote = {Doped strontium titanate becomes superconducting at a density as low as n = 5 × 1017 cm-3, where the Fermi energy is orders of magnitude smaller than the longitudinal-optical-phonon frequencies. In this limit, the only optical mode with a frequency which is smaller than the Fermi energy is the plasmon. In contrast to metals, the interaction strength is weak due to screening by the crystal, which allows the construction of a controllable theory of plasmon superconductivity. We show that plasma mediated pairing alone can account for the observed transition temperatures only if the dielectric screening by the crystal is reduced in the slightly doped samples compared with the insulating ones. We also discuss unique features of the plasmon mechanism, which appear in the tunneling density of states above the gap.},

  doi          = {10.1103/physrevb.94.224515},

  journal      = {Physical Review. B},

  number       = 22,

  volume       = 94,

  place        = {United States},

  year         = {Thu Dec 22 00:00:00 EST 2016},

  month        = {Thu Dec 22 00:00:00 EST 2016}

}

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Attenuated total reflectance (ATR) measurements were performed using Fourier transform infrared (FTIR) spectroscopy in the ATR mode with a thallium iodobromide (KRS-5) crystal to measure the frequencies of the {nu}{sub 3} and {nu}{sub 4} phonon absorption bands in thin strontium titanate films deposited on single-crystal yttrium-barium copper oxide (YBCO), lanthanum aluminate, magnesium oxide, and strontium titanate substrates. The KRS-5 crystal enabled FTIR-ATR measurements to be made at frequencies above 400 cm{sup {minus}1}. Atomic force microscopy (AFM) and X-ray diffraction (XRD) measurements were also made to further characterize the films. The measurements were repeated on single-crystal specimens of strontium titanate andmore »« less
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Superconductivity near a Ferroelectric Quantum Critical Point in Ultralow-Density Dirac Materials

Journal Article Kozii, Vladyslav ; Bi, Zhen ; Ruhman, Jonathan - Physical Review. X

The experimental observation of superconductivity in doped semimetals and semiconductors, where the Fermi energy is comparable to or smaller than the characteristic phonon frequencies, is not captured by the conventional theory. In this paper, we propose a mechanism for superconductivity in ultralow-density three-dimensional Dirac materials based on the proximity to a ferroelectric quantum critical point. We derive a low-energy theory that takes into account both the strong Coulomb interaction and the direct coupling between the electrons and the soft phonon modes. We show that the Coulomb repulsion is strongly screened by the lattice polarization near the critical point even in the case of vanishing carrier density. Using a renormalization group analysis, we demonstrate that the effective electron-electron interaction is dominantly mediated by the transverse phonon mode. We find that the system generically flows towards strong electron-phonon coupling. Hence, we propose a new mechanism to simultaneously produce an attractive interaction and suppress strong Coulomb repulsion, which does not require retardation. For comparison, we perform same analysis for covalent crystals, where lattice polarization is negligible. We obtain qualitatively similar results, though the screening of the Coulomb repulsion is much weaker. We then apply our results to study superconductivity in the low-density limit. We find strong enhancement of the transition temperature upon approaching the quantum critical point. Finally, we also discuss scenarios to realize a topologicalmore »« less
Cited by 26
https://doi.org/10.1103/PhysRevX.9.031046
Blocking effect of crystal–glass interface in lanthanum doped barium strontium titanate glass–ceramics

Journal Article Wang, Xiangrong ; Zhang, Yong ; Baturin, Ivan ; ... - Materials Research Bulletin

Graphical abstract: The blocking effect of the crystal–glass interface on the carrier transport behavior in the lanthanum doped barium strontium titanate glass–ceramics: preparation and characterization. - Highlights: • La{sub 2}O{sub 3} addition promotes the crystallization of the major crystalline phase. • The Z″ and M″ peaks exist a significant mismatch for 0.5 mol% La{sub 2}O{sub 3} addition. • The Z″ and M″ peaks separate obviously for 1.0 mol% La{sub 2}O{sub 3} addition. • Crystallite impedance decreases while crystal–glass interface impedance increases. • La{sub 2}O{sub 3} addition increases blocking factor of the crystal–glass interface. - Abstract: The microstructures and dielectric propertiesmore »« less
https://doi.org/10.1016/J.MATERRESBULL.2013.05.088
Published Tunneling Results of Binnig et al Interpreted as Related to Surface Superconductivity in SrTiO{sub 3}

