<p>A distinctive identifier of nodal intrinsic topological superconductivity (ITS) would the appearance of an Andreev bound state on crystal surfaces parallel to the nodal axis, in the form of a topological quasiparticle surface band (QSB) appearing only for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(T &lt; T_{C}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>T</mi> <mo>&lt;</mo> <msub> <mi>T</mi> <mi>C</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>. Moreover, the theory shows that specific QSB characteristics observable in tunneling to an <i>s</i>-wave superconductor can distinguish between chiral and non-chiral ITS order parameter <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Delta_{{\varvec{k}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Δ</mi> <mrow> <mi mathvariant="bold-italic">k</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>. To search for such phenomena in UTe<sub>2</sub>, <i>s</i>-wave superconductive scan-tip scanning tunneling microscopy (STM) imaging was employed. It reveals an intense zero-energy Andreev conductance maximum at the UTe<sub>2</sub> (0–11) crystal termination. The development of the zero-energy Andreev conductance peak into two finite-energy particle-hole symmetric conductance maxima as the tunnel barrier is reduced and then signifies that UTe<sub>2</sub> superconductivity is non-chiral. Quasiparticle interference imaging (QPI) for an ITS material should be dominated by the QSB for energies within the superconductive energy gap <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\left| E \right| \le {\Delta }\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close="|" open="|"> <mi>E</mi> </mfenced> <mo>≤</mo> <mi mathvariant="normal">Δ</mi> </mrow> </math></EquationSource> </InlineEquation>, so that bulk <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\Delta_{{\varvec{k}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Δ</mi> <mrow> <mi mathvariant="bold-italic">k</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> characteristics of the ITS can only be detected excursively. Again using a superconducting scan-tip, the in-gap quasiparticle interference patterns of the QSB of UTe<sub>2</sub> were visualized. Specifically, a band of Bogoliubov quasiparticles appears as a characteristic sextet <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({\varvec{q}}_{i} :i = 1 - 6{ }\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">q</mi> </mrow> <mi>i</mi> </msub> <mo>:</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mn>6</mn> <mrow /> </mrow> </math></EquationSource> </InlineEquation> of interference wavevectors, showing that QSB dispersions <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\varvec{k}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold-italic">k</mi> </mrow> </math></EquationSource> </InlineEquation>(<i>E</i>) occur only for energies <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\left| E \right| \le \Delta_{\max }\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfenced close="|" open="|"> <mi>E</mi> </mfenced> <mo>≤</mo> <msub> <mi mathvariant="normal">Δ</mi> <mo movablelimits="true">max</mo> </msub> </mrow> </math></EquationSource> </InlineEquation> and only within the range of Fermi momenta projected onto the (0–11) crystal surface. In combination, these phenomena are consistent with a bulk <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\Delta_{{\varvec{k}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Δ</mi> <mrow> <mi mathvariant="bold-italic">k</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> exhibiting spin-triplet, time-reversal conserving, odd-parity, <i>a</i>-axis nodal, <i>B</i><sub><i>3u</i></sub> symmetry in UTe<sub>2</sub>.</p>

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Visualizing the Odd-Parity Superconducting Order Parameter and Its Quasiparticle Surface Band in UTe2

  • Shuqiu Wang,
  • J. C. Séamus Davis

摘要

A distinctive identifier of nodal intrinsic topological superconductivity (ITS) would the appearance of an Andreev bound state on crystal surfaces parallel to the nodal axis, in the form of a topological quasiparticle surface band (QSB) appearing only for \(T < T_{C}\) T < T C . Moreover, the theory shows that specific QSB characteristics observable in tunneling to an s-wave superconductor can distinguish between chiral and non-chiral ITS order parameter \(\Delta_{{\varvec{k}}}\) Δ k . To search for such phenomena in UTe2, s-wave superconductive scan-tip scanning tunneling microscopy (STM) imaging was employed. It reveals an intense zero-energy Andreev conductance maximum at the UTe2 (0–11) crystal termination. The development of the zero-energy Andreev conductance peak into two finite-energy particle-hole symmetric conductance maxima as the tunnel barrier is reduced and then signifies that UTe2 superconductivity is non-chiral. Quasiparticle interference imaging (QPI) for an ITS material should be dominated by the QSB for energies within the superconductive energy gap \(\left| E \right| \le {\Delta }\) E Δ , so that bulk \(\Delta_{{\varvec{k}}}\) Δ k characteristics of the ITS can only be detected excursively. Again using a superconducting scan-tip, the in-gap quasiparticle interference patterns of the QSB of UTe2 were visualized. Specifically, a band of Bogoliubov quasiparticles appears as a characteristic sextet \({\varvec{q}}_{i} :i = 1 - 6{ }\) q i : i = 1 - 6 of interference wavevectors, showing that QSB dispersions \(\varvec{k}\) k (E) occur only for energies \(\left| E \right| \le \Delta_{\max }\) E Δ max and only within the range of Fermi momenta projected onto the (0–11) crystal surface. In combination, these phenomena are consistent with a bulk \(\Delta_{{\varvec{k}}}\) Δ k exhibiting spin-triplet, time-reversal conserving, odd-parity, a-axis nodal, B3u symmetry in UTe2.