Journal Article Eagles, D. M., E-mail: d.eagles@ic.ac.uk - Journal of Superconductivity and Novel Magnetism

In 1980, Binnig et al. reported tunneling measurements on Nb-doped SrTiO{sub 3}, and interpreted their results as indicating two-band superconductivity in the bulk of SrTiO{sub 3}. However, (1) effective masses determined from tunneling results in the normal state by Sroubek in 1969 and 1970 are much smaller than those determined by most other methods. The much smaller masses were attributed to properties of a surface layer by the present author in 1971. (2) The only other reports of two-band superconductivity in bulk SrTiO{sub 3} can be used to infer much smaller values for the band separations than found by Binnigmore »« less
https://doi.org/10.1007/S10948-017-4289-9

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Title: Superconductivity at very low density: The case of strontium titanate

Abstract

Citation Formats

Critical Doping for the Onset of a Two-Band Superconducting Ground State in SrTiO 3 − δ journal, May 2014

Observation of the Interaction of Plasmons with Longitudinal Optical Phonons in GaAs journal, May 1966

Possible Pairing without Superconductivity at Low Carrier Concentrations in Bulk and Thin-Film Superconducting Semiconductors journal, October 1969

Soft-Mode Superconductivity in SrTi O 3 − x journal, April 1969

Theory of Superconductivity in Polar Semiconductors and Its Application to N-Type Semiconducting SrTiO 3 journal, October 1980

Effective Tunneling Density of States in Superconductors journal, April 1963

Odd-Parity Superconductivity in the Vicinity of Inversion Symmetry Breaking in Spin-Orbit-Coupled Systems journal, November 2015

Tunable conductivity threshold at polar oxide interfaces journal, January 2012

Strong energy–momentum dispersion of phonon-dressed carriers in the lightly doped band insulator SrTiO 3 journal, February 2010

Interface superconductivity in LaAlO 3 − SrTiO 3 heterostructures journal, May 2014

Mechanism of superconductivity in SrTiO3 journal, August 1981

Pressure as a probe of dielectric properties and phase transition of doped quantum paraelectrics: Sr 1 − x Ca x TiO 3 ( x = 0.007 ) journal, June 2003

Superconducting Transition Temperatures of Semiconducting SrTi O 3 journal, November 1967

Accurate determination of the far-infrared dispersion in SrTi O 3 by hyper-Raman spectroscopy journal, September 1981

Electric field control of the LaAlO3/SrTiO3 interface ground state journal, December 2008

Common Fermi-liquid origin of T 2 resistivity and superconductivity in n -type SrTiO 3 journal, November 2011

Towards Two-Dimensional Metallic Behavior at LaAlO 3 / SrTiO 3 Interfaces journal, May 2009

Superconductivity in Cu x Bi 2 Se 3 and its Implications for Pairing in the Undoped Topological Insulator journal, February 2010

Electron-Phonon Interaction and Charge Carrier Mass Enhancement in SrTiO 3 journal, June 2008

Electron pairing without superconductivity journal, May 2015

Interface superconductor with gap behaviour like a high-temperature superconductor journal, October 2013

Plasmon Mechanism of Superconductivity in Two- and Three-Dimensional Electron Systems journal, September 1978

The low‐temperature infrared optical functions of SrTiO 3 determined by reflectance spectroscopy and spectroscopic ellipsometry journal, July 1995

First-Principle Calculation of Superconducting Transition Temperature of MOS Inversion Layers journal, November 1980

Giant LO-TO splittings in perovskite ferroelectrics journal, May 1994

Superconductivity in Semiconducting SrTi O 3 journal, April 1964

Observation of topological order in a superconducting doped topological insulator journal, September 2010

Two-Band Superconductivity in Nb-Doped SrTi O 3 journal, October 1980

Reliable Padé analytical continuation method based on a high-accuracy symbolic computation algorithm journal, February 2000

Nonadiabatic Superconductivity: Electron-Phonon Interaction Beyond Migdal's Theorem journal, August 1995

Two-dimensional electron gas with universal subbands at the surface of SrTiO3 journal, January 2011

A New Method in the Theory of Superconductivity journal, May 1960

Refined treatment of the model of linearly coupled anharmonic oscillators and its application to the temperature dependence of the zone-center soft-mode frequencies of KTaO 3 and SrTiO 3 journal, April 1995

Bulk Superconducting Phase with a Full Energy Gap in the Doped Topological Insulator Cu x Bi 2 Se 3 journal, March 2011

Phonon mechanism in the most dilute superconductor n -type SrTiO 3 journal, April 2016

Dielectric properties of single crystals of SrTiO3 at low temperatures journal, October 1959

Polaron coupling coustants in SrTiO3 journal, March 1965

Quantum Critical Origin of the Superconducting Dome in SrTiO 3 journal, December 2015

Role of electron Coulomb interaction in superconductivity journal, November 1983

Fermi Surface of the Most Dilute Superconductor journal, April 2013

Anisotropic Migdal-Eliashberg theory using Wannier functions journal, January 2013

Superconductivity with Topological Surface State in Sr x Bi 2 Se 3 journal, August 2015

Interplay between antiferrodistortive, ferroelectric, and superconducting instabilities in Sr 1 − x Ca x TiO 3 − δ journal, January 2015

Electric Field Dependence of Optical-Phonon Frequencies journal, November 1967

Electric-field-induced superconductivity in an insulator journal, October 2008

A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface journal, January 2004

Optical properties of highly reduced SrTiO 3 − x journal, May 1999

SrTi O 3 : An intrinsic quantum paraelectric below 4 K journal, April 1979

The description of superconductivity in terms of dielectric response function journal, January 1973

Superconductivity from nonphonon interactions journal, June 1984

Soft modes in semiconducting SrTiO3: II. The ferroelectric mode journal, December 1980

Quantum Critical Origin of the Superconducting Dome in SrTiO₃ text, January 2015

Effective Tunneling Density of States in Superconductors book,

Anisotropic Migdal-Eliashberg theory using Wannier functions text, January 2012

Fermi surface of the most dilute superconductor text, January 2012

Odd-parity superconductivity in the vicinity of inversion symmetry breaking in spin-orbit-coupled systems text, January 2015

Second Harmonic Generation Investigation of Symmetry Breaking and Flexoelectricity Induced by Nanoindentations in SrTiO 3 journal, July 2019

Back to Mechanisms of Superconductivity in Low-Doped Strontium Titanate journal, February 2017

A Local Maximum in the Superconducting Transition Temperature of Nb-Doped Strontium Titanate Under Uniaxial Compressive Stress journal, August 2019

Precision Measurements of the AC Field Dependence of the Superconducting Transition in Strontium Titanate journal, September 2019

Superconductivity in SrTiO3: Dielectric Function Method for Non-Parabolic Bands journal, January 2019

A ferroelectric quantum phase transition inside the superconducting dome of Sr1−xCaxTiO3−δ journal, April 2017

The physics of quantum materials journal, October 2017

Universal superconducting precursor in three classes of unconventional superconductors journal, June 2019

Polaronic behavior in a weak-coupling superconductor journal, January 2018

Quantum critical phenomena in a compressible displacive ferroelectric journal, May 2020

Dynamical screening in monolayer transition-metal dichalcogenides and its manifestations in the exciton spectrum journal, March 2019

Prospects and applications near ferroelectric quantum phase transitions: a key issues review journal, September 2017

Physics of SrTiO 3 -based heterostructures and nanostructures: a review journal, February 2018

Kohn-Luttinger correction to T c in a phonon superconductor journal, January 2020

Marrying Excitons and Plasmons in Monolayer Transition-Metal Dichalcogenides journal, November 2017

Enhancing superconductivity in SrTiO 3 films with strain journal, April 2019

Quantum critical phenomena in a compressible displacive ferroelectric text, January 2020

Marrying Excitons and Plasmons in Monolayer Transition-Metal Dichalcogenides text, January 2017

Physics of SrTiO$_3$-based heterostructures and nanostructures: a review text, January 2017

Superconductivity in three-dimensional spin-orbit coupled semimetals text, January 2017

Dynamical screening in monolayer transition-metal dichalcogenides and its manifestations in the exciton spectrum text, January 2018

Critical Doping for the Onset of a Two-Band Superconducting Ground State in ${SrTiO}_{3 - δ}$
journal, May 2014

Observation of the Interaction of Plasmons with Longitudinal Optical Phonons in GaAs
journal, May 1966

Possible Pairing without Superconductivity at Low Carrier Concentrations in Bulk and Thin-Film Superconducting Semiconductors
journal, October 1969

Soft-Mode Superconductivity in $SrTi O_{3 - x}$
journal, April 1969

Theory of Superconductivity in Polar Semiconductors and Its Application to N-Type Semiconducting SrTiO ₃
journal, October 1980

Effective Tunneling Density of States in Superconductors
journal, April 1963

Odd-Parity Superconductivity in the Vicinity of Inversion Symmetry Breaking in Spin-Orbit-Coupled Systems
journal, November 2015

Tunable conductivity threshold at polar oxide interfaces
journal, January 2012

Strong energy–momentum dispersion of phonon-dressed carriers in the lightly doped band insulator SrTiO ₃
journal, February 2010

Interface superconductivity in ${LaAlO}_{3} - {SrTiO}_{3}$ heterostructures
journal, May 2014

Mechanism of superconductivity in SrTiO3
journal, August 1981

Pressure as a probe of dielectric properties and phase transition of doped quantum paraelectrics: ${Sr}_{1 - x} {Ca}_{x} {TiO}_{3}$ $(x = 0.007)$
journal, June 2003

Superconducting Transition Temperatures of Semiconducting SrTi $O_{3}$
journal, November 1967

Accurate determination of the far-infrared dispersion in SrTi $O_{3}$ by hyper-Raman spectroscopy
journal, September 1981

Electric field control of the LaAlO3/SrTiO3 interface ground state
journal, December 2008

Common Fermi-liquid origin of $T^{2}$ resistivity and superconductivity in $n$ -type SrTiO $_{3}$
journal, November 2011

Towards Two-Dimensional Metallic Behavior at ${LaAlO}_{3} / {SrTiO}_{3}$ Interfaces
journal, May 2009

Superconductivity in ${Cu}_{x} {Bi}_{2} {Se}_{3}$ and its Implications for Pairing in the Undoped Topological Insulator
journal, February 2010

Electron-Phonon Interaction and Charge Carrier Mass Enhancement in ${SrTiO}_{3}$
journal, June 2008

Electron pairing without superconductivity
journal, May 2015

Interface superconductor with gap behaviour like a high-temperature superconductor
journal, October 2013

Plasmon Mechanism of Superconductivity in Two- and Three-Dimensional Electron Systems
journal, September 1978

The low‐temperature infrared optical functions of SrTiO ₃ determined by reflectance spectroscopy and spectroscopic ellipsometry
journal, July 1995

First-Principle Calculation of Superconducting Transition Temperature of MOS Inversion Layers
journal, November 1980

Giant LO-TO splittings in perovskite ferroelectrics
journal, May 1994

Superconductivity in Semiconducting SrTi $O_{3}$
journal, April 1964

Observation of topological order in a superconducting doped topological insulator
journal, September 2010

Two-Band Superconductivity in Nb-Doped SrTi $O_{3}$
journal, October 1980

Reliable Padé analytical continuation method based on a high-accuracy symbolic computation algorithm
journal, February 2000

Nonadiabatic Superconductivity: Electron-Phonon Interaction Beyond Migdal's Theorem
journal, August 1995

Two-dimensional electron gas with universal subbands at the surface of SrTiO₃
journal, January 2011

A New Method in the Theory of Superconductivity
journal, May 1960

Refined treatment of the model of linearly coupled anharmonic oscillators and its application to the temperature dependence of the zone-center soft-mode frequencies of ${KTaO}_{3}$ and ${SrTiO}_{3}$
journal, April 1995

Bulk Superconducting Phase with a Full Energy Gap in the Doped Topological Insulator ${Cu}_{x} {Bi}_{2} {Se}_{3}$
journal, March 2011

Phonon mechanism in the most dilute superconductor n -type SrTiO ₃
journal, April 2016

Dielectric properties of single crystals of SrTiO3 at low temperatures
journal, October 1959

Polaron coupling coustants in SrTiO3
journal, March 1965

Quantum Critical Origin of the Superconducting Dome in ${SrTiO}_{3}$
journal, December 2015

Role of electron Coulomb interaction in superconductivity
journal, November 1983

Fermi Surface of the Most Dilute Superconductor
journal, April 2013

Anisotropic Migdal-Eliashberg theory using Wannier functions
journal, January 2013

Superconductivity with Topological Surface State in Sr _x Bi ₂ Se ₃
journal, August 2015

Interplay between antiferrodistortive, ferroelectric, and superconducting instabilities in ${Sr}_{1 - x} {Ca}_{x} {TiO}_{3 - δ}$
journal, January 2015

Electric Field Dependence of Optical-Phonon Frequencies
journal, November 1967

Electric-field-induced superconductivity in an insulator
journal, October 2008

A high-mobility electron gas at the LaAlO3/SrTiO3 heterointerface
journal, January 2004

Optical properties of highly reduced ${SrTiO}_{3 - x}$
journal, May 1999

SrTi $O_{3}$ : An intrinsic quantum paraelectric below 4 K
journal, April 1979

The description of superconductivity in terms of dielectric response function
journal, January 1973

Superconductivity from nonphonon interactions
journal, June 1984

Soft modes in semiconducting SrTiO3: II. The ferroelectric mode
journal, December 1980

Quantum Critical Origin of the Superconducting Dome in SrTiO₃
text, January 2015

Effective Tunneling Density of States in Superconductors
book,

Anisotropic Migdal-Eliashberg theory using Wannier functions
text, January 2012

Fermi surface of the most dilute superconductor
text, January 2012

Odd-parity superconductivity in the vicinity of inversion symmetry breaking in spin-orbit-coupled systems
text, January 2015

Second Harmonic Generation Investigation of Symmetry Breaking and Flexoelectricity Induced by Nanoindentations in SrTiO ₃
journal, July 2019

Back to Mechanisms of Superconductivity in Low-Doped Strontium Titanate
journal, February 2017

A Local Maximum in the Superconducting Transition Temperature of Nb-Doped Strontium Titanate Under Uniaxial Compressive Stress
journal, August 2019

Precision Measurements of the AC Field Dependence of the Superconducting Transition in Strontium Titanate
journal, September 2019

Superconductivity in SrTiO3: Dielectric Function Method for Non-Parabolic Bands
journal, January 2019

A ferroelectric quantum phase transition inside the superconducting dome of Sr1−xCaxTiO3−δ
journal, April 2017

The physics of quantum materials
journal, October 2017

Universal superconducting precursor in three classes of unconventional superconductors
journal, June 2019

Polaronic behavior in a weak-coupling superconductor
journal, January 2018

Quantum critical phenomena in a compressible displacive ferroelectric
journal, May 2020

Dynamical screening in monolayer transition-metal dichalcogenides and its manifestations in the exciton spectrum
journal, March 2019

Prospects and applications near ferroelectric quantum phase transitions: a key issues review
journal, September 2017

Physics of SrTiO ₃ -based heterostructures and nanostructures: a review
journal, February 2018

Kohn-Luttinger correction to $T_{c}$ in a phonon superconductor
journal, January 2020

Marrying Excitons and Plasmons in Monolayer Transition-Metal Dichalcogenides
journal, November 2017

Enhancing superconductivity in SrTiO 3 films with strain
journal, April 2019

Quantum critical phenomena in a compressible displacive ferroelectric
text, January 2020

Marrying Excitons and Plasmons in Monolayer Transition-Metal Dichalcogenides
text, January 2017

Physics of SrTiO$_3$-based heterostructures and nanostructures: a review
text, January 2017

Superconductivity in three-dimensional spin-orbit coupled semimetals
text, January 2017

Dynamical screening in monolayer transition-metal dichalcogenides and its manifestations in the exciton spectrum
text, January 2018

Quantum Critical Phenomena in a Compressible Displacive Ferroelectric
text, January 2018

Precision measurements of the AC field dependence of the superconducting transition in strontium titanate
text, January 2019

A local maximum in the superconducting transition temperature of Nb-doped strontium titanate under uniaxial compressive stress
text, January 2019